The Pennsylvania State University

The Graduate School

Department of Astronomy and Astrophysics

X-RAY AND OPTICAL EMISSION FROM

NEUTRON STARS AND PULSAR WIND NEBULAE

A Thesis in

Astronomy and Astrophysics

by

Oleg Kargaltsev

°c 2004 Oleg Kargaltsev

Submitted in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

December 2004 We approve the thesis of Oleg Kargaltsev.

Date of Signature

George G. Pavlov Professor of Astronomy and Astrophysics Thesis Adviser Chair of Committee

William N. Brandt Professor of Astronomy and Astrophysics

John A. Nousek Professor of Astronomy and Astrophysics

Renee D. Diehl Professor of Physics

Gordon P. Garmire Evan Pugh Professor of Astronomy and Astrophysics

Lawrence W. Ramsey Professor of Astronomy and Astrophysics Head of the Department of Astronomy and Astrophysics iii Abstract

This dissertation is devoted to X-ray and optical-UV observations of Neutron Stars (NSs) and Pulsar-Wind nebulae (PWNe). I begin with Introduction (Chapter 1) where I briefly review the astrophysics of pulsars, their winds and synchrotron radiation. I also present an overview of the results of previous X-ray and optical observations of pulsars and PWNe which are relevant to the content of the dissertation. To provide a broader (and more complete) view of the NS population, I then describe observational properties of its more exotic representatives (e.g., Anomalous X-ray Pulsars and Central Compact Objects in Supernova Remnants), many of which have emerged only recently. Part I of the dissertation describes the UV and X-ray observations of the famous Vela pulsar and its spectacular PWN (Chapter 2). The observations which I analyzed were carried out with the Chandra X-ray Observatory and Hubble Space Telescope. I begin by presenting the spectrum and lightcurves of the pulsar as they are seen in different bands of electromagnetic radiation. I then turn to imaging observations of the Vela PWN. Thirteen observations of the Vela PWN with Chandra, spanning a period of 3 years, reveal its complex and variable structure which consists of arcs, jets, knots and diffuse emission. Especially interesting is the long external jet which changes its shape on a timescale of weeks and contains blobs moving at speeds of (0.5-0.6)c. In addition to the fine structure of the inner PWN, a much larger and fainter asymmetric X-ray nebula emerges in the deep summed images. The shape of this outer PWN is similar to that of the radio PWN. I also present the high-resolution spectral map of the Vela PWN and compare its X-ray properties with those of other PWNe. To see if other PWNe are alike and to study the connection between the pulsar and the PWN properties, I retrieved data on rotation-powered pulsars and PWNe from the Chandra archive. Using these data, I performed a uniform statistical analysis of the PSR/PWN X-ray properties. The results, which potentially provide powerful diagnostic of the energetics and emission mechanisms of neutron stars, are presented in Chapter 3. Part II focuses on the individual observations of two middle-aged pulsars (Gemiga and B0656+14; Chapters 4 and 5), very old millisecond pulsar J0437−4715 (Chapter 6), and the enigmatic central source in the Supernova Remnant G266.2−1.2 (Chapter 7). The observations were carried out with HST and Chandra. For each of these objects, I describe the observation setups, data reduction, quantitative results (e.g., fluxes, spectra, light curves) and their astrophysical implications (e.g., origin of the observed radiation, NS surface temperature, connection between the X-ray and optical radiation). iv Table of Contents

List of Tables ...... vii

List of Figures ...... viii

Acknowledgments ...... xvi

Chapter 1. Introduction ...... 1 1.1 Rotation-powered pulsars and pulsar-wind nebulae (PWNe)...... 1 1.1.1 Essential pulsar/PWNe physics...... 2 1.1.2 Synchrotron radiation...... 5 1.1.3 X-ray, optical and radio observations of PWNe...... 7 1.2 X-ray and optical spectra of rotation-powered pulsars...... 11 1.2.1 Overview of X-ray spectra...... 11 ˙ 1.2.2 Luminosities of pulsars and PWNe. LX − E relations. . . . . 12 1.2.3 Overview of optical spectra of pulsars...... 13 1.2.4 Connection between the X-ray and UV/optical properties. . . 14 1.3 Diversity of NS population ...... 14 1.3.1 Radio-Quiet Neutron Stars ...... 14 1.3.2 AXPs and SGRs ...... 16 1.3.3 Central Compact Objects in SNRs...... 17 1.3.4 Hypotheses on the nature of CCOs...... 18

I Young pulsars and Pulsar Wind Nebulae. 20

Chapter 2. The Vela pulsar and its Pulsar Wind Nebula...... 22 2.1 Earlier X-ray and optical observations and their results...... 22 2.2 Chandra observations of the Vela pulsar...... 23 2.2.1 Observations and data reduction...... 24 2.2.2 X-ray spectrum and pulsations...... 24 2.3 HST observations of the Vela pulsar...... 27 2.3.1 Observations and data reduction...... 27 2.3.1.1 NUV photometry...... 28 2.3.1.2 FUV spectrum...... 30 2.3.2 Broad-band optical-UV spectrum. X-ray connection...... 34 2.3.2.1 Timing...... 34 2.3.3 Summary...... 37 2.4 Chandra observations of the Vela PWN...... 40 2.4.1 Observations and data reduction...... 40 2.4.2 Inner PWN: Structure (arcs, jets, knots). Variability. Spectra. Models...... 42 v

2.4.3 The Outer Jets of the Vela pulsar...... 53 2.4.3.1 Spatial variation ...... 54 2.4.3.2 Spectrum and luminosity ...... 57 2.4.3.3 Geometry ...... 65 2.4.3.4 Magnetic field and energetics ...... 69 2.4.3.5 End bend and outer PWN: Effect of SNR wind? . . 72 2.4.3.6 Loop-like structures and blobs: Instabilities in pinched flow? ...... 73 2.4.3.7 Summary and Conclusions ...... 74 2.4.4 Global structure of the Vela PWN in X-rays ...... 76 2.4.4.1 Deep X-ray images ...... 76 2.4.4.2 Photon index maps ...... 80 2.4.4.3 Comparison with the Crab PWN...... 81 2.5 Vela PWN in radio and optical: The multiwavelength picture. . . . . 86 2.5.1 Radio PWN ...... 86 2.5.2 Comparison between the radio and X-ray PWNe morphologies. 86 2.5.3 Search for a compact optical nebula ...... 86 2.5.4 Search for an extended nebula ...... 92 2.5.4.1 Implications of non-detection of optical PWN. . . . 92 2.5.5 Multiwavelength spectrum of the Vela PWN ...... 95 2.6 Observational perspectives. Optical, X-ray and radio polarimetry. . 98

Chapter 3. Chandra observations of pulsars and PWNe...... 99 3.1 Overview of the observations. Data reduction...... 99 3.1.1 Images...... 99 3.1.2 Spectra...... 103 3.2 Correlations between pulsar and PWNe properties...... 104

II Thermal and magnetospheric emission from neutron stars. 109

Chapter 4. HST and XMM observations of the Geminga pulsar...... 111 4.1 Introduction...... 111 4.2 Previous observations of Geminga...... 111 4.3 Optical/UV observations with HST ...... 112 4.3.1 Photometry with STIS/NUV-MAMA...... 112 4.3.2 FUV Spectrum...... 115 4.3.3 NIR through FUV spectrum ...... 121 4.3.4 Timing analysis of NUV and FUV data...... 125 4.4 X-ray spectrum and pulsations of Geminga ...... 128 4.4.1 X-ray spectrum ...... 128 4.4.2 X-ray pulsations ...... 131 4.5 Discussion ...... 134 4.5.1 Thermal component(s) of the Geminga’s spectrum ...... 134 4.5.2 Pulsations in thermal emission ...... 139 vi

4.5.3 Nonthermal emission of Geminga ...... 141 4.6 Summary and conclusions ...... 142

Chapter 5. HST observations of PSR B0656+14...... 144 5.1 Previous observations...... 144 5.2 STIS/FUV-MAMA observation...... 145 5.2.1 FUV Spectrum...... 145 5.2.2 Timing analysis...... 147 5.3 Broadband optical-UV spectrum. Summary...... 148

Chapter 6. HST observations of the millisecond pulsar J0437−4715...... 151 6.1 Optical observations of millisecond pulsars...... 151 6.2 HST Observation ...... 152 6.3 Data reduction...... 153 6.4 Neutron star or white dwarf? ...... 160 6.4.1 Thermal origin of the FUV spectrum. Broadband Spectrum. 160 6.5 Heating mechanisms...... 163 6.5.1 Internal heating ...... 163 6.5.2 External heating ...... 165 6.6 Are millisecond pulsars hotter than ordinary old neutron stars? . . . 166 6.7 Possible spectral line at 1372 A˚ ...... 168 6.8 Magnetospheric component in J0437 spectrum ...... 169 6.9 Summary and conclusions ...... 169

Chapter 7. Chandra observations of CCO J0852−4617...... 171 7.1 Previous observations...... 171 7.2 Chandra observations and data reduction...... 172 7.3 Spectrum...... 172 7.4 Timing. No pulsations? ...... 173 7.5 The nature of CCO in G266.2–1.2 ...... 175 7.5.1 Accretion-powered X-ray pulsar? ...... 175 7.5.2 Isolated cooling neutron star? ...... 177 7.6 Conclusion...... 178

Chapter 8. Overview and summary...... 179

Bibliography ...... 182 vii List of Tables

2.1 Parameters of the two-component fits to the Vela pulsar spectrum for HRC-S/LETG and ACIS/HETG-CC data. The radii and luminosities are for a distance of 300 pc...... 25 2.2 Parameters of the two-component fits to the Vela pulsar spectrum for ACIS-CC data. The radii and luminosities are for a distance of 300 pc. . 25 2.3 FUV-MAMA counts and fluxes in λ-bins ...... 33 2.4 Summary of Chandra observations of the Vela PWN...... 40 2.5 Shifts applied to the ACIS images to improve their alignment...... 42 2.6 Spectral parameters and surface brightnesses for the ACIS observations of the the outer jet...... 64 2.7 Available optical datasets for the Vela pulsar field...... 88 2.8 3σ upper limits to the surface optical brightness of the X-ray PWN struc- tures...... 93

3.1 Pulsars and PWNe observed with Chandra ...... 100

4.1 Numbers of NUV counts for different extraction aperture sizes . . . . . 114 4.2 FUV-MAMA counts and fluxes in λ-bins ...... 118

6.1 Counts and fluxes in λ-bins...... 156 6.2 Blackbody temperatures of nearby old neutron stars...... 167 viii List of Figures

1.1 Multiwavelength image of the Crab PWN (from Kaspi et al. 2004). Blue – X-rays, green – optical, red – radio...... 2 1.2 Top: P − P˙ diagram for pulsars from the ATNF catalog (Manchester et al. 2003). Pulsars with detected X-ray emission are indicated by the squares (filled – nonthermal, empty – thermal emission). Bottom: P − P˙ diagram for the pulsars from the ATNF catalog (Manchester et al. 2003). Pulsars with known X-ray PWNe are marked by stars. . . . 3 1.3 Correlation between the radio (1-10 GHz) and X-ray (0.5-8.0 keV) fluxes for center-filled and composite SNRs with known PWNe (black error- 1.3 bars). The solid line is the best-fit correlation, FX ∝ FR . The dashed line shows a lower limit on the X-ray flux at a given radio flux. The blue arrows are the upper limits on PWN X-ray fluxes obtained from the ROSAT, ASCA, and XMM data for 12 SNRs with plerionic radio cores located within 8 kpc radius from the Earth. These are the best candidates to look for X-ray PWNe with Chandra...... 9 1.4 A sample of 20 PWNe observed with Chandra ACIS (see http://www.astro.psu.edu/ users/green/ChandraPWNe.html for better quality color images). . . . 10 1.5 Optical/UV spectra of four pulsars. The youngest is the Crab pulsar (top), the oldest is the Geminga pulsar (bottom). In addition to our results reported below we used the data points from Sollerman (2003, 2000), Shibanov et al. (2003) and Koptsevich et al. (2001)...... 15

2.1 The high-energy spectrum of the Vela pulsar. The data shown include OSSE (Strickman et al. 1996), COMPTEL (Sch¨onfelderet al. 2000) and EGRET (Kanbach et al. 1994). The soft X-ray flux corresponds to the NS atmosphere model for the thermal component. The dotted line is the unabsorbed flux while the solid line is the observed flux from the Vela pulsar. The pulsed fluxes corresponding to the three HRC peaks (see Fig. 2.2) are marked with horizontal bars...... 25 2.2 Left: The pulse profiles from the HRC observations. The three peaks (P1, P2 and P3) are marked in the top panel. Right : Energy-resolved pulse profiles from the ACIS/HETG-CC observation. The top panel shows the pulse profile for E < 1.8 keV corresponding to the thermal component dominated regime. The bottom panel shows the profile for E > 1.8 keV, where non-thermal component dominates...... 26 2.3 MAMA-NUV image of the Vela pulsar field. North is up, East is to the left...... 28 2.4 Model flux F2299 (see text) versus PL model index for different values of E(B-V)...... 29 ix

2.5 The measured (absorbed) FUV spectrum of Vela pulsar. The dashed line shows best fit absorbed PL model with αλ = −2.06 for E(B-V)=0.05 (see text)...... 31 2.6 The UV-optical spectrum of the Vela pulsar. The solid and dashed lines show the best fit R-J+PL model and the PL component of this model. The dash-dotted line shows best-fit PL model with αν = 0.01 ± 0.02. . 35 2.7 Top: NUV lightcurve of the Vela pulsar. The background level is at 27 counts/bin. Bottom: FUV lightcurve of the Vela pulsar. The background level is at 13 counts/bin...... 36 2.8 NUV and FUV light curves in comparison to the X-ray light curves from the latest ACIS-CC and XMM EPIC-pn observations (courtesy of Divas Sanwal and Slava Zavlin)...... 38 2.9 The gamma-ray and optical pulse profiles of the Vela pulsar (from (Kan- bach et al. 1994 and Gouiffes 1998, respectively)...... 39 2.10 The near-infrared through X-ray spectrum of the Vela pulsar. The lines show the extrapolations of the PL to the optical spectrum and X-ray PL component (thermal component is fitted with the NS hydrogen at- mosphere model; see Table 2.2 in §2.2.2). In the latter case 1σ uncer- tainties of the extrapolation are also shown by the dashed lines. . . . . 39 2.11 ACIS-S images of a central part (5700 × 5500) of the Vela PWN of 2000 Apr 30 (top) and Nov 30 (bottom). The pixel size is 000. 492. The white contours in the top panel define the PWN elements in the first image. In the bottom panel, the white contours correspond to the contours in the top panel, while the blue contours demonstrate the displaced nebular elements in the second observation. The brightest spot is the piled-up Vela pulsar...... 43 2.12 Surface brightness vs. hardness ratio h1.3 for different PWN regions for the two ACIS-S observations. For the second observation, the values for the regions 1–4 were calculated within the blue contours in the bottom panel of Fig. 2.11. (The differences would be even larger if exactly the same regions were used for the two observations.) ...... 44 2.13 The difference image (14200 × 14200) of the Vela PWN. The color scale is in counts ks−1 arcsec−2. The dashed rectangle corresponds to the size of images in Fig. 2.11. The blue and red structures within the 300. 5 circle at the center correspond to the “blob” in the pulsar image in the first and second observation, respectively (see text for details). The blue and yellow linear structures are the pulsar trailed images...... 46 2.14 ACIS images of the inner part of the Vela PWN from ObsID 2813 (top) and ObsID 2820 (bottom). Note structural/brightness changes for the outer arc, bright spot, jets and knots...... 48 2.15 The plot of photon index versus surface brightness for the bright spot for each of the eight ACIS observations (ObsIDs 2813-1820). The arrows connect the subsequent observations starting with the 1st (marked by 1) and ending with the 8th (marked by 8)...... 49 x

2.16 Differences between the ACIS images taken during different visits demon- strating variability of the inner PWN...... 50 2.17 The same as in Figure 2.15 but for the outer arc and inner jets. . . . . 51 2.18 The summed ACIS-S3 image of the Vela PWN (top) and its adaptively smoothed version (bottom). Total exposure time in the images is about 160 ks)...... 53 2.19 Images of the outer jet from the observations of year 2000. The HRC-I and ACIS-S3 images are in blue and orange, respectively. The panels are numbered in accordance with Table 2.5. The size of each panels is 7300 × 5300. The boxes, 2800 × 200. 6, at same sky position in all the panels, are overplotted to guide the eye. The points P and Q mark westward extremes of the bent jet in the two HRC observations; they were used to estimate the jet’s motion between the two observations (see text for details)...... 55 2.20 Sequence of Chandra images of the outer jet observed in 2001–2002. The 7300 by 5300 panels are numbered according to Table 2.5. The letters A, B, and C label the moving bright blobs identified in observations 5 through 11. The boxes, 2800 × 200. 6, at same sky position in all the panels, were used to demonstrate the jet’s sideways motions (see Fig. 2.21)...... 56 2.21 Smoothed distributions of counts across the outer jet at a distance of 5000 from the pulsar in eight ACIS observations (ObsID 2813–2820). The number of counts (per arcsecond) integrated along the short dimension of the boxes in Figure 2.20 is plotted as a function of coordinate φ along the box length...... 58 2.22 Proper motion of blob A in panels 5–11 of Figure 2.20. The upper and lower panels show the motions along the right ascension and declination, respectively. The straight lines are the least-square fits assuming constant speeds. Under this assumption, the apparent speed of blob A is (0.35 ± 0.06) d300 c...... 59 2.23 Proper motion of blob B in panels 5–8 of Figure 2.20. The apparent speed of blob B is (0.51 ± 0.16) d300 c...... 60 2.24 Power-law fit to the spectrum of the outer jet for the merged data set (observations 2813–2816). The best-fit parameters are Γ = 1.29 ± 0.06, −5 −2 −1 −1 2 and NΓ = 3.90±0.40×10 photons cm s keV at 1 keV (χν = 0.98, for 68 dof)...... 61 2.25 One-sigma confidence contours for photon index Γ and spectral surface brightness at 1 keV, B = NΓ/A, for 10 ACIS observations of the outer jet using background A (left panels) and background B (right panels). The contours are separated into the upper and lower panels for clarity of presentation...... 62 2.26 True speed β = v/c versus angle θ between the line of sight and direction of motion for three values of the apparent speed βa = va/c. The dashed lines (β cos θ = 0.20 and 0.33) bracket the domain of allowed β,θ assuming intrinsically similar outer jet and outer counter-jet streaming in opposite directions. See text for details...... 66 xi

2.27 Smoothed ROSAT HRI image (50.7 × 30.8) of the Vela PWN from the observation of November of 1997 (exposure 33 ks). The blob to the northwest of the PWN is indication that the outer jet has persisted at least 5 years...... 68 2.28 Summed ACIS-S3 image of the Vela PWN (top) and its adaptively smoothed version (bottom). Total exposure time in the images is about 160 ks)...... 77 2.29 Summed HRC image of the Vela PWN (top) and its adaptively smoothed version (bottom). Total exposure time in the images is about 150 ks. The HRC field-of-view is 300 × 300...... 78 2.30 Left: ROSAT PSPC image of the Vela PWN region. Right: 1.4 GHz ATCA image of the Vela PWN region which also includes the brightest filament of Vela X (dark structure near the bottom; radio image adopted from Bock et al. 1998)...... 79 2.31 Photon index maps (40.2×40.2 – top panel; 10 ×10 – bottom panel) with X- ray contours overlayed. In the top panel, black color corresponds to the pixels with low S/N ratio for which the spectral index is not calculated. 82 2.32 Chandra ACIS images of the Crab (200. 7 × 200. 7; left) and Vela (30 × 30; right) PWNe...... 83 2.33 Spectral morphology of the Crab PWN (from Mori et al. 2004; see text for details)...... 84 2.34 Top: Photon index versus surface brightness for different Vela PWN regions. Bottom: Shows color coding that is used in the upper panel to distinguish different PWN regions...... 85 2.35 8.5 GHz image with the X-ray contours overlayed...... 87 2.36 Image of the Vela pulsar field obtained by combining all the WFPC2 555W observations listed in Table 2.7 (North to the top, East to the left). The gaps among different CCD chips are evident. The overall integration time on the central part, corresponding to the PC field of view, is 11 800 s (see text). The overlayed contours (logarithmic scale) correspond to the X-ray intensity maps obtained from the Chandra ACIS image of the field in the energy band 1–8 keV. The point source within the innermost X-ray contour is the optical counterpart of the Vela pulsar. 90 2.37 The upper panel shows the combined UBVR image of the Vela pulsar field obtained from the NTT/EMMI observations listed in Table 2.7. The lower panel shows the ESO/2.2m Hα image. In both cases the image size is ≈ 40 × 40 . North is up, East to the left. The X-ray contour plots of the Vela PWN derived from the ACIS observations (§2.4.1) are overlayed. 91 2.38 Spectra of surface brightness (in erg cm−2 s−1 Hz−1 arcsec−2) in X-rays (solid lines) and radio (points), together with the optical upper limits, for the inner/outer arc (upper panel) and diffuse emission southwest of the pulsar (lower panel). Expected brightness levels in optical, based on extrapolations of the X-ray and radio data, are shown with dashed lines. 94 xii

2.39 Top: The spatially integrated spectrum of the Vela PWN. Bottom: The EGRET upper limits on the unpulsed GeV emission from the Vela PWN. The solid line shows the extrapolation of ACIS spectrum with associated uncertainties (the dashed lines)...... 96 2.40 Multiwavelengths spectrum of the Crab PWN (from Atoyan 1999). . . . 97

3.1 PWN count rate (in the 0.1−10 keV band; Table 3.1) versus pulsar spin- down flux E/˙ 4πd2...... 101 3.2 Pulsar count rate (in the 0.1−10 keV band; Table 3.1) versus pulsar spin-down flux E/˙ 4πd2...... 102 3.3 Pulsar count rate versus PWN count rates (in the 0.1−10 keV band). . 103 3.4 PWN luminosity (3 − 8 keV) versus E˙ ...... 105 3.5 PWN luminosity (0.5 − 8.0 keV) versus E˙ ...... 105 3.6 PWN luminosity (3 − 8 keV) versus pulsar luminosity (3 − 8 keV). . . . 106 3.7 Pulsar photon index versus PWN photon index...... 106 3.8 The lack of correlation between the pulsar photon index and E˙ ...... 107 3.9 Pulsar luminosity (0.5 − 8.0 keV) versus E˙ ...... 108 3.10 Pulsar luminosity (2 − 8 keV) versus E˙ ...... 108

4.1 NUV-MAMA image of the field around the Geminga pulsar (at the center of the image). The only other point source in the field is “star G” (e.g., Halpern, Grindlay, & Tytler 1985) used for acquisition. The inset shows brightness contours in the 200. 4 × 200. 4 region centered on Geminga. . . . 114 4.2 Model flux F2299 (see text) versus PL index for different values of E(B-V). 116 4.3 Raw Geminga FUV spectrum. Boxes show approximate regions for the source and background extraction used in spectral analysis...... 117 4.4 The measured (absorbed) FUV spectrum of Geminga pulsar. The dashed line shows the best-fit absorbed BB model (T = 0.31 MK; R = 13d200 km; E(B-V)=0.03)...... 120 4.5 Confidence levels (67% and 90%) for the absorbed power-law model fit, for E(B-V)=0.01, 0.03, 0.05 and 0.07...... 122 4.6 Confidence levels (67% and 90%) for the absorbed black-body model fit, for E(B-V)=0.03 and E(B-V)=0.07...... 123 4.7 NIR through FUV spectrum of Geminga. The broadband fluxes were measured with the HST NICMOS (F110W and F160W; Koptsevich et al. 2001), Subaru SuprimeCam (Ic and Rc; Komarova et al. 2003), HST ACS/WFC (F555W; this work), and HST FOC (F430W, F342W, and F195W; Bignami et al. 1996 and Mignani et al. 1997). The solid and dash-dotted lines show the fits with the absorbed blackbody + power-law model for E(B−V)=0.03 and 0.07, respectively. The model components are shown by the dashed and dotted lines (see text for details). . . . . 124 xiii

4.8 UV light curves of Geminga plotted folded with the J02 ephemeris. Top: NUV-MAMA light curve, obtained using the data from all four orbits. The estimated average background level in the 20-bin light curve is 44.3 counts per phase bin. Middle: FUV-MAMA light curve, obtained using the data from all four orbits. Bottom: FUV-MAMA light curve, obtained using only the data from the first two orbits. The dashed lines with associated errorbars shows the corresponding background light curves (see text)...... 127 4.9 Confidence contours (68%, 90% and 99%) in the temperature-radius plane obtained from fitting the EPIC-pn spectra (solid lines) with the TS+TH+PL and BB+PL models (labels near the contours). The TS+TH+PL contours were obtained at the fixed parameters of the PL component; nH was free for upper contours,while it was fixed at the value obtained from ROSAT data for the lower contours. All the model parameters were free for the EPIC-pn BB+PL contours. The dashed and dash-dotted lines show the confidence contours obtained from fitting the FUV-MAMA spectrum with a blackbody model for two values of the color index E(B−V)...... 130 4.10 Near-infrared through X-ray spectrum of Geminga for different X-ray spectral models and different color indices. The solid lines show the best-fit (absorbed) spectra in the X-ray range and their extrapolations into the NIR-FUV range. The short-dash and dash-dot lines show the (soft) thermal and PL components, respectively, the dotted lines in three lower panels show the TH component (its contribution is negligible in the NIR-FUV range), and the long-dash lines present the unabsorbed total spectra. The crosses depict the measured NIR-FUV spectral fluxes (cf. Fig. 7). The hatched areas along the PL and thermal components in the NIR-FUV range demonstrate propagated uncertainties of the cor- responding extrapolations. The upper panel shows a two-component (BB+PL) X-ray fit, while three lower panels show TS+TH+PL fits with fixed parameters of the PL component. The fit shown in the lower panel was obtained at a fixed nH value, while nH was a fitting parameter in three upper panels. (See text for more details.) ...... 132 4.11 ASCA GIS and XMM EPIC-pn light curves in the 0.5–2 keV range folded with the J02 ephemeris...... 133 4.12 Background-subtracted light curves of Geminga in UV (NUV-MAMA + FUV-MAMA), X-rays (EPIC-pn) and γ-rays (EGRET) bands, folded with the J02 ephemeris. The γ-ray light curve is taken from J02. . . . 135 4.13 Temperature-radius confidence contours (68%, 90%, and 99%) for the isolated neutron star RX J1865.5-3754 as obtained from the X-ray ob- servations with different instruments (solid contours) and FUV-MAMA observations (dash and dash-dot lines)...... 136 4.14 Multiwavelength spectrum of Geminga including gamma-ray data points from OSSE (Strickman et al. 1996), COMPTEL (Schonfelder et al. 2000), and EGRET (Kanbach et al. 1994)...... 142 xiv

5.1 Pulse profiles in soft X-rays (upper panel) and the NUV range (lower panel). Adopted from Zavlin et al. (2004). Note that these light curves are not aligned in phase with the FUV light curve in Figure 6.4. . . . . 145 5.2 The measured (absorbed) FUV spectrum of PSR B0656+14. The dashed line shows best fit absorbed BB model (T = 0.6 MK; R = 13 km; d = 288 pc; E(B-V)=0.02) ...... 146 5.3 FUV pulse profile of PSR B0656+14...... 148 5.4 De-reddened optical/UV spectrum of PSR B0656+14 with the best fit R-J + PL model shown by the dashed line (separate components of this model are also shown by the dashed lines). The extrapolation of the best-fit thermal soft-X-ray component (Zavlin & Pavlov 2003) is shown by the dotted line. The dash-dotted lines show the extrapolation of the X-ray PL component with associated 1σ uncertainties...... 149 5.5 The near-infrared through X-ray spectrum of PSR B0656+14. The solid line shows the fit to X-ray data with PL+TH+TS model (see §5.1). The model components are also shown separately by the dotted and dash- dotted lines. For the PL component 1σ uncertainties of the fit are also shown by the dash-dotted lines. Notice that the observed UV fluxes are above the extrapolation of the X-ray model (see §5.3)...... 150

6.1 Distribution of counts on the FUV-MAMA detector. The spatial (Y) and dispersion (X) axes are in the vertical and horizontal directions, re- spectively. The spectrum of J0437 is shown by horizontal arrows. The background is clearly dominated by the nonuniformly distributed “ther- mal glow” which is the strongest at the upper left corner and the weakest at the bottom. The vertical arrow shows the location of the possible spec- tral feature (see §6.7 and Fig. 6.3 )...... 154 6.2 FUV spectrum of J0437. The error bars on the left represent the mea- sured average fluxes in four λ-bins. The dash-dotted line is the fit with the absorbed power-law model for E(B − V ) = 0.03. The dotted line shows the same model but dereddened. The dashed line is a blackbody spectrum with the temperature of 4 000 K, fitting the dereddened B,V,R,I WD fluxes, taken from Danzinger et al. (1993)...... 157 6.3 Total (source + background) count rate distribution in the region around the possible emission feature at 1372 A.˚ ...... 158 6.4 Pulsar light curve for 4 phase bins. The smooth line shows the light curve averaged over the reference phase...... 159 6.5 Confidence levels (68% and 90%) for the absorbed power-law model fit, for E(B − V ) = 0, 0.03, 0.07...... 161 6.6 Confidence levels (68% and 90%) for the absorbed blackbody model fit, for E(B−V ) = 0.03. The contours are cut (the dashed line in the top left corner) because the X-ray model flux exceeds the observed one at higher temperatures and smaller radii (see Fig. 6.7). The horizontal dashed line shows the temperature corresponding to a plausible NS radius of 13 km. 162 xv

6.7 Multiwavelength spectrum of J0437. The data points on the left represent the measured FUV fluxes; the unabsorbed (dereddened) fluxes are only slightly higher for plausible values of E(B − V ) (see Fig. 6.2). The data points on the upper right are the unabsorbed X-ray fluxes from Chandra ACIS and ROSAT PSPC observations (Zavlin et al. 2002). Three dashed lines marked with temperature and radius values show the range of for- mally acceptable blackbody models (see §6.4 for details). The dashed line marked “WD” corresponds to the blackbody with the temperature of 4 000 K (cf. Fig. 6.2). The dash-dotted line that goes through the X-ray data points is the two-temperature hydrogen atmosphere + power-law model (see §6.4.1, §6.8, and Zavlin et al. 2002). The power-law compo- nent with the photon index Γ = 1.6 is shown separately by the dotted line...... 164

7.1 Fit of the ACIS-S3 spectrum of J0852 with a blackbody model. The contours correspond to 68%, 90% and 95% confidence levels...... 174 xvi Acknowledgments

I am deeply indebted to my adviser, Prof. George Pavlov for his continuous sup- port, kind advice and patient guidance through my graduate career. Most of what I know about neutron stars I learned from George. I also would like to thank George for being incredibly patient in teaching me skills of scientific writing. I am grateful to Prof. Peter M´esz´arosfor welcoming and supporting me during my first year at the Astronomy Department. I had a unique opportunity to learn about the theory of gamma-ray bursts from one of its creators. I also wish to thank the members of my thesis committee for their encouraging and valuable comments on my dissertation. I am grateful to Divas Sanwal, Slava Zavlin, and Marcus Teter for all their input and collaboration. I am espe- cially thankful to Divas Sanwal for invaluable assistance with analysis of Chandra ACIS data. I take this opportunity to thank Prof. Robin Davis for welcoming me to United States and helping me will all problems which I encountered upon my arrival. I will always remember his constant care and distinct British sense of humor. Finally, this work would be impossible without the support and help of Igor, Tanya and significant others. xvii

Statement of originality.

The content of this thesis is the result of my own work, with the following excep- tions. Chapter 1 (Introduction) is a review of known results and recent developments in high-energy astrophysics of neutron stars, and is mostly the work of other authors. The same is true for the introduction sections within the other Chapters. In Chapter 2 (§2.2.2) the work on X-ray timing of the Vela pulsar was mostly done by Divas Sanwal. Figures 2.19–2.21 and 2.24 in §2.4.3 were produced by Marcus Teter. In §2.4.3.4, §6.7 and §6.5.1 a number of estimates belong to George Pavlov. Parts of sections 2.5.3 and 2.5.4 were done in collaboration with Roberto Mignani and Andrea De Luca. In Chap- ter 4 (§4.4), fits to the X-ray spectra of Geminga were carried out by Slava Zavlin. The NUV and X-ray light curves in Chapter 5 were also produced by Slava Zavlin. Finally, many of the ideas that were elaborated and confronted with the data in this thesis were originally suggested by George Pavlov. 1

Chapter 1

Introduction

The discovery of pulsed radio emission (by Jocelyn Bell and Anthony Hewish in 1967) from the direction of the Crab Supernova Remnant (SNR) provided the first observational evidence for Neutron Stars (NSs) that were predicted to exist by Lev Landau (1932) on purely theoretical grounds. Very soon Franco Pacini (1967, 1968) and Thomas Gold (1968, 1969) recognized that the observed radio pulsations can be produced by a rapidly spinning, magnetized NS emitting a beam of radiation that sweeps across the Earth as the star spins. The discovery of optical and X-ray pulsations has followed shortly afterwards (Cocke, Disney, & Taylor 1969; Fritz et al. 1969; Bradt et al. 1969). Pacini (1968) also suggested that the pulsating neutron star (pulsar) powers the surrounding Crab nebula, and that the underlying energy source of the Crab nebula is the rotational energy of rapidly spinning NS. The Crab nebula has long been known to optical astronomers (discovered by John Bevis in 1731). It was associated with the remnant of 1054 A.D. supernova explosion (Lundmark 1921). The X-ray emission from the Crab Nebula was detected by rocket-borne Geiger counters (Bowyer et al. 1964), just four years before the Pacini’s paper. Thus, if the Crab pulsar is often considered as a prototypical example of a pulsar, the Crab nebula is a canonical example of the pulsar-wind nebula (PWN; see Fig. 1.1). To date, more than 1400 pulsars has been discovered in radio, ∼ 60 in X-rays (e.g., Kaspi, Roberts & Harding 2004; Pavlov, Zavlin & Sanwal 2002c, Becker & Aschenbach 2002; Becker & Pavlov 2002; see also Fig. 1.2) and ∼ 10 in UV/optical (Mignani et al. 2004), with the numbers constantly growing. It is now clear that the population of neu- tron stars is remarkably diverse. Neutron stars can manifest themselves observationally as the spin-powered pulsars with very different properties or as more rare and exotic objects such as Soft Gamma-Ray Repeaters and Anomalous X-ray pulsars (see Kaspi & Gavriil 2004; Kaspi 2004 for a review), Radio Quiet NS (which could be just “off-beam pulsars”; Pavlov & Zavlin 2003) and recently discovered Central Compact Objects in Supernova Remnants (see Pavlov, Sanwal & Teter 2004 for a review).

1.1 Rotation-powered pulsars and pulsar-wind nebulae (PWNe).

Spin-powered pulsars are isolated (non-accreting) neutron stars (NSs) with fast rotation (P ∼ 0.001–10 s) and strong magnetic fields (B ∼ 109–1013 G). This makes them capable of generating strong electric fields which accelerate particles to ultrarelativistic energies and create new particles in pair-multiplication cascades above the NS magnetic poles. A fraction of these particles is accelerated back to the NS surface (e.g., Harding & Muslimov 2002, and references therein) and their energy is released at the polar caps. The inward-directed radiation from the returning particles or even precipitating 2

Figure 1.1 Multiwavelength image of the Crab PWN (from Kaspi et al. 2004). Blue – X-rays, green – optical, red – radio.

secondary particles, created in the closed field line zone of the dipolar magnetic field, can heat the surface outside of the canonical polar caps (Wang et al. 1998). The rest of the particles fills in the NS magnetosphere, where they emit non-thermal radiation via curvature and synchrotron emission mechanisms, and eventually escape as a pulsar wind which carries most of the pulsar’s spin-down energy loss.

1.1.1 Essential pulsar/PWNe physics. The periods and period derivatives (P and P˙ ) of the radio pulsars provide an estimate of the rotational energy loss rate, E˙ ≡ 4πIPP˙ −3 = 3.9 × 1046PP˙ −3 ergs s−1, for a typically assumed NS moment of inertia I = 1045 erg cm2. The other two quantities that are commonly derived from the radio data are the pulsar characteristic age, τ, and magnetic field, B. Unlike E˙ , the latter estimates are model dependent. The widely used expression, τ = P/2P˙ , assumes that the initial pe- riod, acquired by the pulsar at its birth, Pi, is much shorter than the observed period. This may not be valid for young pulsars residing in SNRs or for£ the pulsars which¤ were ˙ n−1 spun-up by the accretion. A more general expression, τ = P P 1 − (Pi/P ) /(n − 1), derived under the assumption that Ω˙ ∝ Ωn (here Ω = 2π/P ), includes another uncer- tain model parameter which is called the braking index, n. If the physical mechanism responsible for the pulsar’s energy loss is magnetic dipole radiation, then one would 3

Figure 1.2 Top: P − P˙ diagram for pulsars from the ATNF catalog (Manchester et al. 2003). Pulsars with detected X-ray emission are indicated by the squares (filled – nonthermal, empty – thermal emission). Bottom: P − P˙ diagram for the pulsars from the ATNF catalog (Manchester et al. 2003). Pulsars with known X-ray PWNe are marked by stars. 4 expect n = 3. Indeed, equating the magneto-dipole losses to the spin-down losses

2B2R6Ω4 sin2 α IΩΩ˙ = (1.1) 3c3 makes it easy to see that Ω˙ ∝ Ω3 (α is the angle between the pulsar’s spin and magnetic axis). Under the same assumption of magnetic dipole braking in vacuum one can derive the equatorial magnetic field on the surface of NS:

à !1/2 3Ic3P P˙ B = = 3.2 × 1019(P P˙ )1/2 G (1.2) 8π2R6 sin2 α for the orthogonal rotator (sin α = 1; I = 1045 erg cm2; R = 106 cm). Note note if the NS magnetic field deviates from that of a dipole, or if the NS magnetosphere is loaded with a plasma, the above estimates become inaccurate. Still, they are relevant for order-of-magnitude estimates. Pulsars are sources of ultrarelativistic electrons which can be produced via several mechanisms. The primary electrons can be pulled out by the strong electric field at the NS surface near the magnetic poles or freely emitted if the NS surface is hot enough (thermoelectronic emission). Alternatively, ultrarelativistic e+e− pairs can be produced via γ-ray absorption in the NS magnetosphere. The primary particles are then rapidly accelerated by the huge electric field component which is parallel to the magnetic field but perpendicular to the NS surface near the magnetic poles and can be as large as 10 −1 −1 Ek ∼ RΩB = 6.3 × 10 P B12 V cm (in polar cap models; Daugherty & Harding 1982). The particles can also be accelerated by the electric field in vacuum gaps which develop in the outer magnetosphere along the last open field line (outer-gap models; Cheng et al. 1986). Currently, there are several competing models which attempt to describe the pair formation and acceleration processes in detail (e.g., polar cap, outer gap, and mixed models; e.g., Kaspi, Roberts & Harding 2004, and references therein). However, the physical mechanisms responsible for particle injection, charge separation and distribution of charges on the surface of NS and within the magnetosphere, and the structure and dynamics of magnetospheric currents are poorly understood so far (e.g., Michel 2004). Observing the non-thermal radiation emitted by particles in a pulsar magnetosphere helps us to advance our understanding of these physical processes. Moving along the bent magnetic field lines, primary electrons emit curvature ra- diation photons which, in turn, produce electron-positron pairs in a strong magnetic field. Then the process repeats itself as long as the photon energy exceeds two electron rest masses. The developing pair cascade may extend from ∼ 100 meters to several NS radii above the NS surface and multiply the number of primary electrons by a factor of κ = 10 − 104 (e.g. Hibschman & Arons 2001; Muslimov & Harding 2003), which is known as the pair multiplication coefficient. The value of this factor is very uncertain and depends on the dynamics of the pair cascade, which is complex and still remains to be fully explored (e.g., Muslimov & Harding 2003). The values of the Lorentz factor γ, acquired by electrons/positrons in the cascade, range between 102 and 105 (Hibschman & Arons 2001). These secondary particles are thought to be responsible for the non-thermal 5 magnetospheric emission as well as for the thermal emission from NS polar caps heated by the backflowing particles. Most of the particles produced in the cascade ultimately escape from the pulsar magnetosphere along the open field lines, thus contributing to the pulsar wind. When the wind, comprised of particles and electromagnetic wave, is launched from the pulsar magnetosphere, its total energy flux is completely dominated by Poynting flux (at least in the equatorial plane). For instance, at the light cylinder radius (defined as Rlc = c/Ω) the ratio of Poynting energy flux to the kinetic energy 2 3 7 2 flux (a.k.a. magnetization parameter), σ = cB /4πmc γn ≈ 3 × 10 µ30/γκP , is a large 3 30 3 30 3 number for typical pulsar parameters (here µ = BR = 10 B12R6 ≡ 10 µ30 G cm is the pulsar magnetic moment). Beyond the light cylinder the particles likely continue to be accelerated by a huge electromagnetic wave propagating away from the pulsar (e.g., Michel & Li 1999) and substantial part of the EM wave energy can be transferred to the particles. Alternatively, magnetic reconnection (Coroniti 1990; Lyubarski & Kirk 2001) and MHD instabilities (Begelman 1998) may play an important role in the conversion of the electromagnetic energy to the kinetic energy of particles. So far, it is not clear which of these mechanisms, if any, operates in the pulsar wind. The observed X-ray emission from PWNe requires electrons with γ ∼ 107 −109 and therefore provides evidence for ad- ditional particle acceleration that occurs between the light cylinder and the termination shock. The wind is shocked in the ambient medium at a distance where the wind pressure ˙ 1/2 balances the pressure of the ambient medium, r ∼ rs = (E/∆Ω cpamb) (∆Ω is the solid angle of the outflow, pamb is the pressure in the ambient medium) forming a pulsar-wind nebula. It is believed that, in order to produce a strong termination shock, the wind flow should become kinetic energy dominated (i.e. σ ¿ 1; Kennel & Coroniti 1984, Gallant et al. 1992). The strong shock is needed to explain the observed radiation from PWNe since the ultra-relativistic wind cannot be seen until it is shocked in the ambient medium (see, however, Kirk et al. 2002). Only beyond the shock the motion of the individual particles (hence, the angular distribution of the synchrotron radiation) becomes nearly isotropic, and the post-shock region manifests itself as a pulsar wind nebula whose spectrum and surface brightness are determined by the particle spectrum and injection rate, the post- shock magnetic field, and the properties of the ambient medium.

1.1.2 Synchrotron radiation. The synchrotron radiation is an important radiation mechanism which is most likely responsible for the PWN emission and, at least partly, for the high-energy mag- netospheric emission from pulsars. Below, we briefly summarize the basic properties of synchrotron radiation that will be used throughout the text. The exact expression for the synchrotron spectral power emitted by a single rel- ativistic electron moving in the magnetic field B~ with a velocity ~v (and corresponding Lorentz-factor γ) can be found, e.g., in Lang (1974) and Rybicki & Lightman (1979). For now, it is sufficient to know that the synchrotron spectrum emitted by a single electron peaks near the characteristic frequency νmax ≈ 0.3νc where νc is the critical frequency 3 eB ν = γ2 sin χ (1.3) c 4π mc 6

(here χ is the pitch angle between B~ and ~v), and total emitted synchrotron power is given by

2 e4 ³v ´2 P = γ2B2 sin2 χ (1.4) 3 m2c3 c if γ sin χ À 1 (e.g., Lang 1974, p.36). Consequently, the electron loses half of its energy via synchrotron radiation during the time

9 m3c5 τ = B−2γ−1 ≈ 7.8 × 108B−2γ−1 s ≈ 246(B/100µG)−2(γ/107)−1 yrs ≈ (1.5) syn 4 e4 ≈ 81.4(B/100µG)−3/2(E/1keV)−1/2 yrs (1.6) where E = (B/100µG)(γ/4.1 × 107)2 keV is the characteristic energy of synchrotron photon with frequency ν (E = hν). The characteristic time τsyn is often called the synchrotron cooling time. The observed PSR/PWN power-law spectra are commonly interpreted as syn- chrotron emission of relativistic electrons and/or positrons. Here and below we adopt the optically thin synchrotron emission model (unless specified otherwise). The power-law photon spectrum with a photon index Γ can be be generated by a power-law distribution of electrons over energies E = mc2γ:

−p dne = Kγ f(~n) dγ dΩ , (1.7) in the range γ1 < γ < γ2, where

p = 2Γ − 1 , (1.8)

~n is the unit vector along theR direction to the observer, f(~n) describes possible anisotropy of the electron distribution ( f(~n) dΩ = 1, f(~n) = 1/(4π) for the isotropic distribution), and K is the normalization:

ne K = K(ne, γ1, γ2, p) = , (1.9) Cp Z ³ ´ γ2 1 C = γ−p dγ = γ1−p − γ1−p . (1.10) p p − 1 1 2 γ1 The electron energy density can be written as

2 2 Cp−1 we = mc KCp−1 = nemc . (1.11) Cp The synchrotron emissivity (in erg cm−3 s−1 Hz−1 rad−2) is given by the following equation (e.g., Lang 1974, p.36):

˜ (p+1)/2 −(p−1)/2 ε(ν, ~n) = K f(~n) ApB⊥ ν , (1.12) 7 where B⊥ = B sin θ is the projection of the magnetic filed onto the plane perpendicular to the line of sight, 1 e3 ³ e ´(p−1)/2 A˜ = a , (1.13) p p 2 mc2 4πmc µ ¶ µ ¶ p + 7/3 3p − 1 3p + 7 a = 2(p−3)/23p/2 Γ Γ . (1.14) p p + 1 12 12

For p = 1, 2, 3 and 4, ap = 9.06, 6.23, 8.37 and 15.15, respectively. If the magnetic field has random direction along the line of sight, then, making use of the relation Z √ µ ¶ · µ ¶¸ 1 π π p + 5 p + 7 −1 (sin θ)(p+1)/2 sin θ dθ = Γ Γ , (1.15) 2 0 2 4 4 ˜ we obtain eq. (1.12), in which B⊥ → B, Ap is given by eq. (1.13), in which ap → cp: µ ¶ µ ¶ µ ¶ · µ ¶¸ √ p + 7/3 3p − 1 3p + 7 p + 5 p + 7 −1 c = 2(p−5)/23p/2 π Γ Γ Γ Γ . p p + 1 12 12 4 4 (1.16) For p = 1, 2, 3 and 4, cp = 7.11, 4.48, 5.58 and 9.46, respectively. The distinct feature of the synchrotron radiation is the high degree of linear polarization (there is also a small circularly polarized component). For electrons with a power-law energy distribution moving in the region with a homogeneous magnetic field the degree of linear polarization observed in the direction perpendicular to the direction of magnetic field is (p + 1)/(p + 7/3).

1.1.3 X-ray, optical and radio observations of PWNe. X-ray and optical observations of pulsars and PWNe provide powerful diagnostics of the energetics and emission mechanisms of rotation-powered neutron stars. As the magnetic dipole braking slows the pulsar’s rotation, the pulsar loses its rotational kinetic energy at a rate E˙ = 4πIPP˙ −3. Although most of the pulsars are observed at radio wavelengths, only a small fraction (10−7 to 10−5) of the spin-down luminosity E˙ is emitted at radio frequencies. A more substantial fraction, ∼ 0.1%−10%, of E˙ is emitted from the NS surface/magnetosphere at X-ray and γ-ray energies while most of the spin- down luminosity emerges as a relativistic wind of positrons, electrons and possibly ions feeding an extended pulsar-wind nebula. The synchrotron radiation from PWNe has been observed from radio to X-rays. Most of the known PWNe are associated with Supernova Remnants (SNRs). At least 25 out of 32 PWNe detected in X-rays (as of March 2004) are associated with so-called center-filled or composite SNRs (Kaspi, Roberts & Harding 2004). In the radio, the “Crab-like” (=plerionic=center-filled) SNRs (Weiler & Panagia 1978) are characterized by compact, center-filled morphology, with a flat spectral index, α = 0.0 − 0.4 (Sν ∝ ν−α), and a relatively high degree of linear polarization, P ∼ 5% − 40%. The common interpretation is that these remnants are pulsar powered, although direct evidence (e.g., pulsations or a clearly seen point source) of an associated pulsar is sometimes lacking. About 6% of the currently cataloged Galactic SNRs (Green 2004; the catalog has 231 8

SNRs) belong to this type, while 10-15% are classified as “composite” remnants showing compact cores accompanied by shells with steeper spectral indices (α ranges from −0.4 α to −0.8; Fν ∝ ν ). The shell-like component is associated with the supernova blast wave and ejecta, while the core component is due to the synchrotron emission from the PWN. In X-rays these remnants generally exhibit morphologies similar to those in radio, although the radio PWN size is typically a factor of 3 − 5 larger than that observed in X-rays (e.g., the Vela SNR, G292.0+1.8, G54.1+0.3, G0.9+0.1, and G11.2– 0.3). Sometimes, the radio emission from a PWN is displaced (up to several arcminutes) relative to the X-ray emission (G327.1–1.1, MSH15–56, G0.9+0.1, W44). For PWNe resolved in both X-rays and radio there is a correlation between the radio and X-ray fluxes (Fig. 1.3). Although the correlation has a large dispersion, it allows one to put a conservative lower limit on the X-ray flux from a PWN candidate if the radio flux from the SNR core is known (the dashed line in Fig. 1.3; twelve center-filled/composite SNRs with known radio fluxes from the presumably plerionic cores are shown by upper limits). To date, only a few optical counterparts of X-ray/radio PWNe have been found. These include the Crab PWN (Hester et al. 1995), PWN in CTB80 (Butler, Golden, & Shearer 2002) and PWN around PSR B0540-69 in LMC (Caraveo et al. 2000; Serafi- movich et al. 2004). In addition, several bow-shock PWNe around fast moving pulsars, which include B2224+65 in the “Guitar nebula”, B0740−28 and three very old (∼> 1 Gyr), recycled pulsars (J0437−4715, J2124−3358, B1957+20), have been detected in Hα emission (see Kaspi, Roberts, & Harding 2004 for references). Attempts to detect optical emission from one of the nearest PWNe, the Vela PWN, have been so far unsuccessful (Mignani, De Luca, Kargaltsev et al. 2003; see also §2.5.3 for details). The half-arcsecond angular resolution, combined with the spectroscopic capabil- ities, makes Chandra a unique tool for studying the X-ray properties of PWNe. Most of what we currently know about the X-ray emission from PWNe comes from Chandra observations. Figure 1.4 shows that the innermost parts of many X-ray PWNe share similar features, such as axisymmetric toroidal structures and jets along the symmetry axis. This suggests that most of the wind is confined to the low-latitude equatorial region while the rest of it escapes through collimated jets. The spectral maps of the Crab and Vela PWNe (Mori et al. 2004; Kargaltsev et al. 2004) show that the spatial variations in spectral index are strongly correlated with the PWN structure. On the other hand, the PWNe are very diverse in their overall appearance. Most of them were caught by Chandra at different evolutionary stages and different orientations with respect to the observer. However, even the pulsars with very similar P and P˙ (hence, E˙ and ages), and similar distances, can produce quite different PWNe (e.g., J1124 − 5916/G292.0 + 1.8 and J1930 + 1852/G54.1 + 0.3; 6th and 10th panels in Fig. 1.4). If the pulsar has a high spatial velocity, the ram pressure caused by its motion can dominate the ambient gas pressure, resulting in a bow-shock PWN (a possible example is shown in panel 16 in Fig. 1.4). Thus, the physical conditions within the SNR, as well as the direction and magnitude of the kick that the neutron star received at birth, can have a profound effect on the PWN morphology by affecting the termination shock geometry and the dynamics of the post-shock wind flow. These environmental effects can cause asymmetry in PWNe which becomes visible in longer exposures. For instance, the inner part of the Vela PWN (panel 2 in Fig. 1.4) looks axisymmetric. However, the deep image obtained with the 9

Figure 1.3 Correlation between the radio (1-10 GHz) and X-ray (0.5-8.0 keV) fluxes for center-filled and composite SNRs with known PWNe (black errorbars). The solid line is 1.3 the best-fit correlation, FX ∝ FR . The dashed line shows a lower limit on the X-ray flux at a given radio flux. The blue arrows are the upper limits on PWN X-ray fluxes obtained from the ROSAT, ASCA, and XMM data for 12 SNRs with plerionic radio cores located within 8 kpc radius from the Earth. These are the best candidates to look for X-ray PWNe with Chandra. 10

Figure 1.4 A sample of 20 PWNe observed with Chandra ACIS (see http://www.astro.psu.edu/ users/green/ChandraPWNe.html for better quality color images). 11

Chandra ACIS reveals a larger and fainter nebula whose asymmetric shape suggests a large-scale flow (or density/pressure gradient) within the Vela SNR (Pavlov et al. 2003; Kargaltsev & Pavlov 2004; see also §2.4.4). Thus, in addition to the properties of pulsar wind, observations of PWNe probe the physical conditions in the host SNRs. High-resolution, multiwavelength studies of PWNe are important since they al- low one to see the effects of the radiative and expansion energy losses, determine the shape and boundaries of the electron injection spectrum, and elucidate the properties of relativistic magnetized outflows and shocks.

1.2 X-ray and optical spectra of rotation-powered pulsars.

In general, the X-ray and optical radiation from pulsars consists of two com- ponents: thermal radiation from the NS surface and non-thermal radiation from the pulsar magnetosphere. In many cases, the non-thermal component completely domi- nates the pulsar spectrum at X-ray/optical frequencies (e.g., in the young Crab pulsar) while in some cases both spectral components can be resolved (e.g., middle-aged Vela and Geminga pulsars, τ ∼ 104 and 105 yrs, respectively). The same applies to the pop- ulation of very old (τ > 109 yrs) millisecond pulsars (clustered in the lower left corner of the P − P˙ diagram; Fig. 1.2), which are thought to be spun-up by accretion from a binary companion.

1.2.1 Overview of X-ray spectra. The spectrum of non-thermal X-ray radiation is typically fitted by a power-law −Γ+1 (PL) model with photon indices Γ = 1 − 2 (Fν ∝ ν ). This radiation is likely to be the synchrotron emission from the relativistic electrons/positrons accelerated in huge electric fields near the neutron star (NS) surface as well as from secondary particles produced in the pair cascade (§1.1.1). Therefore, non-thermal spectra of pulsars provide a direct probe of particle acceleration in the magnetosphere, dynamics of pair cascades, injection rates of the primary particles, and the geometry of the magnetic field. The magnetospheric radiation is emitted by ultra-relativistic particles with an anisotropic velocity distribution and usually shows strong pulsations whose shape tells us about the beam geometry. The thermal X-ray radiation is thought to be emitted from the NS surface. In several cases two thermal components with different temperatures are needed to fit the X-ray spectrum (e.g., spectra of the pulsars B0656+14 and B1055-52 require Tcool ≈ 0.07 keV and Thot ≈ 0.15 keV; Zavlin & Pavlov 2003). The hard (hot) component can be associated with the magnetic polar caps heated by relativistic particles created in the pulsar’s acceleration zones and bombarding the NS surface (e.g., Harding & Muslimov 2002, and references therein). It is commonly believed that the soft component is emitted from the bulk of NS surface, which radiates away the residual heat associated with the NS interior and possibly the additional energy released in the interior via different re- heating processes (e.g., Schaab et al. 1999). Indeed, the observed soft (cool) component temperatures generally decrease with pulsar age. However, they cannot be put on a monotonically decreasing model cooling curve, which suggests that different NSs have 12 different masses (e.g., Yakovlev & Pethick 2004). Measuring the temperature of the soft component allows one to constrain the equation of state for the superdense matter in the NS interior. Thermal radiation usually shows weaker and broader pulsations that can be explained by a nonuniform temperature distribution on the surface of NS.

˙ 1.2.2 Luminosities of pulsars and PWNe. LX − E relations. Since the spin-down power, E˙ , is the source of the energy that powers the non- thermal emission ordinary radio pulsars (i.e. excluding SGRs, AXPs and CCOs; see §1.3), the pulsar’s luminosity is expected to be correlated with E˙ (see Zhang & Harding 2000 for analytical approach). The same argument can be applied to PWNe. From the obser- vational point of view it is preferable (easier) to study the correlation between LX,PWN and E˙ since PWN emission is not expected to be substantially beamed and therefore does not depend on the orientation of the PWN with respect to the observer. However, the PWN luminosity may depend on often unknown properties of the ambient medium. On the other hand, the pulsar magnetospheric emission is known to be strongly beamed and therefore the observed pulsed luminosity would depend on the angles between the line-of-sight and the pulsar magnetic and rotation axes which are different for each pulsar and in most cases unknown. Therefore, one would a priori expect a large dispersion to ˙ be associated with the empirical LX − E relation for pulsars. There have been several attempts to derive such a relationship from the X-ray data. The X-ray band is preferable for this purpose because the radio emission is en- ergetically unimportant and produced via poorly understood coherent mechanism (e.g., Melrose 2004 and references therein), and only few pulsars have their optical and/or gamma-ray spectra accurately measured. Based on Einstein Observatory data, Seward & Wang (1988) derived the relation, ˙ ˙ log LX,(0.2−4.0) = 1.39 log E − 16.6, between the E and total luminosity of PSR+PWN (in the 0.2 − 4.0 keV band) for a sample of eight objects. The accuracy of this relation is limited by the angular resolution and sensitivity of the Einstein Observatory which precluded the separation between the pulsar and PWN emission components. For the young/middle-aged pulsars from this sample the total PSR+PWN emission should be dominated by the nebular component (it is usually a factor of 3-10 brighter than pulsar emission; see Chapter 3) while some older pulsars show no (or very little) nebular emission in X-rays (e.g., PSR B0656+14 or PSR J2225+6535 in the Guitar Hα nebula). The distances to some pulsars from the sample were also very uncertain at that time. Later, using the ROSAT data on 26 pulsars, Becker & Trumper¨ (1997) found ˙ a different relation, log LX,(0.1−2.4) = 1.03 log E − 3, between the pulsar luminosity in the 0.1 − 2.4 keV band and the spin-down power. Again, the contribution of the PWN emission was not completely excluded, and the thermal emission component was not separated from the non-thermal component in the pulsar spectrum. Furthermore, in the cases with no/scarce spectral information, a typical photon index Γ = 2 has been assumed rather than measured. From the Chandra and XMM observations, we know that the pulsar photon indices may, in fact, vary between 0.5 and 2.0 (e.g., Gotthelf 2003; see also §3.2). 13

Possenti et al. (2001) compiled the results on 39 pulsars, most of which have been observed with ROSAT and ASCA, and derived the relation between E˙ and pulsar ˙ luminosity in the 2–10 keV band, log LX,(2−10) = 1.34 log E − 15.34, which is close to that obtained by Seward & Wang (1988). Possenti et al. (2001) note that although the 2 reported relation fits the data best, the quality of the fit is very low (χν ∼ 7) reflecting a large scatter present in the data. This analysis has suffered from the same drawbacks as in the two previous cases. Finally, Gotthelf (2003) analyzed (and used the published results on) Chandra ACIS observations of 9 pulsars with PWNe and found correlations between pulsar and ˙ ˙ PWN photon indices and pulsar photon index and E. No LX − E relation has been derived from these data. In principle, the superior quality of the Chandra data and the large number of observed PSRs/PWNe allow one to determine the correlation law(s) more accurately than it has been done so far. The superb Chandra angular resolution allows one to cleanly separate pulsar and PWN contributions from each other in most cases. Moreover, in many cases the large number of collected counts permits separate measurements of thermal and non-thermal components in the pulsar’s spectrum. In Chapter 3 we report the results of such an investigation.

1.2.3 Overview of optical spectra of pulsars. To date about 16 neutron stars (NS) have been detected in IR, optical and ultra- violet (UV), of which nine are spin-powered pulsars. Most of these pulsars are too faint even for moderate-resolution spectroscopy in the optical band (with the notable exception of the Crab pulsar; Fig. 1.5). There are only a few pulsars for which multicolor photom- etry exists (Mignani et al. 2004). These include two middle-aged pulsars (Geminga and B0656+14; ' 300 and ' 100 kyr, respectively), a younger Vela pulsar (' 10 kyr), and two very young pulsars Crab (950 yrs) and B0540−69 (' 1.7 kyr). Only the youngest and brightest Crab pulsar permits high-resolution and high S/N spectral studies in the IR/optical and UV. The spectra of the Crab (Fig. 1.5) and its twin PSR B0540−69 are purely non-thermal (featureless power-laws with varying slopes) from near-IR to very high γ-ray energies. For the Crab, the spectral index was found to be roughly constant, α α ' 0.2 (Fν ∝ ν ), from IR/optical through UV (Sollerman 2003). The Vela pulsar and two middle-aged pulsars belong to an older, less energetic population and have much weaker magnetospheric emission components. This makes it possible to see both ther- mal (emitted from the NS surface) and nonthermal (magnetospheric) components in their spectra (Fig. 1.5). The spectra of the two middle-aged pulsars also show hints of spectral features in the optical (Fig. 1.5) while no spectral features have been detected in the X-rays. Using the data obtained with the Space Telescope Imaging Spectrometer (STIS) on board HST, we are able to constrain the temperature of the NS surface and the slope of the non-thermal component for the Geminga pulsar (Chapter 4) and PSR B0656+14 (Chapter 5). Measuring NS surface temperature is important for discriminat- ing between the existing NS cooling models (see Yakovlev & Pethick 2004 for a review) and can eventually constrain the poorly known equation of state for the super-dense NS interior. On the other hand, measuring the slope of the non-thermal component 14 may help to distinguish between the competing models of pulsar magnetospheric emis- sion, such as the polar cap models (Daugherty & Harding 1994) and outer gap models (Romani & Yadigaroglu 1995). It is also possible that in very young pulsars the non- thermal emission is dominated by synchrotron radiation produced by energetic electrons close to the light cylinder (outer gap models), while in older pulsars it is dominated by synchrotron radiation produced close to polar caps (in X-rays) and by resonant-Inverse- Compton (RIC) scattering of radio photons above polar caps (in the optical). Finally, detecting spectral lines in the optical/IR/UV could provide the direct measurement of the NS magnetic field. Until recently, no optical/UV emission has been detected from old millisecond pul- sars despite a number of attempts (e.g., Koptsevich et al. 2003; Mignani & Becker 2003). We recently observed the millisecond pulsar J0437−4715 with STIS and discovered the emission from the pulsar in the far-ultraviolet (FUV). The shape of the observed FUV spectrum suggests thermal emission from the neutron star surface with a surprisingly high temperature of about 1 × 105 K, above the upper limit on the surface temperature of the younger “ordinary” pulsar J0108−1431. For the few-Gyr-old J0437−4715, such a temperature requires a heating mechanism to operate. Since no other optical/NUV data are available for J0437−4715, we used the X-ray data to constrain the slope of the magnetospheric component in the far-ultraviolet (Kargaltsev et al. 2004; see also Chapter 6).

1.2.4 Connection between the X-ray and UV/optical properties. Only a few nearby and bright pulsars permit detailed study of both X-ray and optical emission. The Crab spectrum clearly changes its slope between the optical and X-ray bands. The spectral index measured in X-rays is by ∼ 0.8 steeper than the index measured in the optical. As for the other pulsars, the uncertainties associated with the data do not allow one to firmly conclude whether the slope of the non-thermal power-law (PL) component remains unchanged from optical to X-rays or, on the contrary, there is a spectral break between these bands. Spectra of the Vela and Geminga pulsars suggest a break while the spectrum of PSR B0656+14 does not. In all cases a multi-temperature thermal component is required to fit the broad-band (UV to X-rays) spectrum (Chapters 2, 5 and 6).

1.3 Diversity of NS population

Since the discovery of the Crab pulsar in 1967, Neutron Stars have not ceased to surprise us with diversity of their observational manifestations. There are at least three types of compact objects (most likely neutron stars) whose properties are quite different from those of spin-powered radio pulsars.

1.3.1 Radio-Quiet Neutron Stars One class of relatively recently discovered (in the ROSAT data) objects is called Radio-Quiet Neutron Stars (RQNSs; sometimes they also called Isolated NSs; Kaspi, Roberts & Harding 2004). These objects (7 are currently known) show no evidence for 15

Figure 1.5 Optical/UV spectra of four pulsars. The youngest is the Crab pulsar (top), the oldest is the Geminga pulsar (bottom). In addition to our results reported below we used the data points from Sollerman (2003, 2000), Shibanov et al. (2003) and Koptsevich et al. (2001). 16 radio pulsations, nebulosity, or accretion. Their X-ray emission is characterized by a very soft spectrum which is well described by a blackbody model (with TX ∼ 50 − 100 eV) and with no apparent magnetospheric component contribution. Four nearby RQNSs were also detected in optical. For the brightest and the best studied of these objects, RX J1856.5-3754, the thermal FUV spectrum has been measured. Interestingly, the UV and optical emission is too bright to be just the low-energy extrapolation of the blackbody fit to X-ray spectra for all four objects. To describe the RX J1856.5−3754’s optical/X-ray spectrum, a two-component blackbody model is required: the cool component (T ∼< 30 eV, R ∼> 15 km, d = 115 pc; Walter & Lattimer 2002) may originate from the bulk of the NS surface and account for the optical emission, while the hot component accounting for the X-ray emission (T ≈ 64 eV, R ≈ 4.3 km), could arise from a hot spot on the NS surface. Van Kerkwijk & Kulkarni (2001) discovered a bow-like shaped Hα nebula around RX J1856.5-3754, similar to those detected around several fast-moving ordinary radio pulsars (§1.1.3), which indicates the presence of a pulsar wind. This suggests that RX J1856.5−3754 and other RQNSs can be the pulsars whose axis orientation is unfavorable for observing the pulsations, i.e. the emission beam may not intersect the observer’s line-of-sight, or the line-of-sight is aligned with the rotation axis of the star, or the magnetic axis is aligned with the rotation axis. This could explain why all attempts to detect pulsations from RX J1856.5-3754 have been unsuccessful despite very deep exposures taken with Chandra and XMM. Recent spectroscopic observations with the Chandra and XMM-Newton X-ray Observatories resulted in the discovery of absorbtion features in the spectra of three RQNSs: RX J0720.4-3125 (P = 8.39 s), RX J1605.3+3249 and RX J1308.6+2127 (P = 10.3 s). The observed features are broad and centered between 0.23 and 0.5 keV. The features have been tentatively interpreted as proton cyclotron lines formed in the NS atmosphere (Harbel et al. 2003). In this case the line energies correspond to magnetic fields of a few times 1013 G. Alternatively, the features could be due to transitions in magnetized neutral Hydrogen (from the ground state to either the continuum and weakly bound states, or to quasi-bound states). This interpretation would imply the magnetic fields in excess of 1014 G (van Kerkwijk et al. 2004). If either of these interpretations is true, it would provide the direct measurement of magnetic field on the surface of NS.

1.3.2 AXPs and SGRs Another two classes of unusual NSs are known as Anomalous X-ray Pulsars (AXPs) and Soft Gamma-ray Repeaters (SGRs). These two classes are likely to be related and now often dubbed magnetars (e.g., Kaspi 2004). The magnetar model (Thompson & Duncan 1992), in which AXPs and SGRs are isolated young neutron stars powered by a decaying ultra-high magnetic field, provides the most compelling explanation for the unusual AXP and SGR properties. To date, 5 − 8 AXPs and 4 − 6 SGRs are known, some of them still being candidates under investigation. AXPs exhibit X-ray pulsations with periods ranging from 6 to 12 s, and lumi- nosities 1034 − 1035 erg s−1. All of the firmly confirmed five AXPs are observed to be spinning down. The periods and period derivatives imply large surface magnetic fields, in the range of 1014 − 1015 G (assuming magnetic dipole braking). These pulsars were 17 dubbed “anomalous” because, unlike spin-powered pulsars, their X-ray luminosities are much greater than the ∼ 1033 erg s−1 available from spin-down energy loss. This means that a different mechanism powers their X-ray emission. AXP light curves exhibit broad pulse profiles.Their X-ray spectra are best described by two components – a blackbody with kT ∼ 0.4 keV plus a power-law like tail with photon index 2.5 − 4. Several AXPs have been recently detected at optical/IR wavelengths. The distinctive feature of SGRs is short (∼ 100 ms) soft-gamma-ray and X-ray bursts, which often come in series, have typical energies ∼ 1041 erg, and rise times on the order of ∼ 10 ms. The burst spectra can be described by optically thin thermal bremsstrahlung models with kT ∼ 20 − 50 keV. The SGR’s bursting behavior is highly episodic, with years of inactivity and weeks in which hundreds of bursts are detected. Occasionally, SGRs exhibit giant gamma-ray bursts with luminosities up to 4 × 1044 erg s−1. Only two such giant bursts have been observed, the first one in 1979 from SGR 0525 − 66 (Mazets et al. 1979), and the second from SGR 1900+14 in 1998 August (Hurley et al. 1999). Similar to AXPs, even the quiescent SGR luminosities exceed the ∼ 1033 erg s−1 available from spin-down energy loss by several orders of magnitude. The X-ray spectra of SGRs in quiescence are much softer than during the bursts, with typical photon indices of 2 − 3 and possibly a thermal component with T ∼ 0.5 keV (e.g. SGR 1900+14; Perna et al. 2001). Three SGRs are known to pulse with periods that range from 5 to 8 s. Two of the three exhibit these pulsations in quiescence, and have clearly been shown to be spinning down (Kouveliotou et al. 1998, 1999). Under the assumption of simple magnetic dipole braking, the periods and period derivatives imply large surface magnetic fields of ∼ 1015 G. In quiescence, AXPs and SGRs exhibit similar properties: specifically, they have similar pulse periods, spin-down rates, and quiescent X-ray spectra. This led to the suggestion that AXPs are actually SGRs which simply have not been seen to burst. Indeed, recently AXP 1E 2259+586 experienced an outburst that was qualitatively and quantitatively similar to those of SGRs (Kaspi et al. 2003). There are still several small distinctions left between SGRs and AXPs: on average, the AXP spectra are softer than are those of the SGRs, more AXPs than SGRs are associated with supernova remnants, and SGRs on average have higher inferred B fields than those of AXPs (Kaspi 2004). However, given the small numbers of known AXPs and SGRs, these differences are statistically insignificant.

1.3.3 Central Compact Objects in SNRs. Finally, there are 6 compact objects that reside near the centers of Supernova Remnants and therefore called Central Compact Objects (CCOs). These objects, pre- sumably isolated NSs, have thermal spectra with BB temperatures 0.2 − 0.5 keV and X-ray luminosities of 1033 −1034 erg s−1. CCO is defined as an X-ray point source which (1) is found near the center of a SNR, (2) shows no radio/γ-ray counterpart, (3) shows no pulsar wind nebula (PWN), (4) has a soft thermal-like spectrum (Pavlov, Sanwal & Teter 2004). A distinctive feature of CCOs is the unusual spectrum which can be fit with a blackbody plus power-law model (in some cases the PL component is not required) and 18 implies very small blackbody radii, 0.3−2.4 km, and high effective temperatures 0.2−0.5 keV (cf. RQNSs spectra; §1.3.1). The photon indices corresponding to the best-fit PL component are soft, Γ = 2.5 − 4.2, i.e. softer than those of spin-powered pulsars, and resemble photon indices found in AXPs and quiescent SGRs. Fits with the light-element (H or He) atmosphere models (Pavlov et al. 1995) give lower temperatures, by a factor of ∼ 2, and larger radii, by a factor of 2–7, but still the radii remain smaller than the conventional NS radius for at least two CCOs. Since the atmosphere spectra are harder than the BB spectra in the X-ray band, the PL components are unconstrained in the atmosphere+PL fits. Among the six CCOs, only one, 1E 1207.4-5259, clearly shows spectral lines (Sanwal et al. 2002; Bignami et al. 2003) while the others are satisfactorily described by featureless continua. 1E 1207.4-5259 is also the only CCO for which 0.424 s period (much shorter than those of AXPs) has been detected (however, with a puzzling time dependence; Zavlin, Pavlov & Sanwal 2004). This CCO has a surprisingly small period derivative, corresponding to a characteristic pulsar age of about 500 kyr (vs. 3–20 kyr for the SNR) and an inferred magnetic field ∼ 3 × 1012 G, typical for a radio pulsar (Pavlov et al. 2002b). None of the six CCOs has shown any long-term variability1. No optical emission has been firmly detected from any of CCOs. No extended emission around CCOs has been detected. The other well studied CCOs is discovered by Chandra CCO J2323+5848 in 300- year old SNR Cassiopeia A. The spectral properties of this source, as well as the absence of any detectable pulsations and PWN, make it very different from those of young spin- powered pulsars. Specifically, Pavlov, Sanwal & Teter (2004) showed that for a blackbody or hydrogen atmosphere model, the temperature of the emission (kT = 0.33 − 0.42 keV) is very high, and the emitting area (R = 0.6 − 2.2 km) too small to be consistent with surface thermal emission from a passively cooling NS. One could argue that hot thermal component comes from polar caps while pulsations are not seen due to the unfavorable geometry. However, in this case the absence of X-ray emission from the rest of the NS surface still remains puzzling because, given the very young age of the NS, the entire surface should be hot enough to emit X-rays. The lack of variability during 4 years of Chandra observations (Pavlov, Sanwal, & Teter 2004) suggests that it is not an accreting object (hence not a black hole). The CCO in the “Vela Junior” (SNR G266.1 − 1.2) SNR has properties which are very similar to those of Cas A CCO (Kargaltsev et al. 2002; see also Chapter 7), except that the age and distance to G266.1−1.2 are less certain.

1.3.4 Hypotheses on the nature of CCOs. So far, the origin of CCOs remains enigmatic. Although the CCO spectra resemble more the spectra of AXPs than the spectra of spin-powered pulsars, the connection be- tween CCOs and AXPs is neither firmly established nor understood. One could speculate that CCOs are actually young magnetars, not mature enough to develop characteristic properties of AXPs/SGRs (e.g., they have not spun down to the 5-12 s period range).

1We do not consider an interesting compact source inside SNR RCW103 (likely also a NS) as a COO since it appears to be in a binary system, unlike the rest of COOs. 19

This hypothesis could, at least, explain the lack of pulsar activity in CCOs (i.e. radio emission and PWN), but it seems to be at odds with the properties of 1E 1207.4 − 5259 (unless the latter is different from the rest of CCOs). Furthermore, the rest of CCOs do not show pulsations in X-rays, whereas AXPs do. Perhaps CCOs could be isolated neu- tron stars composed of more exotic particles (e.g., quarks), and therefore having smaller radii than conventional NSs. Part I

Young pulsars and Pulsar Wind Nebulae.

20 21

Pulsars are generally considered to be young if their age is ∼< 10 kyrs (cf. Fig. 1.2). Such pulsars are more energetic than those from an older population and, as a rule, more luminous. The spectra of young pulsars are usually dominated by the non-thermal emis- sion, although the thermal spectral component may also be seen (e.g., Vela pulsar). Many of the young pulsars also emit γ-rays (Harding 2002). Recent radio and X-ray observations have shown that young pulsars produce strong winds which power spectac- ular nebulae emitting nonthermal synchrotron radiation (e.g., Kaspi, Roberts & Harding 2004, and references therein). This part of the dissertation is devoted to a detailed analy- sis of multiwavelength data on the Vela pulsar and its PWN (Chapter 2) and a statistical study of PSR/PWN X-ray properties based on a sample of 35 PSRs/PWNe observed with the Chandra X-ray Observatory (Chapter 3). 22

Chapter 2

The Vela pulsar and its Pulsar Wind Nebula.

The Vela pulsar is located close to the center of the very large (∼ 8◦ in diameter) Vela supernova remnant. The pulsar has a period of 89.3 ms, characteristic age τ = P/(2P˙ ) ≈ 11 kyr (the true age may be a factor of 2–3 larger – see Lyne et al. 1996) and spin-down power of 7 × 1036 erg s−1. The distance to the pulsar was determined from its annual parallax – Caraveo et al. (2001) measured the parallax of the pulsar’s +76 +19 optical counterpart and obtained d = 294−50 pc, Dodson et al. (2003) found d = 293−17 pc from the radio parallax. Therefore, we parameterize the distance to the Vela pulsar as d = 300d300 pc for the rest of this chapter.

2.1 Earlier X-ray and optical observations and their results.

The launch of SAS-2 in November 1972 (one of the first satellites entirely ded- icated to γ-ray observations) led to the discovery of gamma-ray pulses from the Vela pulsar (Thompson et al. 1975), which was found to be the strongest persistent gamma- ray source in the sky. The gamma-ray lightcurve of the Vela pulsar is characterized by two relatively sharp peaks, separated by 0.4 in phase (similar to the Crab pulsar). However, contrary to the Crab pulsar, these peaks are not aligned in phase with the radio and optical peaks (see Fig. 2.9). Observation with the Einstein satellite firmly established the Vela pulsar as the X-ray source (Harnden et al. 1985). These and sub- sequent observations with the ROSAT and ASCA X-ray satellites (Ogelman,¨ Finley & Zimmerman 1993; Markwardt & Ogelman¨ 1997, 1998) have shown that the pulsar is em- bedded in a compact (∼ 10–20) “kidney-bean” nebula. Ogelman,¨ Finley & Zimmerman (1993) fitted the overall PWN spectrum in the 0.1–2.4 keV band using the ROSAT Po- sition Sensitive Proportional Counter (PSPC) data, with the power-law (PL) model and −Γ+1 found a photon index Γ = 2.0 ± 0.2 (Fν ∝ ν ). The same observations revealed the soft, thermal-like spectrum of the Vela pulsar. Based on the shape of the PWN as seen in the images obtained with the ROSAT High-Resolution Imager (HRI), Markwardt & Ogelman¨ (1998) suggested that the observed PWN could be a bow-shock nebula formed due to the supersonic motion of the pulsar through the ambient medium. The nebula around the Vela pulsar was also detected at higher X-ray energies. First indication of the PWN around the Vela pulsar at energies up to 25 keV was obtained by Willmore et al. (1992) with the Birmingham Spacelab 2 mission. Even more energetic emission from the PWN was observed with the OSSE detector of the Compton Gamma- Ray Observatory (CGRO) by de Jager et al. (1996), who found the photon index Γ = 1.8 ± 0.4 in the 44–370 keV range. Since the launch of the Chandra X-ray Observatory, the Vela pulsar and its PWN have been a subject of intense investigation. Both have been observed with the Chandra 23

High Resolution Camera (HRC) and Advanced CCD Imaging Spectrometer (ACIS) on multiple occasions(Pavlov et al. 2001a, 2001b, 2003; Helfand, Gotthelf, & Halpern 2001). The first Chandra observation revealed the complex structure of the PWN, reminiscent of the Crab PWN. This and subsequent observations have demonstrated that the bow- shock interpretation of the nebular X-ray emission (based on the low-resolution ROSAT HRI images) can not be satisfactory. The sound speed in the Vela SNR is likely to be higher than the velocity of the pulsar and, most importantly, there is no simple bow-shock model which can explain the double-arc PWN structure as it is seen with a high resolution (see Fig. 2.11 in §2.4). Following the discovery of Vela PWN variability (Pavlov et al. 2001b; see also §2.4.2), the PWN has been regularly observed with the Chandra ACIS , primarily with the goal of monitoring changes in the PWN structure (§2.4). Prior to the Chandra observations the nature of the Vela pulsar’s X-ray spectrum remained elusive because the angular resolution of the X-ray telescopes was insufficient to separate the pulsar radiation from that of the bright PWN. The first clean, high- quality spectrum of the Vela pulsar was obtained from Chandra HRC-LETG and ACIS CC-mode1 observations (Pavlov et al. 2001a, Sanwal et al. 2002, see also §2.2.2). These observations clearly reveal the presence of two components in the pulsar spectrum: ther- mal and non-thermal. The X-ray light curves obtained with Chandra (Sanwal et al. 2002; §2.2) and RXTE (Harding et al. 2002) show multiple peaks likely originating from different regions of magnetosphere or/and corresponding to physically different spectral components. The discovery of optical pulsations from the Vela pulsar (Wallace et al. 1977) had followed shortly after the discovery of γ-ray pulsations. Owing to its proximity, the Vela pulsar is relatively bright in the optical (V = 23.6), compared to the other pulsars of a similar or older age. The photometric observations in UBVRIHJ filters with different telescopes have shown that the dereddened, phase-averaged optical spectrum of −α the pulsar is predominantly non-thermal and can be fitted with a power law, Fν ∝ ν , with α ≈ 0.12, assuming the color excess E(B-V) = 0.05 (e.g., Shibanov et al. 2003 and references therein). To investigate the shape of the pulsar’s UV spectrum, we carried out observations of the Vela pulsar with the Space Telescope Imaging Spectrograph (STIS) onboard HST (§2.3). These observations also yielded pulse profiles in the near- and far-ultraviolet.

2.2 Chandra observations of the Vela pulsar.

The spectra of the Vela pulsar obtained with Chandra ACIS operated in the imaging mode had suffered from a substantial pile-up 2. The Vela pulsar was also

1Continuous Clocking (CC) mode of ACIS provides a spectrum and a 3 msec time resolution at the expense of one dimension of spatial resolution 2Pile-up occurs at high count rates when two different events (photons) are recorded by the detector as a single event at a higher energies, which distorts the spectrum. 24 observed with HRC-LETG3 and ACIS in Continuous Clocking (CC) mode (with and without HETG4). These data were not affected by the pile-up and, therefore, we use them to investigate the X-ray spectrum of the Vela pulsar.

2.2.1 Observations and data reduction. About 16,000 pulsar counts in the range 0.25 − 2.0 keV were extracted from two HRC-LETG observations of 25 ks each (ObsIDs 127 and 1852). No deviations of counts in the individual bins from the mean value of neighboring 10 − 20 bins were found with statistical significance higher than 2.7σ. This indicates that no heavy elements are present on the NS surface, otherwise spectral lines should be seen. The spectral fits with thermal models show excess counts at the high energy end (> 1.5 keV). To get a better handle on the harder component, we used the ACIS/HETG data obtained in the Continuous Clocking mode (ObsIDs 131 and 3860). In the observation with the HETG we used only the zero-order image, which is equivalent to about 3 ks observation without the grating. The background was estimated by interpolating between the neighboring regions in the 1D image of the pulsar and its nebula. Since the ACIS response is not well calibrated at low energies, and the particle background dominates the spectrum above 8.0 keV in the CC mode, we use only events in the energy range 0.8 − 8.0 keV for further analysis of the ACIS data.

2.2.2 X-ray spectrum and pulsations. The simultaneous spectral fit to the HRC-S/LETG and ACIS/HETG-CC data (ObsIDs 127 1852 and 131) has been done first because this data were acquired two years before the ACIS-CC observation without the grating (ObsID 3860). The fit clearly shows two components – a soft thermal component, which fits equally well with a blackbody or a magnetic hydrogen atmosphere model, and a harder component, which we fit with a power-law (PL). The parameters of the fit depend on the model chosen for the soft thermal component. Table 2.1 shows the fitting parameters for the combined data (see Pavlov et al. 2001a for details). We then fitted the more recent ACIS-CC data with the same models. A long 39 ks exposure and increased sensitivity in the absence of the grating make these data by far superior to the ACIS/HETG-CC for the purpose of constraining the high-energy part of the spectrum. Table 2.2 shows the fitting parameters obtained with the ACIS-CC data. The differences between the corresponding best-fit parameters from Table 2.1 and Table 2.1 are sometimes larger than the statistical uncertainties of the best-fit parameter values. This suggests that the systematic uncertainties (e.g., in calibration) dominate over the statistical uncertainties. Figure 2.1 shows the broadband spectrum of the Vela pulsar. In this figure the soft X-ray component corresponds to the atmosphere model.

3HRC-LETG – High Resolution Camera combined with the Low Energy Transmission Grat- ing. This observational setup provides the highest spectral resolution on Chandra at low (0.08 - 0.2 keV) energies. 4ACIS-HETG – Advanced CCD Imaging Spectrometer combined with the High Energy Trans- mission Grating, provides resolving power up to 1000 in the band in 0.4 − 10.0 keV band. 25

Table 2.1 Parameters of the two-component fits to the Vela pulsar spectrum for HRC- S/LETG and ACIS/HETG-CC data. The radii and luminosities are for a distance of 300 pc.

th nonth Thermal nH (fixed) Teff Reff Lbol γ L0.5−8.0keV Model (1020 cm−2) (MK) (km) (erg s−1) (erg s−1) Blackbody 2 1.45 ± 0.05 2.4 ± 0.3 2.2×1032 2.7 ± 0.2 2.0 × 1031 H Atmosphere 3 0.68 ± 0.03 18 ± 2 5.5×1032 1.5 ± 0.3 1.5×1031

Table 2.2 Parameters of the two-component fits to the Vela pulsar spectrum for ACIS-CC data. The radii and luminosities are for a distance of 300 pc.

th nonth Thermal nH (fixed) Teff Reff Lbol γ L0.5−8.0keV Model (1020 cm−2) (MK) (km) (erg s−1) (erg s−1) Blackbody 2 1.65 ± 0.02 1.6 ± 0.4 1.4×1032 2.3 ± 0.1 3.0 × 1031 H Atmosphere 3 0.70 ± 0.02 13 ± 1 2.9×1032 2.01 ± 0.11 2.6×1031 PL in 2.8−8.0 keV 3 − − − 2.0 ± 0.3 2.3×1031

Figure 2.1 The high-energy spectrum of the Vela pulsar. The data shown include OSSE (Strickman et al. 1996), COMPTEL (Sch¨onfelderet al. 2000) and EGRET (Kan- bach et al. 1994). The soft X-ray flux corresponds to the NS atmosphere model for the thermal component. The dotted line is the unabsorbed flux while the solid line is the observed flux from the Vela pulsar. The pulsed fluxes corresponding to the three HRC peaks (see Fig. 2.2) are marked with horizontal bars. 26

Figure 2.2 Left: The pulse profiles from the HRC observations. The three peaks (P1, P2 and P3) are marked in the top panel. Right : Energy-resolved pulse profiles from the ACIS/HETG-CC observation. The top panel shows the pulse profile for E < 1.8 keV corresponding to the thermal component dominated regime. The bottom panel shows the profile for E > 1.8 keV, where non-thermal component dominates. 27

The Vela pulsar was observed twice with the HRC-I and twice with the HRC- S/LETG. Both of the HRC-I observations and the first LETG observation suffered from the HRC timing problem 5. The times have been corrected by shifting to the time of the next event in the Level 1 event list taking only the events with time correction less than 4 ms. The second LETG observation was in the special operating mode which allows all event times to be recovered. The radio ephemeris of the Vela pulsar was based on the observations at the Hobart and Parkes radio observatories. The phase of each event was determined and the light curve was folded to get the pulse profiles. The left panel of Figure 2.2 shows the observed pulse profiles of the HRC observations. The pulse profiles show three peaks separated by about 1/3 of phase, with a total pulsed fraction of 9% (see also Helfand et al. 2001). The pulsed fluxes in the three peaks are shown in Figure 2.1 (left panel). For the ACIS/HETG-CC observation, the times recorded in the file are the event readout times. The latter have been corrected for the dither and SIM motion, and for the time that is needed for the event to reach the readout. Although the absolute times calculated in this way may not be accurate enough, the relative times are accurate. The right panel of Figure 2.2 shows the pulse profiles in two energy bands (E < 1.8 keV and E > 1.8 keV). The difference in the profile shapes and the pulsed fraction is striking. We estimate the intrinsic pulsed fraction of the pulsar to be 8 ± 2% and 62 ± 20% in the E < 1.8 keV and E > 1.8 keV bands, respectively.

2.3 HST observations of the Vela pulsar.

In this section we describe the results of the HST STIS observations which were carried out to measure the ultraviolet (UV) spectrum of the Vela pulsar, evaluate con- tribution of the thermal emission component at the far-UV (FUV) wavelengths, and determine the shape of the pulse profile in UV.

2.3.1 Observations and data reduction. The Vela pulsar was observed with the HST STIS FUV-MAMA (Far-Ultraviolet Multi Anode Micro-channel Array ) on 2002 May 28 (start date is 52, 422.42051614 MJD UT). The low-resolution grating G140L (which covers the wavelength interval ≈ 1150– 1700 A)˚ with the 5200 × 000. 5 slit was used. The data were taken during two consecutive orbits (including the target acquisition). The total scientific exposure time was 5373.38 s. The Vela pulsar was also imaged with the STIS NUV-MAMA on 2002 May 28 (start date is 52, 422.54739096 MJD UT). The broad-band filter F25SRF2 (pivot wave- length 2299 A,˚ FWHM 1128 A)˚ was used in this imaging observation to minimize the contribution of geocoronal lines. The data were taken during two consecutive orbits. The total scientific exposure time was 5951.40 s.

5A problem has been discovered in HRC event times. A wiring error in the detector causes the time of an event to be associated not with that event, but with the following event, which may or may not be telemetered. 28

Both FUV- and NUV-MAMA were operated in TIME-TAG mode which allows the photon arrival times to be recorded with 125 µs resolution.

2.3.1.1 NUV photometry. As an input, we used four flat-fielded “low-resolution” images (1024×1024 pixels; plate scale 000. 0244 pixel−1). The target is clearly seen in each of these images. To improve the signal-to-noise ratio (S/N), we combined the images from two exposures into a single image using the STSDAS6 task “mscombine”. Figure 2.3 shows the NUV image of a region centered on the Vela pulsar. The image in Figure 2.3 is binned by a factor of 4 compared to the native NUV-MAMA pixel size (000. 0244 pixel−1) and then smoothed with the gaussian kernel of 5 new pixels. The image of the pulsar, which is clearly seen in the Figure 2.3, has the size compatible with the width of the STIS point-spread function (PSF of NUV-MAMA has FWHM of ≈ 000. 2). We have also thoroughly inspected the original 2400. 5 × 2400. 5 NUV image, applying various binning and smoothing scales, and found no evidence of PWN emission down to the limiting unabsorbed surface brightness of 0.8 µJy arcsec−2 (for E(B-V)= 0.05).

0.5''

Figure 2.3 MAMA-NUV image of the Vela pulsar field. North is up, East is to the left.

We measured the numbers of source counts, Ns in the combined image, by per- forming standard aperture photometry with the IRAF task “phot” from the “digiphot” 7 package , and obtained Ns = 4183 ± 70 for the 4-pixel-radius aperture which provides optimal S/N.

6Space Telescope Data Analysis System at http://www.stsci.edu/resources/software hardware/stsdas 7http://stsdas.stsci.edu/gethelp/pkgindex noao.html 29

The source spectral flux Fλ is connected with the number of source counts in a given aperture by the integral relation Z

Ns = t RλλFλ²λ dλ , (2.1) where t is the exposure time, Rλ is the integrated system throughput, including the 8 Optical Telescope Assembly and filter throughputs , and ²λ is the wavelength-dependent encircled energy fraction. One can estimate an average flux in the filter passband defined as either ¯ Ns Fλ = R (2.2) t Rλλ²λ dλ or Ns hFλi = R , (2.3) t²¯ Rλλ dλ where² ¯ is in average encircled energy fraction in the filter passband, and Ns/(t²¯) = C is the source count rate corrected for the finite aperture.

Figure 2.4 Model flux F2299 (see text) versus PL model index for different values of E(B-V).

8We corrected the throughputs supplied with the data for the time-dependent sensitivity loss (see http://www.stsci.edu/hst/stis/calibration/reference files/tds.html). 30

¯ −18 −2 −1 −1 We found that the mean fluxes, Fλ ' hFλi ' 6.5 × 10 ergs cm s A˚ are close to each other for r ∼> 3 pixels. The uncertainty of these values, ∼ 10%, is mostly due to systematic errors in the encircled energy fraction. Another way to evaluate the flux is to assume some form for the spectral flux Fλ and determine its normalization making use of equation (2.1). We approximate the spectral flux in the F25SRF2 passband as an absorbed power law: −α −0.4A(λ)E(B−V ) Fλ = F2299(λ/2299 A)˚ 10 , where F2229 is the intrinsic source spectral ¯ flux at the pivot wavelength [it coincides with Fλ in the special case α = 0, E(B−V)=0], and A(λ) is the ultraviolet extinction curve (Seaton 1979). The color index, E(B−V) is poorly known. An estimate based on the hydrogen column density found from the X-ray fits (see §2.2.2) gives E(B−V)' 0.05; below we will adopt E(B−V)=0.01–0.07 as a plausible range. We calculated the dependencies of F2299 on the spectral slope α in a reasonable range 0 ≤ α ≤ 4 for several values of E(B−V), based on the Ns values mea- sured in the 4-pixel radius aperture (see Fig. 2.4). We see that, at given E(B−V), F2299 varies with α by up to 20%. We estimate the uncertainty of the F2299 values at given α and E(B−V) as ≈ 8%–10%, mostly associated with unpredictable changes of the MAMA imaging PSF between individual observations that cause systematic uncertainties of ²λ (see Proffitt et al. 2003 and §16.1 of STIS IHB).

2.3.1.2 FUV spectrum. For each FUV exposure, we processed the raw “high-resolution” images (2048 × 2048 pixels; plate scale of 000. 0122 per pixel — see §11 of the STIS IHB) using the calibration files available on 2003 July 1. As an output, we obtained flat-fielded low- resolution (1024 × 1024 pixels; plate scale 000. 0244 pixel−1; spectral resolution 0.58 A˚ pixel−1) images and used them for the spectral analysis. The processed images show a nonuniform detector background that consists of a flat (constant) component and the so-called “thermal glow” component (Landsman 1998) that dominates over most of the detector area and grows with increasing the FUV- MAMA low-voltage power supply temperature. The thermal glow is the strongest in the upper-left quadrant of the detector, where the dark count rate can exceed the nominal value, 6 × 10−6 counts s−1 pixel−1, by a factor of 20. To reduce the contamination due to the thermal glow background, the source was placed close to the bottom edge of the detector. We find the spectrum centered at Y = 126 ± 2 pixels in each of the flat-fielded images (the centroid slightly varies with X), where X and Y are the image coordinates along the dispersion and spatial axes, respectively. Even at this location on the detector the background still exceeds the nominal value by a factor of 1.5–5, depending on the position along the dispersion axis. To improve S/N, we combined the images from four exposures into a single image using the STSDAS task mscombine. The Y -positions of the centroids differ by less than 3 pixels for different exposures and different wavelengths (X-positions). Accurate subtraction of the enhanced, nonuniform background (typical values are 1–3 ×10−5 counts s−1 pixel−1) is crucial to measure the spectrum of our faint target. 31

Figure 2.5 The measured (absorbed) FUV spectrum of Vela pulsar. The dashed line shows best fit absorbed PL model with αλ = −2.06 for E(B-V)=0.05 (see text). 32

The spectral extraction algorithm implemented in the standard STIS pipeline (task X1D) does not adequately correct for the nonuniform background while extracting the spec- trum of such a faint source and does not allow to vary the extraction box size with the position along the dispersion axis. Therefore, we used an IDL routine with additional capabilities of grouping and fitting the background and selecting an optimal extraction box size depending on the position along the dispersion axis (see Kargaltsev, Pavlov, & Romani 2004). Since the source spectrum occupies only a small region on the detector, we do not attempt to subtract the background globally. Instead, we scan the count distribution within two strips, 96 ≤ Y ≤ 116 and 136 ≤ Y ≤ 156, adjacent to the source region, 117 ≤ Y ≤ 135. To obtain the spectrum with a sufficiently high S/N, we have to bin the spectrum heavily; after some experimenting, we chose 12 spectral bins (λ-bins; see Table 2.3). The bins chosen exclude the regions contaminated by the geocoronal emission (Lyα line and OI lines at 1304 A˚ and 1356 A)˚ and by an artificial background structure at λ ≈ 1379–1384 A,˚ Y ≈ 96–103. The bins outside the contaminated regions were chosen to have comparable S/N (≈ 6–8), whenever possible. For each of the λ-bins, we calculate the total number of counts, Nt, within the extraction boxes of different heights (one-dimensional apertures): As = 3, 5, 7, 9, 11, 13, 15, and 17 pixels, centered at Y = 125 for the first two λ-bins and at Y = 126 for the rest of the λ-bins. To evaluate the background, we first clean the background strips (see above) from outstanding (> 10−3 cts s−1 pixel−1) values (“bad pixels”) by setting them to local average values. Then, for each of the λ-bins, we fit the Y -distribution of the background counts with a first-order polynomial (interpolating across the source region), estimate the number Nb of background counts within the source extraction aperture As, and evaluate the number of source counts, Ns = Nt − Nb (Table 2.3). 2 The uncertainty δNs of the source counts can be evaluated as δNs = [Ns+δNb (1+ 1/2 As/Ab)] , where δNb is the background uncertainty in the source aperture. We binned the distribution of background counts along the Y -axis with the bin sizes equal to As and calculated δNb as the root-mean-square of the differences between the actual numbers of background counts in the bins and those obtained from the fit to the background. We calculated δNs and S/N for various extraction box heights and found that As = 11 value provides S/N close to optimal for all λ-bins. Therefore, we used As = 11 pixels in further calculations. We calculated the average spectral fluxes in the λ-bins defined as R Rλλ Fλ dλ C hF i = ∆Rλi = R i , (2.4) λ i R λ dλ R λ dλ ∆λi λ ∆λi λ where Ci is the source count rate in the i-th λ-bin uncorrected for the finite size of the source extraction aperture, and Rλ is the system response that includes the Optical Telescope Assembly throughput and accounts for the grating and slit losses, finite extrac- tion aperture size and time-dependent sensitivity losses (Bohlin, 1999; see also §3.4.12 33

of the HST Data Handbook for STIS9 for details). The resulting flux values are given in Table 2.3, while the spectrum is shown in Figure 2.5. TheP total fluxP in the 1153– ˚ ˚ −1 1701 A range (∆λ = 548 A), can be estimated as F ' ∆λ ( ihFλii∆λi)( i ∆λi) ' −15 −1 −2 2 (8.19 ± 0.36) × 10 erg s cm , corresponding to the luminosity LFUV = 4πd F = 28 2 −1 (8.78 ± 0.39) × 10 d300 erg s .

Table 2.3 FUV-MAMA counts and fluxes in λ-bins

a b λ-bin (A)˚ As Nt Nb δNb Ns δNs S/N hFλi ± δhFλi 1153−1185 11 167.833 97.137 10.51 70.69 13.5 4.6 23.4 ± 4.45 1247−1258 11 125.627 47.568 5.577 78.06 10.4 6.3 20.1 ± 2.69 1259−1269 11 117.112 31.561 5.796 85.55 10.9 5.8 20.7 ± 2.64 1270−1281 11 111.492 34.963 5.691 76.53 10.4 6.6 18.1 ± 2.46 1315−1331 11 134.440 42.175 5.527 92.26 11.1 6.9 15.2 ± 1.82 1332−1346 11 115.704 32.880 5.060 82.82 10.4 6.7 17.0 ± 2.13 1356−1373 11 116.825 32.896 6.170 83.93 11.0 6.3 14.9 ± 1.96 1404−1421 11 90.9397 25.781 5.718 65.16 9.9 6.2 13.9 ± 2.11 1422−1450 11 147.031 43.524 6.867 103.51 12.3 7.8 14.7 ± 1.74 1451−1491 11 161.428 48.020 5.065 113.41 11.8 8.5 13.6 ± 1.41 1492−1544 11 166.790 53.229 5.528 113.56 12.0 8.0 13.7 ± 1.44 1545−1701 11 307.984 143.71 8.541 164.27 15.4 9.3 12.9 ± 1.21 Summedc 11 1763.21 633.45 22.61 1232.95 40.51d 30.4 14.97 ± 0.67e

aHeight of extraction box, in pixels. bAverage spectral flux and its statistical uncertainty, in units of 10−18 erg s−1 cm−2 A˚−1, corrected for the finite aperture. cValues for summed λ-bins. P dDefined as [ (δN )2]1/2. h i s,i i e P ¡P 2 2¢1/2 ¡P ¢−1 Defined as ihFλii∆λi ± ihδFλii ∆λi i ∆λi .

αλ We fit the spectrum with the absorbed power-law model, Fλ = F1500 (λ/1500 A)˚ × 10−0.4A(λ) E(B−V ). For a plausible value of E(B − V ) = 0.05 (e.g., Shibanov et al. 2003), we found the power-law index αλ = −2.06 ± 0.39, and the normalization F1500 = −17 −2 −1 ˚−1 2 2.09 ± 0.09 × 10 erg cm s A , respectively; the corresponding χν value is 0.53 for 10 degrees of freedom (d.o.f.).

9http://www.stsci.edu/hst/stis/documents/handbooks/currentDHB/STIS longdhbTOC.html 34

2.3.2 Broad-band optical-UV spectrum. X-ray connection. Figure 2.6 shows the spectrum of the Vela pulsar from optical to UV, with the optical data points adopted from Shibanov et al. (2003). Overall, the spectrum looks very flat. Therefore, we first fit it with a PL model. The best fit spectral index and 15 normalization are αν = 0.01±0.02 and Fν = 1.50±0.03 µJy at ν = 10 Hz, respectively (χν = 0.48 for 18 d.o.f.). The spectral index is flatter than that obtained by Shibanov et al. (2003), αν = −0.12, from fitting only IR and optical data with a PL model. It is also flatter than the slope of the non-thermal X-ray component −αν = 0.5 − 1.0 in the two- component fit with Hydrogen atmosphere + PL model (Table 2.1 and 2.2). To investigate whether there is an appreciable contribution of the thermal emission (which could arise from the NS surface or atmosphere) at FUV frequencies, we also fit two-component Rayleigh-Jeans (R-J) plus PL model to the optical and UV data. In this case, the best fit (χν = 0.58 for 17 d.o.f.) spectral index, αν = −0.05 ± 0.07, and normalization, 15 Fν = 1.42±0.098 µJy at ν = 10 Hz, are marginally consistent with the values obtained by Shibanov et al. (2003) for the PL fit to the IR and optical data. However, the addition of thermal component is not statistically justified (for two-component model χν = 0.46 2 for 17 d.o.f.). The best fit Rayleigh-Jeans parameter G ≡ T6(R13/d300) = 0.41 ± 0.24 MK can be considered as a upper limit on the NS surface temperature if it emits as a black-body (BB). The contribution of 0.41 MK BB, if present, is negligible in the X-ray band and, hence, such a cool component would not change the parameters of the X-ray fits (see Tables 2.1 and 2.2). Note that if the NS has an atmosphere, then the inferred R-J limiting surface temperature of ' 0.65 MK (1σ upper limit) will be inaccurate due to the large difference in the best-fit temperatures of the BB and Hydrogen atmosphere models fitted to the same data. For instance, the spectrum of the hydrogen atmosphere with T ≈ 0.7 MK (Table 2.1) has a low-energy tail whose contribution to the FUV flux is similar to that of a T ≈ 0.4 MK blackbody.

2.3.2.1 Timing. For the timing analysis of the FUV-MAMA data, we used the so-called TIME- TAG data files that contain the photon arrival times, recorded at a 125 µs time resolution, and high-resolution detector coordinates associated with each of the events. The arrival times are corrected for the Earth and spacecraft motions and transformed to barycen- tric dynamical times (TDB) at the solar system barycenter, using the STSDAS task “odelaytime”. For the two FUV-MAMA exposures (total Tspan = 5373 s), we extracted 1389 events from the λ-bins that exclude geocoronal line emission, with the height of extraction box equal to 11 high-resolution pixels (≈ 71% of these counts are expected to come from the source). For the two NUV-MAMA exposures (Tspan = 5951 s), we extracted 5308 events from the 10 high-resolution pixels circle (r = 000. 244) centered at the pulsar (≈ 84% of these counts are expected to come from the source). 2 2 The Zn test (Buccheri et al. 1983) shows that the peak values of Z1,FUV = 100.1 2 and Z1,NUV = 410.9 are attained at the frequencies fFUV = 11.193499(35) Hz and fNUV = 11.193503(35) Hz, respectively. These frequencies differ only by +5 and +9 µHz 35

Figure 2.6 The UV-optical spectrum of the Vela pulsar. The solid and dashed lines show the best fit R-J+PL model and the PL component of this model. The dash-dotted line shows best-fit PL model with αν = 0.01 ± 0.02. 36

Figure 2.7 Top: NUV lightcurve of the Vela pulsar. The background level is at 27 counts/bin. Bottom: FUV lightcurve of the Vela pulsar. The background level is at 13 counts/bin. 37

(i.e. deviations are well within the uncertainties of the frequencies) from the frequencies derived from the Vela pulsar ephemeris (f = 11.1935036403881 Hz, f˙ = −1.56027×10−11 s−2 for the MJD epoch 52408.000000282; ATNF Pulsar database10) for the times and dates of FUV and NUV observations, respectively. Figure 2.7 shows the folded light curves of the source plus background counts. The pulsed fractions11 in the observed (source + background) radiation are 52% (the corresponding intrinsic pulsed fraction is 73%) and 73% (the corresponding intrinsic pulsed fraction is 87%) for the FUV and NUV lightcurves, respectively.

2.3.3 Summary. The optical, FUV, NUV and X-ray light curves show complex structures. Four peaks are clearly seen in the NUV and FUV light curves and at least 3 peaks in the optical and X-ray light curves (Figs. 2.8 and 2.9). This suggests contributions from several emission components and/or a complex geometry of the emitting region. Although the optical, NUV and FUV pulse profiles are very similar, one can notice that the height of the first peak (Figs. 2.7 and 2.9) monotonically decreases from optical through NUV to FUV. This indicates that the emission component which is responsible for this peak becomes weaker at higher frequencies. The strong first and second peaks (see Fig. 2.8) are certainly due to the non-thermal emission (cf. gamma-ray light curve in Fig. 2.9). The soft X-ray band (0.3−1.5 keV) light curve, should be dominated by the thermal emission from the NS surface (Fig. 2.10). The non-uniform surface temperature distribution may be responsible for the broad hump between the phases 0.6 an 1.3. The origin of the two small peaks (3 and 4) sitting on top of the thermal hump and the dip at the phase of ∼ 0.95 (in 0.3 − 1.5 keV panel; Fig. 2.8) is less clear. The extrapolation of the best fit RXTE PL component (αν ≈ −0.4; fitted to the phase integrated spectrum excluding the 5th most energetic RXTE band) to the optical range falls a factor of 1.4−1.6 below the BVR optical points (Shibanov et al. 2003). However, the RXTE spectrum accounts only for the pulsed flux component and therefore the total flux is underestimated. Furthermore, the non-thermal emission in the RXTE band is likely to be comprised of several components with different spectral slopes (see Harding et al. 2003 for phase-resolved spectroscopy). The two-component fits to the phase-integrated Chandra spectrum (see Tables 2.1 and 2.2 in §2.2.2) give much steeper PL slopes than those observed in the optical, which suggests spectral flattening at lower frequencies (Fig 2.10) This conclusion may not hold if the hard-band (1.5-8.0 keV) Chandra spectrum also contains contributions of several non-thermal components (with different spectral slopes) of which only one extends to the optical. An accurate phase-resolved spectroscopy is needed to determine the connection between the non- thermal optical and X-ray spectra. The scheduled infra-red observations with Spitzer should even better constrain the slope of the spectrum in the optical.

10http://www.atnf.csiro.au/people/pulsar/psr/archive/data.html 11traditionally defined as a ratio of the number of counts above the level determined by the bin with the minimal number of counts (minimum level) to the total number of counts in the lightcurve. 38

Figure 2.8 NUV and FUV light curves in comparison to the X-ray light curves from the latest ACIS-CC and XMM EPIC-pn observations (courtesy of Divas Sanwal and Slava Zavlin). 39

Figure 2.9 The gamma-ray and optical pulse profiles of the Vela pulsar (from (Kanbach et al. 1994 and Gouiffes 1998, respectively).

Figure 2.10 The near-infrared through X-ray spectrum of the Vela pulsar. The lines show the extrapolations of the PL to the optical spectrum and X-ray PL component (thermal component is fitted with the NS hydrogen atmosphere model; see Table 2.2 in §2.2.2). In the latter case 1σ uncertainties of the extrapolation are also shown by the dashed lines. 40

2.4 Chandra observations of the Vela PWN.

Since the first Chandra HRC observation, which revealed the complex and puz- zling structure of the Vela PWN (Pavlov 2000), the PWN has been imaged twice more with HRC-I and ten times with ACIS-S (see Table 2.4). These observations led to the discovery of variability of the PWN features (Pavlov, Kargaltsev, Sanwal & Garmire 2001; Kargaltsev et al. 2002) including the discovery of the extended north-western jet (the most dynamic PWN feature; Pavlov, Teter, Kargaltsev & Sanwal 2003; Kargaltsev et al. 2003). The combined ACIS images were used to produce the detailed spectral map of the PWN (Kargaltsev & Pavlov 2004). Below we describe the observations and discuss the published and new results in detail.

Table 2.4 Summary of Chandra observations of the Vela PWN.

Panel Obs ID Instrument Date of observation Exposure time (s) 1 1518 HRC-I 2000-01-20 49,765 2 364 HRC-I 2000-02-21 48,050 3 128 ACIS-S 2000-04-30 10,577 4 1987 ACIS-S 2000-11-30 18,851 5 2813 ACIS-S 2001-11-25 17,933 6 2814 ACIS-S 2001-11-27 19,870 7 2815 ACIS-S 2001-12-04 26,960 8 2816 ACIS-S 2001-12-11 18,995 9 2817 ACIS-S 2001-12-29 18,938 10 1966 HRC-I 2002-01-13 49,464 11 2818 ACIS-S 2002-01-28 18,663 12 2819 ACIS-S 2002-04-03 19,920 13 2820 ACIS-S 2002-08-06 19,503

2.4.1 Observations and data reduction. Ten observations of the Vela pulsar and its PWN were carried out with ACIS from 2000 April 30 through 2002 August 6 (see Table 2.4). In all the observations the target was imaged on the back-illuminated chip S3, less affected by the radiation-induced changes in CCD charge transfer efficiency than the front-illuminated chips. To ensure that the whole PWN is imaged on one chip, the pulsar was offset from the ACIS-S aim- point by −10.5 along the chip row in each observation. In the first two observations only half of the chip was read out (1/2 Subarray mode), with a frame time of 1.5 s, to reduce the pile-up for the bright pulsar. The rest of the observations were done in the Full Array mode, with a frame time of 3.24 s. The telescope focal plane temperature for all ACIS 41 observations was −120 C. We used the CIAO software12, v.2.2.1 (CALDB 2.10) for the data analysis, proceeding from Level 1 event files. The energy and grade of each event were corrected for charge transfer inefficiency (CTI) using the tool developed by Townsley et al. (2000). We then produced Level 2 files with the help of acis process events and applied the ASCA grade filter and Good Time Intervals (GTIs) supplied by the pipeline 13. An accurate alignment between the images taken in different observations is im- portant for assessing the variability of the inner PWN elements. First, we recomputed sky coordinates 14 in each observation to a common tangent point 15 of ObsID 2817 with the help of CIAO script reproject events. Applying the CIAO tool wavdetect to the individual images, we found 15 point-like sources on the S3 chip; 9 of them, including the Vela pulsar, we see in at least 4 images. The rms deviation of the Chandra pipe-line coordinates for 8 of the 9 sources is ≤ 000. 7, while for one off-axis source it is about 100. 4. This source is likely to be extended since the wavdetect algorithm finds two sources at this location in some of the images. Therefore, we exclude the suspicious source and conclude that the astrometry is better than 000. 7. The faintness of the background sources and their off-axis positions preclude accurate determination of the source positions by wavdetect and celldetect16, i.e. the accuracy of the positions for background sources in the individual images is comparable to the above rms error of 0.700. Moreover, we found no optical counterparts for the X-ray background sources. This hampered our attempts to improve the astrometry using the background sources. Instead we used the Vela pulsar itself to improve the alignment of the images. The pulsar is so bright that its image suffers from pile-up; as a result the source looks ring-shaped with a hole in the center (where pileup is the most severe). We modeled the distribution of pulsar counts in the piled-up image using a Gaussian multiplied by a hyperbolic tangent in radius, with a minimum at at r = 0.0. We fitted this function to the pulsar images in the eight latest ACIS observations that were carried out in the Full Array mode (Table 2.4) and used the resulting best-fit centroid coordinates to calculate the shifts that are needed to better align the images (the image from ObsID 2813 was chosen as a reference). We than applied the shifts (see Table 2.5) to the images (using the coordshift script17). The uncertainty of this procedure is limited by systematic effects (e.g. imperfect alignment of the mirrors) to about 000. 5 (Aldcroft et al. 2000), furthermore it does not correct for the misalignment completely if the images are rotated with respect to each other. Therefore, we conservatively conclude that the image alignment accuracy is better than 000. 5 near the pulsar position and better that 000. 7 further away from the pulsar (but still on the S3 chip). In addition to the ACIS observations, there were three imaging observations with Chandra HRC with the total exposure time of 147 ks (Table 2.4). In all the three

12Chandra Interactive Analysis of Observations — see http://cxc.harvard.edu/ciao/. 13http://cxc.harvard.edu/ciao/threads/createL2/ 14http://cxc.harvard.edu/ciao3.0/threads/ds9/ 15http://cxc.harvard.edu/ciao/threads/combine/ 16another CIAO tool 17http://www.astro.psu.edu/xray/acis/recipes/non www scripts/coordshift.pl 42

Table 2.5 Shifts applied to the ACIS images to improve their alignment.

Number Obs ID Date of observation Exposure time (s) X-shifta Y-shifta 1 2813 2001-11-25 17,933 0 0 2 2814 2001-11-27 19,870 0.15 0.10 3 2815 2001-12-04 26,960 0.15 0.32 4 2816 2001-12-11 18,995 0.06 0.48 5 2817 2001-12-29 18,938 0.41 0.52 6 2818 2002-01-28 18,663 0.44 0.78 7 2819 2002-04-03 19,920 −0.56 0.60 8 2820 2002-08-06 19,503 −0.99 0.61

a Shifts (in physical pixels) that have been applied to align the images as calculated by fitting the distributions of pulsar counts (see text)

observations the Vela PWN was imaged close to the center of the HRC-I (imaging) plate. Pipe-line processed Level 2 event files from the archive were used for the analysis, without further reduction.

2.4.2 Inner PWN: Structure (arcs, jets, knots). Variability. Spectra. Mod- els. The discovery of temporal variability in the Vela PWN was first reported by Pavlov, Kargaltsev, Sanwal & Garmire (2001) on the basis of the first two ACIS obser- vations carried out in 1/2 Subarray mode (ObsIDs 128 and 1987 in Table 2.4). Therefore, we first briefly describe these results, and then continue with the discussion of the results from the more recent ACIS observations carried out in the Full Array mode (Table 2.4). The images of the central part of the PWN are shown in the upper and lower pan- els of Figure 2.11 for the first and second observation, respectively. The white contours in the upper panel enclose PWN regions chosen for the comparison with the second observa- tion. The regions numbered 1 through 7 enclose well-defined bright features such as the outer arc (2a+2b) with a brightened spot (1) at its apex, NW jet (3), inner arc (4a+4b), SE jet (5), NE knot (6), and SW knot (7). In addition, to examine the variability in the diffuse emission, we define regions 8a and 8b. The white contours in the bottom panel are plotted at the same positions as those in the upper panel. A visual comparison of surface brightnesses within the white contours immediately shows substantial differences between the two images — e.g., the SW jet is brighter, the spot is dimmer, and the NE knot is invisible in the second image. Moreover, we see that some elements appear at different locations — the SW knot moved 200 westward, and the outer arc shifted by, on average, 200 north-west from the previous positions. Therefore, we defined new positions of six PWN elements in the second image with blue contours which enclose the same areas as (and are congruent to) the corresponding white contours. 43

2a 8a 4a 1

3 2b

6 5 4b

7

8b

2a 8a 4a 1

3 2b

6 5 4b

7

8b

Figure 2.11 ACIS-S images of a central part (5700 ×5500) of the Vela PWN of 2000 Apr 30 (top) and Nov 30 (bottom). The pixel size is 000. 492. The white contours in the top panel define the PWN elements in the first image. In the bottom panel, the white contours correspond to the contours in the top panel, while the blue contours demonstrate the displaced nebular elements in the second observation. The brightest spot is the piled-up Vela pulsar. 44

Figure 2.12 Surface brightness vs. hardness ratio h1.3 for different PWN regions for the two ACIS-S observations. For the second observation, the values for the regions 1–4 were calculated within the blue contours in the bottom panel of Fig. 2.11. (The differences would be even larger if exactly the same regions were used for the two observations.) 45

To quantify the changes in the surface brightness, we measured the numbers of counts per unit area per unit time within the white and blue contours for the first and second observations, respectively (see Fig. 2.12), and found that the changes are indeed quite significant for some elements — e.g., 32% ± 4% for the SE jet, −26% ± 2% for the spot, and −19% ± 2% for the outer arc (the uncertainties are 1σ statistical errors), while they are comparable with statistical fluctuations for the others (e.g., for the shifted inner arc). To visualize the spatial distribution of the brightness/morphology change, we scaled the images to the same exposure time (10,577 s), adaptively smoothed them with CIAO task csmooth, and subtracted the first image from the second one. The difference image (Fig. 2.13) clearly shows the displacements of the arcs and the SW knot, brightening of the SE jet, and dimming of the spot and the NE knot. It also shows some brightening (dimming) of the diffuse emission at the NE (SW) outskirts of the PWN and the large displacement, ≈ 800 toward SW, and shape variation of the filamentary structure18 in the upper right corner of the image (7500 NW from the pulsar). To evaluate systematic errors of the brightness changes, one should take into account that, although the pulsar was imaged at almost the same location on the chip in the two observations, the PWN regions are imaged on different sites because the roll angles were different (260◦.3 and 55◦.2). Since the CCD quantum efficiency varies over the chip19, this may lead to artificial changes of brightness. To examine this effect, we employed two sets of on-orbit calibration exposures (28 ks and 35 ks, at dates close to those of our observations), during which the ACIS chips were illuminated by on- board radioactive X-ray sources. For each of the calibration datasets, we measured the surface brightnesses of eight domains on the chip where four PWN elements (regions 1, 2b, 4a and 5) were imaged in the first and second observations of the Vela PWN. The differences of the brightnesses of the domains corresponding to the same PWN elements, both in the separate calibration datasets and between the two datasets, are about 2%– 3%, comparable to the statistical errors. This puts an upper limit of 3% on both spatial and temporal variability of quantum efficiency within the chip area (∼ 10 × 10) where the bright PWN elements were imaged. As an independent test, which additionally accounts for the effect of dither on the exposure times, we constructed exposure maps (e.g., Davis 2001) for the two PWN observations, for an energy of 1 keV close to the maxima of the count rate spectra. Inspection of these maps shows that the effective area varies by about 20% over the whole 80 ×40 field-of-view, but these large variations are associated with the boundaries between the four chip nodes. Since the PWN elements under investigation are all imaged within the same node 1, the variations are much smaller, ≈ 2%. Thus, the large, ∼ 20%–30%, brightness changes that were detected are not instrumental artifacts — they characterize real PWN variations. Comparison of the two observations allows one, in principle, to check whether the pulsar luminosity has changed in 7 months. A change of the luminosity could be caused by the strong glitch of 2000 January 16 because glitch effects can manifest themselves on time scales from weeks to years, depending on the depth where the energy release occurred. We measured the radial count distribution of the piled-up pulsar image and

18as it will become apparent from §2.4.3 the filament is the extension of the NW jet 19see http://asc.harvard.edu/ciao/wrkshp/esa1.pdf 46

Figure 2.13 The difference image (14200 × 14200) of the Vela PWN. The color scale is in counts ks−1 arcsec−2. The dashed rectangle corresponds to the size of images in Fig. 2.11. The blue and red structures within the 300. 5 circle at the center correspond to the “blob” in the pulsar image in the first and second observation, respectively (see text for details). The blue and yellow linear structures are the pulsar trailed images. 47 found that its very central part, within a 100 radius, became brighter by 30%±5%, whereas the brightness did not change at larger radii. In obvious contradiction with this result, the difference in the pulsar count rates, −8% ± 9%, estimated from the “trailed images” (one-dimensional images formed during the frame read-outs) is statistically insignificant. Since the trailed images do not suffer from the pile-up, we consider the latter result more reliable. The apparent variation of the central part of the pulsar image is likely caused by a small fluctuation of observing conditions (e.g., focal plane temperature), which may lead to a considerable change in the nonlinear regime associated with strong pile-up. It should also be mentioned that the piled-up images are very asymmetric. In particular, in both observations we see a “blob” of 000. 7 radius at a distance of 100. 5 from the center of ◦ the pulsar image, at an angle of about 22 from the Z+ axis of the spacecraft. The blob is most likely due to a tilt between the telescope mirrors in the innermost shell (Jerius et al. 2001). It can hardly be seen when there is no pile-up because it is much fainter than the core of the point source image, but it appears quite bright in a strongly piled-up image because the pile-up reduces the core brightness. In addition to the shifts and brightness changes, we have examined the spectral changes of the PWN elements. To characterize the spectra, we use the hardness ratio h1.3, defined as the ratio of counts above and below E = 1.3 keV. For the comparative analysis, this empirical quantity is more convenient than spectral fitting parameters because it does not depend on the spectral model, and does not suffer from uncertainties of the detector spectral response. We see some evidence of hardness changes, up to +29% ± 8% in the SE jet (see Fig. 2.12), but their statistical significance, < 3.6σ, is not as high as that of the brightness changes. This concludes the analysis of the first two ACIS observations of the Vela PW. Now, we will focus on the variability of the inner PWN elements as seen from the eight latest ACIS observations (see Table 2.4). We defer the discussion of the outer NW jet variability until §2.4.3. The definitions and notations of the inner PWN regions that are used below are the same as shown in Figure 2.11. Thorough inspection of the PWN images from these eight ACIS observations confirms that the inner PWN elements change with time both in brightness and shape (e.g., compare the upper and lower panels of Fig. 2.14). One can see that the morphology of the outer arc has changed noticeably, namely in the image of ObsID 2820 the arc became broader, more diffuse and bent on its SW side compared to the image from ObsID 2813 (region 2b in Fig. 2.11). The bright spot (region 1 in Fig. 2.11) located at the intersection of the NW jet and outer arc has grown in size and also become more diffused in ObsID 2820. The relative brightnesses of SE and NE jets (regions 3 and 5 in Fig. 2.11, respectively) and knots (regions 6 and 7 in Fig. 2.11) has also changed between these two observations. In fact, the bright spot is the most dynamic element of the inner PWN and it also shows a hint of spectral variability (see Fig. 2.15). Interestingly, for the bright spot the spectral and brightness changes seem to follow the evolutionary track shown by the arrows in Figure 2.15. We also produced similar plots for the other PWN elements which also show temporal changes in brightness (see Fig. 2.17). To characterize the variability of the inner PWN independently of the region definitions, we also produced difference images between the consecutive observations and images from ObsIDs 2820 and 2813 (Fig. 2.16). 48

Figure 2.14 ACIS images of the inner part of the Vela PWN from ObsID 2813 (top) and ObsID 2820 (bottom). Note structural/brightness changes for the outer arc, bright spot, jets and knots. 49

Figure 2.15 The plot of photon index versus surface brightness for the bright spot for each of the eight ACIS observations (ObsIDs 2813-1820). The arrows connect the subsequent observations starting with the 1st (marked by 1) and ending with the 8th (marked by 8). 50

Figure 2.16 Differences between the ACIS images taken during different visits demon- strating variability of the inner PWN. 51

NE Inner Arc (4a) SW Outer Arc (2b) 1.50 1.60

1 1.45 1.55 2 8 6 3 8 3 7 5 1.40 1.50 4 5 7 1

2 1.35 4 1.45

6

Photon index 1.30 Photon index 1.40

1.25 1.35

1.30 3.6 3.8 4.0 4.2 4.4 3.6 3.8 4.0 4.2 4.4 Surface brightness, (counts ks-1 arcs-2) Surface brightness, (counts ks-1 arcs-2)

NW jet (3) SE jet (5) 1.60 1.60

1.50 1.50

1 2 3 6 1.40 7 1.40 2

5 84 1.30 1.30 7 3 8 6 5

Photon index 1.20 Photon index 1.20

4 1.10 1 1.10

1.00 1.00 4.0 4.5 5.0 5.5 6.0 4.0 4.5 5.0 5.5 6.0 Surface brightness, (counts ks-1 arcs-2) Surface brightness, (counts ks-1 arcs-2)

Figure 2.17 The same as in Figure 2.15 but for the outer arc and inner jets. 52

From Figures 2.15, 2.17 and the images in 2.16, all spanning a period of 26 weeks, we see that the most noticeable changes in the morphology of the inner PWN occur on the time-scale of a month, i.e. much shorter than typical synchrotron −3/2 −1/2 cooling time tsyn = 39(B/100µG) (E/1 keV) years for the electrons responsible for X-ray emission in a plausible magnetic field (here E is the energy of synchrotron photon). This time-scale is comparable with the flow time from the pulsar to the bright 16 spot (distance of 7×10 d300 cm) if the flow speed assumed to be (0.3−0.7)c – such speeds have been measured for the blobs within the outer NW jet (see §2.4.3). The variability does not resemble steady motion (e.g., expansion with respect to some geometric center, or motion along some preferred direction) but rather appears as asymmetric distortions of shape (e.g., outer arc, bright spot) and changes in brightness (NW and SE jets, knots). The bright spot is the only element of the inner PWN that shows spectral variability at > 3σ significance possibly indicating that the spot is a distinct PWN feature which could be originating from the interaction between the NW jet and outer arc. This may occur if what appears as the outer arc is in fact an umbrella-like region (viewed from a side) comprised of pulsar wind plasma compressed due to the additional ram pressure in the direction of the pulsar’s proper motion. In this case the NW jet would be piercing through this “umbrella”. Such interaction could modify particle energy distribution within this presumably turbulent and unstable interaction region and explain the varying spectrum. This would also explain why the bright spot is the most variable feature of the inner PWN. The comparison of the ACIS observations shows that the Vela PWN is by no means static — we have detected considerable brightness changes and/or shifts of some PWN elements, which are possibly accompanied by spectral changes. The appearance and disappearance of the knots, deformations of the outer arc shape and brightness variations of the other PWN elements imply that the changes are more complicated than simple steady motion of plasma inhomogeneities (cf. moving blobs in the outer jet; §2.4.3). 53

2.4.3 The Outer Jets of the Vela pulsar. The large-scale X-ray structure of the Vela PWN is shown in the summed ACIS image of observations 2813–2820 in Figure 2.18. The NW outer jet (thereafter just outer jet which is clearly seen in the image) looks like an extension of the much brighter inner jet, well beyond the apparent termination point of the inner jet at its apparent intersection with the outer arc. Although much dimmer, the SE outer jet (thereafter outer counter-jet) is also clearly visible in the summed image. As we demonstrated in the previous section, the comparison of individual images shows that many of the inner PWN elements are variable, and so is the outer jet. Throughout this section, we will concentrate our analysis upon the dynamic outer jet, though the inner jet and counter-jet will be considered for comparison.

N 90''

E

Figure 2.18 The summed ACIS-S3 image of the Vela PWN (top) and its adaptively smoothed version (bottom). Total exposure time in the images is about 160 ks).

17 The outer jet extends away ≈ 0.14 d300 pc (4.3 × 10 d300 cm = 0.45 d300 lt- yr) from the pulsar, where d300 is the distance to the pulsar in units of 300 pc. The 16 characteristic width (diameter) of the outer jet is about 3 × 10 d300 cm. Because the outer jet is generally co-aligned with the inner jet, it is natural to assume that the inner and outer jets are connected at the intersection with the outer arc, although the dim 54 outer jet can hardly be seen within the shell. Figure 2.18 shows a typical view of the outer jet structure. It is not as straight as the inner jet; in the image it slightly bends southward from the inner jet/counter-jet direction near the end. Other individual images (Figs. 2.19 and 2.20) show different, sometimes more extreme, bending (e.g., panel 2 in Fig. 2.19 and panel 13 in Fig. 2.20). The average (background-subtracted) surface brightness of the outer jet in the ten ACIS images is about 0.05 counts arcsec−2 ks−1, in the 1–8 keV band, with extremes of variablilty from 0.032 ± 0.004 to 0.060 ± 0.003, in the same units (errors here and below are 1 σ errors). It is seen from Figure 2.18, that the outer jet brightness varies along its length. Choosing yet another brightness scale (Figs. 2.19 and 2.20), we resolve compact regions of enhanced emission within the outer jet (blobs, hereafter), with brightness up to 0.16±0.02 counts arcsec−2 ks−1, typically 2–3 times brighter than the remainder of the outer jet. In turn, the outer jet is approximately 3 times brighter than the background on the northeast side of the jet, with brightness 0.021 ± 0.002 counts arcsec−2 ks−1. The background on the southwest side of the outer jet is about 50% brighter than that on the northeast side. This difference is quite clearly seen from Figure 2.18, which also shows that the increased background is connected to a region of enhanced diffuse emission on the southwest side of the bright PWN. The average surface brightnesses of the inner jet and counter-jet are 1.5 and 1.8 counts arcsec−2 ks−1, respectively, ranging from 1.1 to 1.9 for the inner jet and from 1.3 to 2.8 for the counter-jet, with typical errors of 0.2 counts arcsec−2 ks−1. The background-subtracted surface brightness of the outer counter-jet is ≈ 0.007 counts arcsec−2 ks−1, as measured from the summed image in Figure 2.18.

2.4.3.1 Spatial variation Figures 2.19 and 2.20 give the time sequence of the ACIS-S3 and HRC-I obser- vations for the outer jet. Each of the panels corresponds to the data set from Table 2.4. The variability of the outer jet is clearly seen, in both the HRC and ACIS images. Over the thirteen observations, with different periods of time between each of them, we distinguish three different types of variability in the outer jet. First, the outer jet shifts from side to side, bending and apparently twisting. Second, the blobs move outward along the outer jet. Finally, the blobs change in brightness and eventually disappear. A very vivid example of the structural change in just one month is demonstrated by the first two Chandra HRC observations (panels 1 and 2 of Fig. 2.19). In panel 1, the outer jet looks like a “hook” attached to the bright spot on the outer arc, with the outer end of the hook pointing due north and terminating at an elongated blob. In panel 2, the hook evolved into a much more bent loop-like structure, which terminates with apparently the same (albeit fainter) blob at approximately the same location. The structure has moved between two observations, indicating that the sideways shift (e.g., from point P in panel 1 to point Q of panel 2) is approximately 1200 in the 32 days separating the observations. This translates to a sideways speed of 0.6 c (all the speeds in this section are given for d = 300 pc). Another example is presented by the first two ACIS images (panels 3 and 4) separated by 7 months. The shape of the outer jet has changed from pointing due north and terminating with a blob to an S-shaped structure. The displacement of the blob (which easily could be another blob given that the time 55

Figure 2.19 Images of the outer jet from the observations of year 2000. The HRC-I and ACIS-S3 images are in blue and orange, respectively. The panels are numbered in accordance with Table 2.5. The size of each panels is 7300 × 5300. The boxes, 2800 × 200. 6, at same sky position in all the panels, are overplotted to guide the eye. The points P and Q mark westward extremes of the bent jet in the two HRC observations; they were used to estimate the jet’s motion between the two observations (see text for details). 56

Figure 2.20 Sequence of Chandra images of the outer jet observed in 2001–2002. The 7300 by 5300 panels are numbered according to Table 2.5. The letters A, B, and C label the moving bright blobs identified in observations 5 through 11. The boxes, 2800 ×200. 6, at same sky position in all the panels, were used to demonstrate the jet’s sideways motions (see Fig. 2.21). 57 between the observations is so long) suggests a speed ∼> 0.1c. In observations 5–11 (Fig. 2.20) the jet appears almost straight, with a slight southward curve. The short time (16 days) between the fifth and eighth observations suggests that the sideways shifts of the jet occur on a time scale of order of weeks. A dramatic change of the jet shape is again seen in the last observation 13, separated by 4 months from the previous observation. In the last image, the jet points due west beyond the PWN shell and then abruptly turns to the north, with a bright blob at the turning point. Overall, the small- scale structural changes are seen in all of the observations. For instance, the “base” of the outer jet (where it leaves the shell — see the white boxes in Figs. 2.19 and 2.20) shifts from one observation to the next. Figure 2.21 shows smoothed one-dimensional distributions of counts across the outer jet (i.e., along the length of the narrow boxes in Fig. 2.20) in eight consecutive ACIS observations. Typical apparent speeds of these shifts are of order a few tenths of speed of light. The apparent speeds of the blobs along the jet are of similar magnitude. The proper motions of the blobs A and B seen in several panels of Figure 2.20 are shown in Figures 2.22 and 2.23. The 100 uncertainty of the position of the blobs is obtained by adding in quadrature the 000. 7 uncertainty from the astrometry and an additional uncertainty, of approximately the same value, from measuring the centroid of the blob from the smoothed images. Blob B vanishes in panel 9, so its apparent speed is calculated from four observations. The apparent speeds of blobs A and B are (0.35 ± 0.06) c and (0.51±0.16) c, respectively. Blob C vanished quickly, having an (unconstrained) apparent speed of (0.6 ± 0.7) c. Assuming that the measurements of the apparent velocities of the blobs inside the outer jet give the bulk flow speed, vflow ∼ (0.3–0.7) c, and the jet does not deviate strongly from the sky plane, we obtain tflow = ljet/vflow ∼ (0.6–1.5) yr for the travel time along the jet. The actual travel time may be significantly different if the jet direction strongly deviates from the sky plane and relativistic effects are important (see §2.4.3.3). The blobs change brightness as they move and disappear. For instance, blob C slightly brightens in two days between observations 5 and 6, then fades somewhat between observations 6 and 7, and disappears completely after another week (by observation 8). Similarly, the brightness of blob B changes noticeably through observations 5–8, while this blob vanishes in observation 9. No such blobs are found in either the inner jet or the counter-jet.

2.4.3.2 Spectrum and luminosity For the spectral analysis of the jets in the ACIS data, we used the XSPEC package, 20 v.11.2.01. In all spectral fits we used the hydrogen column density fixed at nH = 3.2×10 cm−2, as determined from the observation of the Vela pulsar with the Chandra Low- Energy Transmission Grating Spectrometer (Pavlov et al. 2001b). Furthermore, because of a build up of a contaminant on either the ACIS CCDs or the filters, additional time- dependent absorption is accounted for in the spectral fits using the ACIS ABS model (see Plucinsky et al. 2002). The degree of absorption was set by the number of days since Chandra launch. Only photons in the energy range of 1–8 keV were used for fitting to 58

Figure 2.21 Smoothed distributions of counts across the outer jet at a distance of 5000 from the pulsar in eight ACIS observations (ObsID 2813–2820). The number of counts (per arcsecond) integrated along the short dimension of the boxes in Figure 2.20 is plotted as a function of coordinate φ along the box length. 59

Figure 2.22 Proper motion of blob A in panels 5–11 of Figure 2.20. The upper and lower panels show the motions along the right ascension and declination, respectively. The straight lines are the least-square fits assuming constant speeds. Under this assumption, the apparent speed of blob A is (0.35 ± 0.06) d300 c. 60

Figure 2.23 Proper motion of blob B in panels 5–8 of Figure 2.20. The apparent speed of blob B is (0.51 ± 0.16) d300 c. 61 avoid contaminations from readout strips from the piled-up pulsar and to reduce the charged particle background.

Figure 2.24 Power-law fit to the spectrum of the outer jet for the merged data set (observations 2813–2816). The best-fit parameters are Γ = 1.29 ± 0.06, and NΓ = −5 −2 −1 −1 2 3.90 ± 0.40 × 10 photons cm s keV at 1 keV (χν = 0.98, for 68 dof).

The photons from the outer jet were extracted using polygons (of somewhat dif- ferent areas for the different observations — see Table 2.6) which enclosed the entire structures beyond the PWN shell. Two background regions were chosen — the first from a dark region north of the outer jet (background A), and the second sandwiching the outer jet (background B). Various spectral models for emission from an optically thin thermal plasma were attempted to test if the emission associated with the outer jet is due to an interaction of the jet with the ambient (SNR) gas. The overall fits are formally acceptable, but the corresponding plasma temperatures, about 30 keV, are very high, in accordance with the lack of spectral lines in the spectra. At such high temper- atures these models are equivalent to the thermal bremsstrahlung model, which, with the statistics available, is indistinguishable from a power-law at energies of interest. The −Γ power-law model, f(E) = NΓ (E/1 keV) , is more physical than the high-temperature bremsstrahlung because it naturally describes non-thermal (e.g., synchrotron) radiation; therefore, we use it for the spectral analysis of the jets. An example of the power-law fit to a data set combined of observations 2813– 2816, chosen because of the similar extraction areas and locations on the chip, is shown 62

Figure 2.25 One-sigma confidence contours for photon index Γ and spectral surface brightness at 1 keV, B = NΓ/A, for 10 ACIS observations of the outer jet using back- ground A (left panels) and background B (right panels). The contours are separated into the upper and lower panels for clarity of presentation. 63 in Figure 2.24, for background B. The results of the fits of the outer jet spectra with the power-law model for each of the individual ACIS observations are given in Table 2.6, for both backgrounds A and B. Figure 2.25 shows the contours of the photon index Γ versus spectral brightness at 1 keV, B = NΓ/A (where A is the area of the extraction region — see Table 2.6). For each of the two backgrounds, the variability of the photon index is statistically insignificant, contrary to the variability of the brightness. Joint spectral fits (fitting all data simultaneously with a common index and individual normalizations) give Γ = 1.36 ± 0.04 and 1.27 ± 0.04 for backgrounds A and B, respectively, coinciding with the weighted average indices that are calculated from the individual fits for each of the two backgrounds. The difference between the average indices can be ascribed to systematic effects associated with the choice of background. Since it is not immediately clear which of the two backgrounds is more adequate, we adopt a conservative estimate, Γ = 1.3 ± 0.1, consistent with both background choices. We searched for a change in power-law index along the length of the outer jet by extracting regions near the beginning of the outer jet, where it exits the shell of the bright PWN, and at its end. Because of the low number of counts, a joint fit of all the ACIS observations was attempted. The normalizations for each observation were allowed to vary (because the extraction areas were different), while the photon index for all observations was fit to a common value. The fits to these combined spectra were 2 2 statistically acceptable, with χν=1.19 (82 degrees of freedom [dof]) and χν = 0.97 (96 dof) for the beginning and the end of the outer jet, respectively (using background B). The change of the index, from 1.36 ± 0.09 at the jet beginning to 1.25 ± 0.08 near its end, is not statistically significant. We also attempted to compare the spectra of the blobs with each other and with the spectrum of the rest of the outer jet. For individual observations, no differences are seen because of the low number of counts. Combined fits, using background B, yield 2 the photon indices 1.36 ± 0.12 (χν=1.01, 70 dof) for blob A (observations 2813–2818), 2 1.07 ± 0.19 (χν=0.47, 20 dof) for blob B (observations 2813–2816), and 1.43 ± 0.21 2 (χν=1.27, 18 dof) for blob C (observations 2813–2815). Thus, the spectral slopes do not show statistically significant differences even for the combined fits. For the inner jet and inner counter-jet, we extracted the source counts from stretched elliptical areas of 12.7 and 18.5 arcsec2, respectively, which enclose as much of the jet/counter-jet emission as possible without contamination from the other structures within the PWN, such as the arcs. Because of the very nonuniform distribution of surface brightness around the inner jet and counter-jet, we had to take backgrounds from small regions; we chose circles (6.8 and 10.6 arcsec2 for the inner jet and inner counter-jet, respectively) in the immediate vicinities northeast and southwest of the source extraction regions. The average values of the photon index for the inner jet and inner counter-jet, Γ = 1.09 and 1.20, respectively, appear somewhat smaller than that for the outer jet. However, the photon indices measured in individual observations show large deviations from the average values (rms deviations are 0.24 and 0.10, respectively), likely associated with statistical fluctuations of the bright background estimated from small regions. Therefore, we cannot firmly establish the spectral differences between the outer jet and its inner counterparts from the data available. 64 photons 5 − dof 2 ν χ 0.4 0.620.4 1.44 13 0.3 1.01 26 0.3 0.81 28 0.3 0.87 31 0.4 1.02 41 0.3 1.04 30 0.3 1.02 27 0.3 0.85 26 0.3 1.05 38 27 B , is in units of 10 ± ± ± ± ± ± ± ± ± ± S Γ N 0.7 3.2 0.4 5.1 0.5 5.6 0.4 5.6 0.4 6.0 0.4 5.5 0.4 5.5 0.4 4.5 0.5 4.5 0.5 3.9 Γ ± ± ± ± ± ± ± ± ± ± N , in the 1–8 keV range. 1 − ks 2 0.27 3.0 0.15 2.7 0.13 4.0 0.13 3.8 0.10 3.8 0.11 3.6 0.14 2.8 0.15 3.7 0.13 4.6 0.15 4.1 − Γ ± ± ± ± ± ± ± ± ± ± 1.23 1.19 1.30 1.27 1.28 1.23 1.12 1.45 1.27 1.46 counts arcsec dof 2 − 2 ν χ . Normalization of the power-law spectrum, 2 0.3 0.92 27 0.2 0.87 38 0.3 1.01 26 0.3 1.02 27 0.4 0.94 30 0.3 0.82 41 0.3 0.79 31 0.3 0.91 28 0.3 1.38 26 0.4 0.71 13 B ± ± ± ± ± ± ± ± ± ± S , is in units of 10 B S 0.5 5.0 0.5 4.7 0.4 3.6 0.4 5.0 0.4 7.3 0.3 6.5 0.4 7.0 0.5 6.7 0.4 5.7 0.7 4.4 Γ ± ± ± ± ± ± ± ± ± ± N Background A Background B 0.10 5.1 0.10 5.9 0.13 4.0 0.13 3.6 0.10 4.3 0.09 4.7 0.11 4.7 0.11 5.1 0.12 3.8 0.20 4.7 Γ ± ± ± ± ± ± ± ± ± ± 1.38 1.37 1.45 1.28 1.29 1.35 1.37 1.41 1.32 1.38 at 1 keV. Mean surface brightness, 1 − ObsID Area 01281987 500 2813 400 2814 449 2815 449 2816 413 2817 455 2818 393 2819 480 2820 656 614 keV 1 − s 2 − Table 2.6 Spectral parameters and surface brightnesses for the ACIS observations of the the outer jet. Area is the polygon extraction area of the outer jet in arcsec cm 65

As the outer counter-jet is hardly seen in the individual images, its spectrum was measured in the joint fit using observations 2813–2820. The source counts were extracted from a polygon area of 336 arcsec2. Because of the faintness of the outer counter-jet, the fit is rather sensitive to the choice of background. Taking background from a region northeast of the end of the outer counter-jet, we obtain the photon index Γ ≈ 1.5, while the index is smaller, Γ ≈ 1.2, for the background from a region which sandwiches the outer counter-jet. Thus, the spectrum of the outer counter-jet remains poorly constrained, its slope being indistinguishable from that of the outer jet, within the uncertainties. Assuming isotropic radiation, the average (unabsorbed) luminosities of the inner jet, inner counter-jet, and outer counter-jet, in the 1–8 keV band, are 2.6, 4.5 and 0.5 ×1030 erg s−1, respectively, for d = 300 pc. The average luminosities are computed from the average spectral parameters of the various components. The outer jet demonstrates some variability in luminosity. For background A, the extremes of the luminosity are 2.7±0.3 and 4.4±0.4 ×1030 erg s−1, with an average of 3.4×1030 erg s−1. For background B, the outer jet luminosity varies from 2.4±0.3 to 3.8±0.4 ×1030 erg s−1, with an average of 3.0 × 1030 erg s−1. For comparison, the luminosity of the whole PWN within 4200 of 32 −1 the pulsar is Lpwn = 6.0 × 10 erg s , in the same energy band.

2.4.3.3 Geometry The detected variability of the outer jet is the most vivid demonstration of the dynamical behavior of the Vela PWN. The observed changes of the overall shape of the outer jet over a time scale of weeks suggest apparent speeds up to (0.3–0.7)d300 c, which is comparable to the apparent speeds of the blobs moving along the outer jet away from the pulsar. The spectra of the outer jet, as well as those of the other PWN elements, fit well with a power-law model, indicating that this is radiation from ultrarelativistic particles. These observations allow one to assume that the outer jet is associated with a polar outflow of relativistic particles from the pulsar’s magnetosphere20. The orientation of the jets is the most important item for explaining the observed dynamical behavior, evaluating the velocities, and calculating the energetics of these outflows. Immediately after the first Chandra observations of the Vela PWN, it was suggested that the bright (inner) jet and counter-jet are co-aligned with the rotational axis of the pulsar and, presumably, with the direction of pulsar’s velocity (Pavlov et al. 2000; Helfand et al. 2001). As we have seen from Figures 2.19 and 2.20, the projection of the outer jet on the sky plane may strongly deviate from the (straight) extension of the projection of the inner jet/counter-jet. However, the outer jet projection was close to that line during the period of 2001 November 25 through 2002 January 13, when the apparent velocities of the bright blobs were measured. Assuming, by analogy with the jets in AGNs and Galactic microquasars, that the apparent motion of blobs is associated with motion of matter along an approximately straight line (e.g., the three- dimensional velocities of the blobs coincide with the bulk flow velocity), one can constrain

20An alternative interpretation –that the “outer jet” is a limb-brightened shell (northeast boundary) of a large diffuse nebula southwest of the pulsar (see Fig. 2.18) or a shock front– looks very unlikely, given the observed variations of its shape and, particularly, the moving blobs. 66

Figure 2.26 True speed β = v/c versus angle θ between the line of sight and direction of motion for three values of the apparent speed βa = va/c. The dashed lines (β cos θ = 0.20 and 0.33) bracket the domain of allowed β,θ assuming intrinsically similar outer jet and outer counter-jet streaming in opposite directions. See text for details. 67 the true speed, v = βc, and the angle θ between the line of sight and the direction of motion. The apparent speed, va = βac, is related to the true speed by the equation −1 βa = β sin θ (1 − β cos θ) . Figure 2.26 shows the dependence β(θ) for typical βa inferred from the observed motions of the blobs. For 0.3 < βa < 0.7, the blobs can be approaching (θ < 90◦) as well as receding (θ > 90◦). The range of minimum values of ◦ ◦ β is 0.28 < βmin < 0.57 (at 73 > θ > 55 ), while the range of maximum allowed θ (at ◦ ◦ ◦ which β → 1), is 147 > θmax > 110 . The latter values are smaller than the θ = 155 , inferred by Helfand et al. (2001) under the assumption that the PWN arcs are Dopler- brightened parts of a torus around the jet/counter-jet, and they are smaller then the θ = 152◦ suggested by Pavlov (2000)21 assuming the arcs are Doppler-brightened parts of ring-like shocks in relativistic conical outflows. If we adopt, e.g., θ = 155◦, then the maximum possible apparent speed (at β → 1) is 0.22 c, which is below the lower limits of 0.30 c and 0.38 c on the apparent speeds of blobs A and B at d = 300 pc. Thus, if any of the above-mentioned interpretations of the arcs and the inner jet/counter-jet are correct, we have to conclude that the outer jet is tilted from the pulsar rotation axis towards the observer even if its projection onto the sky looks almost straight, like in panels 5–9 of Figure 2.20. Moreover, we cannot rule out the possibility that the outer jet in these observations is strongly bent in the plane perpendicular to the sky plane — e.g., similar to the jet’s sky projections in panels 1, 2 or 13. In this case the directions of the local flow velocities vary along the jet, which might explain the different apparent velocities of the blobs A and B. Such bending opens up a possibility that the bright regions of the jet are merely due to the projection effect — the segments of a uniformly bright, bent jet, which are oriented along the line of sight, appear brighter because of the increased optical depth, and the brightness is further enhanced by the Doppler boosting if the flow in these segments is streaming toward the observer. For instance, if the loop-like jet in panel 2 of Figure 2.19 were a two-dimensional structure, the southern segment of the loop would look like a bright blob if it were observed from the southwest direction. If this interpretation is correct, then the observed motions are caused by changing geometrical shape of the jet rather than the flow of locally bright material along the jet. An argument against such an interpretation is that the outer jet apparently terminates with a bright blob in at least 10 of 13 observations, and it is hard to believe that the end segment of a randomly bent jet is so often directed toward the observer. However, the extension of the jet beyond these bright blobs, as seen in the summed image of Figure 2.18 (see also §2.4.3.5), suggests that this may still be the case. Another interesting fact related to the jet geometry is that the outer jet is consis- tently brighter than the outer counter-jet, with the ratio of surface brightnesses fb = 4–9 (the large uncertainty in the brightness ratio is due to the nonuniform backgrounds). If the two jets are energetically similar and, on average, are oriented along a straight line, then the outer jet is approaching while the outer counter-jet is receding, contrary to the receding inner jet and approaching inner counter-jet in the geometry assumed by Pavlov et al. (2000) and Helfand et al. (2001). Within this interpretation, the bright- Γ+2 ness ratio is fb = [(1 + β cos θ)/(1 − β cos θ)] , where Γ is the photon index. For ◦ ◦ fb = 4–9 and Γ = 1.2–1.4, it gives β cos θ = 0.20–0.33, θ < 71 –78 . Furthermore, these

21see also http://online.itp.ucsb.edu/online/neustars c00/pavlov/oh/34.html 68

Figure 2.27 Smoothed ROSAT HRI image (50.7 × 30.8) of the Vela PWN from the obser- vation of November of 1997 (exposure 33 ks). The blob to the northwest of the PWN is indication that the outer jet has persisted at least 5 years.

values of β cos θ are consistent with βa = 0.3–0.7, inferred from the blob’s motion, if 0.31 < β < 0.59 and 31◦ < θ < 70◦ (see Fig. 2.26). To reconcile this result with the previously suggested orientation of the inner jets, one has to assume that the outer jet is tilted by a large angle (≈ 90◦–100◦) from the inner jet direction towards the observer, while the outer counter-jet is tilted by a similar angle away from the observer. Contrary to the observed variable bendings of the outer jet, such tilts would have persisted for at least 5 years, since we confirm the existence of the brighter outer jet as far back as the 1997 ROSAT HRI observation (Fig. 2.27). It is not clear what could cause such persistent tilts. Furthermore, it not clear why the outer jet and counter-jet are so much dimmer than their inner counterparts, and what causes the abrupt decrease of brightness in the outer jet and counter-jet, with bright knots at the junctions of the inner and outer parts. In particular, the transition from the inner jet to the outer jet apparently occurs at the intersection of the jet with the outer arc, which hints that the outer arc is not a part of a ring-like structure but an umbrella-like shell pierced by the jet (Kargaltsev et al. 2002; see also §2.4.2). Such a shell could be a bow shock created by the (inner) jet in the ambient medium, or it could form as a result of compression of the plasma outflow (hence, amplification of the frozen-in magnetic field) by the pulsar’s motion in the am- bient SNR matter (similar to that suggested by Aschenbach & Brinkmann 1975 for the Crab PWN). Another possible effect of the pulsar’s motion is distortion of the ring-like structure(s) (e.g., the post-shock region presumably associated with the inner arc) by the ram pressure of the ambient matter, if the pulsar’s rotational axis is not co-aligned with its velocity. In this case the leading part of the ring can be flattened by the ram pressure so that the assumption that the ring’s sky projection is a perfect ellipse can result in wrong values for the inclination angles. Finally, one could consider a possibility that the structures appearing as the bright inner jet and counter-jet are, in fact, merely 69 traces of particle beams in conical outflows brightened by the Doppler boosting (e.g., Radhakrishnan & Deshpande 2001; Pavlov 2000), while the outer jet and counter-jet are the “true pulsar jets”. Such an assumption would imply a quite different interpretation of the whole PWN and will not be discussed here. Currently, we cannot unambiguously determine the orientation of the jets or the true velocities. However, from the observed variations of the shape of the outer jet, with mildly relativistic apparent velocities, we can conclude that the true velocities are neither ultrarelativistic nor nonrelativistic; 0.3 c and 0.7 c can be adopted as conservative lower and upper limits.

2.4.3.4 Magnetic field and energetics The power-law spectra of the outer jet and the other PWN elements can be interpreted as optically thin synchrotron emission from ultrarelativistic electrons (and/or −p 2 positrons) with a power-law spectrum: dN(γ) = Kγ dγ, where γ = ε/mec is the Lorentz factor, γm < γ < γM. The electron index p is related to the photon index as p = 2Γ − 1, i.e., p = 1.4–1.8 for Γ ' 1.2–1.4 observed in the outer jet. A characteristic 2 energy E of the synchrotron photon depends on γ and magnetic field B as E ∼ 5 B−4γ8 −4 8 keV, where B−4 = B/(10 G), γ8 = γ/10 . If the minimum and maximum energies of the photon power-law spectrum are Em and EM, respectively, then the corresponding 7 1/2 −1/2 boundaries of the electron power-law spectrum are γm ≈ 2.4 × 10 [Em/(ym,pδ)] B−4 7 1/2 −1/2 and γM ≈ 2.4 × 10 [(EM/(yM,pδ)] B−4 , where the photon energies are in units of keV, δ = (1 − β2)1/2(1 − β cos θ)−1 is the Doppler factor (β c is the speed of the bulk motion), and ym,p and yM,p are dimensionless factors. The values of these factors are given in Table II of Ginzburg & Syrovatskii (1965; GS65 hereafter); e.g., ym,p = 1.3 and 1.8, yM,p = 0.011 and 0.032, for p = 1.5 and 2.0, respectively. We will use the well-known formulae for synchrotron radiation to estimate the magnetic field and energetics of the outer jet. Since the bulk motions observed in the jet are only mildly relativistic (β ∼ 0.5 is a plausible estimate), the Doppler factor is not strongly different from unity; moreover, its actual value is unknown because of the uncertain orientation of the jet. Therefore, we will neglect the bulk motion of the jet’s matter for most of the estimates below. From the Chandra ACIS observations, the power-law spectrum of the outer jet is seen in the energy range between E1 ≈ 0.5 keV and E2 ≈ 8 keV. Since Em < E1 and EM > E2, we can constrain the minimum and maximum energies of the electron 7 −1/2 8 −1/2 power-law distribution: γm < 1.4 × 10 B−4 , γM > 5 × 10 B−4 . One can put a lower limit on the magnetic field in the outer jet using the condition that the Larmor radius of most energetic electrons responsible for the X-ray emission, 15 −1 15 1/2 −3/2 rL = 1.7 × 10 γ8B−4 cm ∼> 6 × 10 (E2/8 keV) B−4 cm, does not exceed the jet 16 1/3 −2/3 radius, rjet ≈ 1.5 × 10 d300 cm. This condition gives B ∼> 60 (E2/8 keV) d300 µG. An upper limit on the magnetic field can be estimated from the fact that the spectrum of the outer jet maintains its power-law shape (shows no appreciable spectral break) at the observed energies E ∼< 8 keV up to the end of the outer jet. This means 8 −1 −2 that the time of synchrotron losses, tsyn = 5.1 × 10 γ8 B−4 s, for the most energetic −1/2 1/2 particles responsible for the observed X-ray spectrum [γ8 ∼> 4 B−4 (E2/8 keV) ] is 7 −1 longer (or comparable to) the flow time, tflow = ljet/vflow ≈ 6.7 × 10 ljet,18(β/0.5) s, 70

18 −1/3 2/3 −2/3 where ljet = 10 ljet,18 cm. This gives B ∼< 150 (E2/8 keV) (β/0.5) ljet,18 µG, i.e., B ∼< 100–300 µG for plausible values of ljet and β. An independent estimate on the plasma parameters for the outer jet can be ob- tained from the brightness of the synchrotron radiation, assuming some value for the 2 ratio km = wmag/wrel of the magneic energy density, wmag = B /(8π), to the energy density of relativistic particles, wrel. We cannot exclude the possibility that there are some relativistic ions in the jet, in addition to the synchrotron-emitting electrons (e.g., Gallant & Arons 1994), so that wrel = (1+ki)we, where ki is the ratio of the energy den- sity of ions to the energy density of electrons, we. Making use of the standard formulae for synchrotron radiation (e.g., GS65; Pacholczyk 1970), one can express the magnetic field in terms of the observable parameters. For a tangled magnetic field (randomly distributed along the line of sight), we obtain

½ h i ¾2/7 km(1 + ki) (3−2Γ)/2 (3−2Γ)/2 B−7 B = 27 EM,p − Em,p µG , (2.5) ap(3 − 2Γ) s¯16

−7 2 2 −1 where B = NΓ/A = 10 B−7 photons (s cm keV arcsec ) is the average spectral sur- face brightness at E = 1 keV, NΓ is the normalization of the photon spectral flux 16 measured in area A,s ¯ = 10 s¯16 cm is an average length of the radiating region along the line of sight, Em,p = Em/ym,p, EM,p = EM/yM,p, Em and EM are the lower and upper energies of the photon power-law spectrum (in keV), and ap is a numerical coefficient given by eq. (3.32) and Table II of GS65 (e.g., ap = 0.165 and 0.117 for p = 1.4 and 1.8 [Γ = 1.2 and 1.4], respectively). The value of B depends on several unknown parameters. Particularly uncertain are the boundary energies of the photon power-law spectrum be- cause of the lack of high-resolution observations outside the X-ray range. Fortunately, (3−2Γ)/7 1.5−Γ 1.5−Γ the dependence on these energies is rather weak: B ∝ EM for Em,p ¿ EM,p 2/7 (which implies Γ < 1.5), and B ∝ [ln(56EM/Em)] , for Γ ' 1.5. For B−7 ' 1 (a typical spectral surface brightness at 1 keV — see Fig. 2.25),s ¯16 ≈ 2–10 (the main reason of the uncertainty is the unknown spatial structure and orientation of the jet), and Γ = 1.2–1.4, −2/7 we obtain 30 µG ∼< B[km(1 + ki)] ∼< 200 µG, for plausible ranges of EM and Em. It is usually assumed that km ≈ 1 (equipartition condition), while the value of ki is rather uncertain. For the lower limit on the equipartition field not to exceed the upper limit 3 estimated from (the lack of) synchrotron cooling, ki should not exceed ∼ 10 . Thus, given the uncertainty of the parameters, we can only state that the equipartion field is consistent with the above-estimated limits, and that a plausible estimate for a typical field in the jet is B ∼ 100 µG, with an uncertainty of a factor of 3. It should be noted that the local field values can differ from the average field. For instance, if the brightness of the blobs is due to an increased magnetic field, at fixeds ¯, then the field in the blobs is a factor of 1.4 higher than the average field in the jet. On the other hand, the higher brightness can be explained by the projection effect (largers ¯) and the Doppler boost (¯s → s¯ δ2+Γ in eq. 2.5 if the bulk motion is taken into account). 2 −10 2 −3 Assuming equipartition, wrel = B /(8π) = 4 × 10 B−4 erg cm , we can 41 2 estimate the total energy of relativistic particles, Wrel = 4 × 10 B−4 V51 erg, where 51 3 V = 10 V51 cm is the volume of the jet. For plausible values of the magnetic field 71 and the volume (V51 ∼ 0.2–1, depending on the shape and orientation of the jet), we 40 42 obtain Wrel ∼ 10 –10 erg. The energy injection rate and the energy flux can be ˙ 33 2 16 2 −1 estimated as W ∼ 2Wrel/tflow ≈ 8 × 10 B−4(rjet/1.5 × 10 cm) (β/0.5) erg s and ˙ 2 2 −2 −1 FW = W/(πrjet) ≈ 10 B−4(β/0.5) erg cm s , respectively, where rjet is the jet radius, and βc is the flow speed. This injection rate is a small fraction of the spin-down energy loss rate of the Vela pulsar, W˙ ∼ 10−3E˙ . On the other hand, it greatly exceeds the −3 ˙ observed X-ray luminosity of the jet, Lx,jet ∼ 10 W , which means that most of the injected energy is emitted outside the X-ray range or, more probably, carried out of the jet without substantial radiation losses. ˙ ˙ One can also estimate the electron (positron) injection rate, Ne,jet = W [2(1 + 2 −1 2−p 2−p 1−p 1−p −1 ki)mec γ¯] , whereγ ¯ = [(p − 1)(γM − γm )][(2 − p)[(γm − γM )] is the average electron Lorentz factor for the power-law distribution. For the mean observed Γ ' 1.3, 0.4 0.6 0.4 0.4 we haveγ ¯ ≈ 1.5 γM γm if γm ¿ γM . Unfortunately, the minimum and maximum electron energies cannot be determined without multiwavelength observations of the jet, therefore we will scaleγ ¯ to a possible (but arbitrary) value of 108, which gives ˙ 31 −1 −1 −1 Ne,jet ≈ 5 × 10 γ¯8 (1 + ki) s . This estimate corresponds to the mean electron −1 2 −1 −12 2 −1 −1 −3 number density ne,jet ∼ wmag(1 + ki) (mec γ¯) ∼ 5 × 10 B−4(1 + ki) γ¯8 cm . ˙ The numerical estimates for Ne,jet and ne,jet strongly depend on the boundary energies of the electron power-law spectrum; in particular, the estimates become 3 orders of 3 magnitude larger if γm is low enough (∼ 10 ) for the jet to be synchrotron-emitting in the radio band. ˙ It is interesting to compare the estimate for Ne,jet with the pair production rate ex- ˙ 2 3 2 3 2 −1 pected for the Vela pulsar: Ne,puls ∼ nGJ(4π R /P )κpair = 4π R Bpuls(ceP ) κpair ' 33 −1 6 1.2 × 10 κpair s , where nGJ is the Goldreich-Julian density, R ≈ 10 cm and P = 12 0.089 s are the neutron star radius and spin period, Bpuls = 3.4 × 10 G is the pul- sar magnetic field, and κpair is the pair multiplication coefficient (its plausible value 3 ˙ ˙ is κpair ∼ 10 — see, e.g., Hibschman & Arons 2001). The ratio Ne,jet/Ne,puls ∼ −5 3 −1 −1 4 × 10 (κpair/10 )¯γ8 (1 + ki) can be interpreted as the fraction of pairs escaping from the pulsar through the outer jet, assuming that no pairs are created in the jet itself. It is worth noting that the maximum Lorentz factor for the pairs created in the pulsar magnetosphere does not exceed a few ×107, for both the polar cap models (Hard- ing, Muslimov, & Zhang 2002, and references therein) and the outer gap models (e.g., 8 Zhang & Cheng 1997). The maximum Lorentz factor in the outer jet, γM > 5 × 10 , is substantially higher, which means that the pairs, created by the pulsar, have been additionally accelerated beyond the pulsar magnetosphere. If ions are pulled out of the neutron star surface layers, their outflow rate is ˙ ˙ −1 33 −1 constrained to the Goldreich-Julian value: Ni,puls ∼ Ne,puls(Zκpair) ' 1.2 × 10 Z s−1, while their characteristic energy may exceed that of electrons/positrons (Gallant & Arons 1994). Although the ions can be further accelerated to even higher energies, the 14 maximum ion energy in the jet cannot exceed εi,M ∼ ZeBrjet ∼ 5×10 ZB−4(rjet/1.5× 16 5 16 10 cm) eV [γi,M ∼ 5 × 10 (Z/A)B−4(rjet/1.5 × 10 cm)] because the Larmor radius of ions with higher energies is larger than the jet radius. Assuming that the ion-to-electron number density ratio in the jet does not exceed that in the magnetosphere outflow, we can constrain the ion-to-electron energy density ratio: ki = (ni,jetε¯i,jet)/(ne,jetε¯e,jet) < 72

˙ ˙ 2 −2 −1 3 16 (Ni,puls/Ne,puls)(ZeBrjet/mec γ¯) ∼ 10 B−4γ¯8 (10 /κpair), at rjet = 1.5×10 cm. This means that relativistic ions do not make a substantial contribution to the energetics of the outer jet. Since the bulk velocities in the outer jet are only mildly relativistic, the bulk kinetic energy of relativistic particles is much lower than the energy of their random motion. However, we cannot rule out the possibility that some nonrelativistic electron- ion plasma from the ambient SNR medium is entrained into the jet via interaction with the jet’s magnetic field. To estimate an upper limit on the maximum density of the nonrelativistic component and maximum kinetic energy of the outer jet, it seems reasonable to assume that the total energy injection rate, including the kinetic energy, into the outer jet cannot exceed a fraction of Ljet/Lpwn ≈ 0.008 of the total power, ˙ 36 −1 ˙ E ≈ 7 × 10 erg s , supplied by the pulsar, which implies Wkin < 0.008 Etflow ∼ 42 −1 4 × 10 ljet,18(β/0.5) erg. This condition requires densities of nonrelativistic particles −4 16 −2 3 −3 (ions or electrons), nnonrel < 2 × 10 (rjet/1.5 × 10 cm) (β/0.5) cm . Thermal X-ray radiation from such a low-density plasma is orders of magnitude fainter than the observed radiation from the outer jet. The corresponding upper limits on the pressure and energy density of the nonrelativistic components depend on the unknown mean energy of nonrelativistic particles; however, they do not exceed the pressure and energy density of relativistic particles and the magnetic field. Furthermore, the density of this plasma is much lower than the density of the ambient medium. On the other hand, the 2 −8 −3 bulk pressure, pbulk ∼ ρvbulk < 7 × 10 erg cm , can be higher than the pressure in −9 −3 the ambient medium, pamb ∼ 10 erg cm .

2.4.3.5 End bend and outer PWN: Effect of SNR wind? We see from Figures 2.19 and 2.20 that the outer jet is never straight, showing either gentle bends (e.g., panels 5–10) or a strongly curved structure (panels 1, 2, and 13). The varying curvature of the outer jet can be explained by its interaction with the ambient medium (SNR plasma) and/or by a kink instability in the jet flow. A strong argument for an external wind to cause jet’s bending is provided by the deep image of the PWN (Fig. 2.18) that allows one to see an extension of the outer jet be- yond the apparent termination points (often associated with outermost blobs) observed in the individual images. It shows that the outer jet does not terminate abruptly, but it rather smoothly bends clockwise (towards west and then southwest) by at least 90◦. Such bending suggests a persistent northeast wind in the ambient medium (approximately per- pendicular to the direction of the pulsar’s proper motion. Such a wind could also explain the very asymmetric diffuse emission outside the bright PWN — the wind “blows off” relativistic electrons, produced in the bright PWN, towards the southwest. Moreover, it could explain, in the same way, the fact that the surface brightness is substantially higher at the southwest side of the outer jet compared with the northeast — some high-energy particles are leaking from the jet and blown away by the wind. Finally, an additional support for the wind comes from the radio image of the (outer) PWN (Lewis et al. 2002; Dodson et al. 2003b; see Fig. 2.35 and §2.5.1). This image shows two lobes, northeast and southwest of the X-ray bright PWN, with a much smaller northeast lobe confined by a brightened northeast boundary. The smaller size and the brightening can be explained 73 by compression of the radio-emitting plasma by the external northeast wind. The bulk pressure of this wind can be crudely estimated as Pwind ∼ (djet/Rcurv)(Θ/A⊥), where djet is the diameter of the jet, Rcurv is the curvature radius of the bending, and Θ is the thrust (jet’s momentum flux) through the jet’s transverse area A⊥ (e.g., Leahy 1991). If the bulk kinetic pressure is much lower than the magnetic pressure within the jet, 2 2 −10 −3 ρjetv ¿ B /(8π) ∼ 10 erg cm , then the main contribution to the thrust comes from the longitudinal component of the magnetic stress tensor that, in turn, depends 2 on the geometry of the magnetic field. For instance, we obtain Θ ∼ A⊥B /(24π) for a −12 2 −3 17 tangled magnetic field, which gives Pwind ∼ 3 × 10 B−4 erg cm , for Rcurv ∼ 3 × 10 cm. This bulk pressure is much lower than the typical thermal pressure in the Vela SNR. −1/2 −1 It corresponds to the wind velocity vwind ∼ 10 nwind B−4 km s , where nwind is the ion (proton) number density in the wind. Attempts at separating the wind’s X-ray emission from the SNR background did not yield conclusive results. Assuming a low-density wind, −2 −3 −1 nwind ∼ 10 cm , we obtain vwind ∼ 100 B−4 km s — high but not improbable ve- locity. Such a velocity is comparable with the pulsar’s proper motion velocity, ' 97 d300 km s−1 (Caraveo et al. 2001), but the pulsar’s motion itself cannot initiate the observed bending because the pulsar moves in the direction of the unbent jet (at least in the sky projection). However, once the jet is substantially bent from its original direction by the putative SNR wind, the pulsar’s motion with respect to the SNR matter can bend it further, so that the jet can become directed backwards (towards southeast). A hint of such a bend is indeed seen in Figure 2.18. Moreover, the relativistic particles blown off the jet by the SNR wind are being picked up by the head wind (in the pulsar’s reference frame) and dragged in the direction opposite to the pulsar’s proper motion, feeding the diffuse nebula. Such a picture is supported by the spectral slope of the diffuse emis- sion, Γ ≈ 1.5, which is softer than the emission of the brighter outer jet (Γ ≈ 1.3), but harder than the emission of the PWN shell (Γ ≈ 1.65). Thus, we can conclude that the outermost observable part of outer jet is likely bent by the combined action of the SNR wind and the pulsar’s proper motion, and the outer jet finally bends backward and get diffused southwest of the pulsar.

2.4.3.6 Loop-like structures and blobs: Instabilities in pinched flow? So far we have discussed only the bending of the jet’s “end”. Explaining more extreme bends in the brighter part of the outer jet (e.g., the hook-like or loop-like structures in panels 1, 2, 4, and 13 in Figs. 2.19 and 2.20) by the wind action is more problematic. Although we see that these bends are convex in the direction of the SNR wind suggested above, the relatively small size (and strong curvature) of these structures would require a strong nonuniformity and very high velocities of the wind. Even a stronger argument is the observed variability of the bent structures, associated with almost relativistic velocities. Therefore, we have to invoke another mechanism to explain these features, not related to external winds. A natural explanation is the kink instability of a magnetically confined, pinched flow. Estimates of the instability growth times and wavelengths depend on the model of such a flow, particularly the distribution of currents and topology of the magnetic field. Such model of the jet is currently under development. Here, we only briefly mention that the (outer) jet can be modeled as a plasma beam 74

32 −1 ˙ carrying a charge current of ∼ 10 e s (∼ Njet — see §2.4.3.4), self-confined by a predominantly toroidal magnetic field (Z pinch). A similar model for pulsar jets was suggested by Benford (1984), while collimation and confinment of AGN jets by magnetic field was reviewed by Begelman, Blandford & Rees (1984) and other authors. Growth times of MHD instabilities in such a flow are proportional to the Alfven crossing time, τA ∼ rjet/vA (e.g., Begelman 1998). Using the expression for the Alfven velocity in 2 −1/2 the ultrarelativistic plasma, vA = cB[4π(wrel + prel) + B ] (Akhiezer et al. 1975), 1/2 we obtain vA = (3/5) c ' 0.77c at equipartition between the magnetic and particle energy densities, which gives τA ∼ 10 days. This time is comparable to the time scales of strong bendings (∼< 30 days), which can be associated with the kink instabilities, and time scales of blob brightening (about a week), which can be associated with the sausage (neck) instabilities.

2.4.3.7 Summary and Conclusions The multiple Chandra observations of the Vela PWN have allowed us to investi- gate the dynamical outer jet and discover a dimmer outer counter-jet outside the bright PWN. Our main results can be summarized as follows. 1. The outer jet extends up to about 0.4–0.5 light years from the pulsar in the sky plane along the direction of the pulsar’s proper motion. Its shape and brightness are variable on time scales of days to weeks. The brightness is nonuniform along the jet, with brighter blobs moving away from the pulsar with apparent subrelativistic speeds. The variations observed suggest typical flow velocities of 0.3–0.7 of the speed of light. 2. The outer jet is, on average, a factor of 7 brighter than the outer counter-jet. If the outer jet and outer counter-jet are intrinsically similar but streaming in opposite directions, then the difference in brightness means that the outer jet is approaching at an angle of 30◦–70◦ to the line-of sight while the outer counter-jet is receding. Such an orientation apparently contradicts to the previously suggested models of the inner jets and the bright arcs. 3. The synchrotron interpretation of the hard (Γ ≈ 1.3) power-law spectrum of the outer jet requires highly relativistic electrons or positrons, with energies of up to ∼> 200 TeV, and a typical magnetic field of about 100 µG. The outer jet’s spectrum is perhaps slightly softer than those of the inner jet and counter-jet, but it does not change appreciably along the outer jet. If the outer jet is a mildly relativistic outflow of an ultrarelativistic electron/positron plasma, the energy injection rate is ∼ 1034 erg s−1 ∼ −3 ˙ 3 10 E ∼ 10 Lx,jet. 4. Outside the bright PWN, there is an asymmetric, dim outer diffuse nebula that is substantially brighter southwest of the jet/counter-jet line. Its spectrum is softer than that of the outer jet, but it is harder than the spectrum of the brighter PWN shell. It is possible that the X-ray emitting particles in the dim nebula are supplied through the outer jet, whose end part turns southwest with respect to its average (northwest) direction in the sky plane. Such a turn can be caused by a northeast SNR wind with a speed of a few times 10 km s−1, which also helps feed the dim nebula. 5. The width of the outer jet, ∼ 3×1016 cm, remains approximately the same along the jet in different observations, including those which show strong bends. This suggests 75 an efficient confinement mechanism, perhaps associated with magnetic fields generated by electric currents in the pinched jet. The current required, ∼ 1032 e s−1 ∼ 1012 amp, is an order of magnitude lower than the Goldreich-Julian current in the pulsar magnetosphere. The bright blobs and strong bends could be caused by the sausage and kink instabilities, respectively, in such a pinched jet. The excellent resolution of the Chandra telescope and high sensitivity of its detectors allowed us to obtain the spectacular pictures of the Vela PWN, including the faint outer jet, and, in particular, to prove the highly anisotropic and dynamical nature of the pulsar outflows. However, as has been often the case with new high-quality data, our results raise new questions and put under doubt the previous simplistic interpretations of PWNe in general and the Vela PWN in particular. The most unclear issue is the interpretation of the complicated morphology of the Vela PWN, particularly the relationship of the outer jet and outer counter-jet with their inner counterparts, the true orientation of the jets, and the actual topology of its arcs. We do not even know the actual three-dimentional orientations of the inner and outer jets and counter-jets, nor do we understand the cause of their different brightness. We can only guess about the nature of the bright blobs moving along the outer jet, the mechanism(s) of the jet confinement, and the origin of the jet bendings. At least some of these issues can be clarified by a series of deeper Chandra observations of the Vela PWN, taken with intervals of a few days, the now- established time scale of the PWN variations. In particular, such observations would allow one to search for the spectral changes along the outer jet and check if the spectra of the blobs are different from those of the rest of the jet. They could also help find blobs in the very dim outer counter-jet and measure their velocities, which would provide a clue to the geometry of the system. The interpretation of the Vela PWN would be much easier if it were detected at other wavelengths, outside the X-ray range. So far, contrary to the much better studied Crab PWN, the Vela PWN has not been detected in the optical, mainly because of numerous relatively bright field stars and SNR filaments in the pulsar vicinity (Mignani et al. 2003; see also §2.5.3). To get rid of their light and detect the PWN or put a stringent upper limit on its brightness, the field must be observed in polarized light. It would also be very important to obtain a deep radio image the field around the Vela pulsar with arcsecond resolution (cf. Dodson et al. 2003b). Both the optical and radio observations would provide estimates on the lower frequencies of the synchrotron spectra (hence, lower energies of relativistic electrons), the critical parameters for evaluating the magnetic fields and the energetics of the observed PWN elements. Measuring polarizations of the optical and radio emission would be crucial to establish the directions of the magnetic field in the PWN elements and understand their nature. 76

2.4.4 Global structure of the Vela PWN in X-rays 2.4.4.1 Deep X-ray images To investigate the fainter, large-scale structure of the PWN, we produced the summed images from the ACIS and HRC data, according to the recipe provided at the CIAO Threads web page22. The summed ACIS and HRC images of the Vela PWN field have effective exposure times of 160 and 150 ks, respectively (see Figures 2.28 and 2.29). The brightness scale in the images is adjusted to emphasize a fainter, more diffuse emission from the PWN. This fainter emission is clearly asymmetric: most of it stretches south-west (SW) of the inner PWN symmetry axis which is approximately co-aligned with the direction of the pulsar’s proper motion (Fig. 2.29). Such an asymmetry, as well as persistent bending of the northeastern jet to SW, suggest the presence of large- scale (∼> 1 pc) density/pressure gradients or a wind (invisible in X-rays) blowing in the SW direction in the ambient SNR medium (see also §2.4.3.5). Another region of even fainter emission is seen at the bottom of the summed HRC image (lower panel in Fig. 2.29). This could be the emission from the wind which was produced by the pulsar when it was located close to its birth place (marked by the cross in Fig. 2.29). Such −2/3 −1/3 interpretation would place an upper limit of ≈ 2(tage/11, 000 yrs) (E/1 keV) µG on the magnetic field in the region. Alternatively, the emission could be due to a background SNR filament(s) in which case spectral lines should be present in the X- ray spectrum. To obtain the X-ray spectrum of this emission and discriminate between these two possibilities, a deep exposure of this region with Chandra ACIS or XMM EPIC is needed. Such observations would also help to establish the relation between the PWN and nearby X-ray/radio bright region (see below). Figure 2.30 (left panel) shows the ROSAT PSPC view (2◦ in diameter) of the Vela pulsar field from Markwardt & Ogelman¨ (1995). Because of a poor PSPC resolution, Markwardt & Ogelman¨ (1995) interpreted the region of extended emission stretching down to the bottom of the image as a jet of the Vela pulsar. Now we know that the true jets are positioned along the direction of the pulsar’s proper motion (see Fig. 2.28) and therefore the nature of the extended emission in the ROSAT image remains puzzling. This region also shows an excess of emission in radio (e.g., Bock 1998 and right panel in Fig. 2.30) and represents a part of a larger radio-bright region that has been dubbed Vela X (Jones & Finlay 1974). The brightest (in radio) part of the Vela X region is located 250 − 350 south-west of the present pulsars position (i.e. in the direction perpendicular to that of the pulsar proper motion; right panel in Fig. 2.30). Although the faint asymmetric PWN emission is more extended in the south-west direction, it seems to fade at shorter distances from the pulsar (bottom panel in Fig. 2.29) than the distance to the brightest (in radio) part of the Vela X (which is outside the HRC field of view shown in Fig. 2.29; the latter is shown in the left panel Fig. 2.30 by the black square). Spectroscopic X-ray observations of the brightest in radio region of Vela X will help to determine if it is indeed related to the PWN or it represents a group of background/foreground filaments compressed by the shock wave produced during the Supernova explosion.

22Merging Data from Multiple Imaging Observations — see http://cxc.harvard.edu/ciao/threads/combine/ 77

N 90''

E

Figure 2.28 Summed ACIS-S3 image of the Vela PWN (top) and its adaptively smoothed version (bottom). Total exposure time in the images is about 160 ks). 78

Figure 2.29 Summed HRC image of the Vela PWN (top) and its adaptively smoothed version (bottom). Total exposure time in the images is about 150 ks. The HRC field-of- view is 300 × 300. 79

Figure 2.30 Left: ROSAT PSPC image of the Vela PWN region. Right: 1.4 GHz ATCA image of the Vela PWN region which also includes the brightest filament of Vela X (dark structure near the bottom; radio image adopted from Bock et al. 1998). 80

2.4.4.2 Photon index maps To better understand the properties of the shocked pulsar wind, it is important to investigate the correlation between the spectral and spatial structures of the PWN. For instance, XMM observations of the Crab PWN (with 500 resolution) have shown that the spatial dependence of the spectral slope is not isotropic, being well correlated with the PWN structure: e.g., the hardest emission comes from the inner torus region (Willingale et al. 2001). The Chandra resolution and the proximity of the Vela pulsar (d ' 300 pc; Dodson et al. 2003a) make it possible to obtain an even better quality spectral map of the Vela PWN, provided that a sufficient number of counts is collected. Here we present the spectral map of the Vela PWN obtained from the last eight observations (see Table 2.4) with the Chandra ACIS detector. To investigate the PWN spectral properties, we produced photon index maps of the PWN from the merged ACIS event list with the aid of CIAO23 software, v.2.3. Al- though extracting the spectra from the merged event list is generally not recommended24, we believe that in this case the uncertainties introduced by doing so are minimal since the PWN was imaged at the same location on the ACIS S3 chip in all 8 observations, and a properly averaged25 ARF was produced from the individual ARFs that have been corrected for the ACIS contamination 26. After some experimenting, we adopted 200. 5 and 1000 cells to be used for spectral extraction, depending on the distance from the pulsar. This provides roughly comparable signal-to-noise ratios for the bright inner and fainter outer PWN parts. We fitted the spectra extracted from each spatial cell with the absorbed power-law model using XSPEC27. The hydrogen column density was fixed 20 −2 at nH = 3.2 × 10 cm in all fits, as determined from the Chandra observation of the Vela pulsar with the HRC-LETG (§2.2.2). The top panel of Figure 2.31 shows the large-scale spectral map of the Vela PWN. The map coverage is determined by the condition that the relative uncertainty of the photon index of the PL fit to the cell’s spectrum (cell sizes are 200. 5 and 1000) should not exceed 20% of the index value. The lower panel of Figure 2.31 shows a close-up view of the PWN spectral structure around the pulsar at a higher spatial resolution (cell size is 200. 5). The most noticeable features in the spectral maps are the shell of soft emission surrounding the inner PWN (which encompasses the arcs and the inner jets with hard spectra) and the relatively hard spectrum of the diffuse emission SW of the pulsar (which is harder, on average, than that of the shell located closer to the pulsar). The harder spec- trum can be explained if the bent outer jet (see Fig. 2.18), whose spectrum is also hard (photon index Γ ≈ 1.3), supplies particles to the region SW of the pulsar on a timescale −3/2 −1/2 shorter than the synchrotron cooling time tsyn ≈ 39(B/100 µG) (E/1 keV) years. The energy losses for the particles carried with the equatorial outflow can be larger than

23Chandra Interactive Analysis of Observations — see http://cxc.harvard.edu/ciao/ 24http://cxc.harvard.edu/ciao2.3/threads/combine/ 25http://cxc.harvard.edu/ciao2.3/threads/wresp multiple sources/index.html#warf 26http://cxc.harvard.edu/ciao/threads/aciscontam/ 27XSPEC v.11.3 is available from http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/ 81 for the jet’s particles, e.g., due to additional expansion losses which are less important for the well-collimated jet. The emission, produced by the particles carried with the equa- torial outflow, can give rise to the soft shell if the particles move outwards sufficiently slowly and have enough time to cool. We also find a clear signature of the outer SE jet (Figure 2.18) in the spectral map (top panel in Fig. 2.31).

2.4.4.3 Comparison with the Crab PWN. The most famous and best-studied example of a pulsar-wind nebula is the Crab PWN. Therefore, it is prudent to compare what we learned about the Vela PWN with what we know about the Crab PWN. The Crab PWN has been extensively studied in radio, optical, X-rays, and gamma- rays (e.g., Bietenholz, Frail & Hester 2001; Hester et al. 1995; Mori et al. 2001; Kuiper et al. 2001; Weisskopf et al. 2000, and references therein). These observations revealed the complex morphology and temporal variability of the Crab PWN as well as correlation between the X-ray, optical and radio PWN features. The first observation with Chandra ACIS (Weisskopf et al. 2000) resulted in high-resolution image of the Crab PWN, which revealed astonishing level of detail (see left panel in Fig. 2.32), and suggested that the spectrum (hardness ratio) changes throughout the nebula. However, the brightest parts of the nebula were substantially piled-up and the results were expected to be only qual- itatively correct (Weisskopf et al. 2000). The ACIS observation of the Crab PWN was followed by the long XMM exposure (not affected by pile-up) which allowed Willingale et al. (2001) to produce a photon index map of the PWN (with a 500 spatial resolution) showing that the innermost nebula is significantly harder than the outer nebula. Mori et al. (2004) analyzed eight recent Chandra ACIS images of the Crab PWN28 to investigate spectral properties of the Crab PWN at an even higher spatial resolution of ≈ 200. 5. Mori et al. (2004) attempted to correct the spectral distortions due to the remaining pile- up and produced a plot of the photon index versus the PWN surface brightness where both are calculated for 200. 5 × 200. 5 cells) within the Crab PWN (Fig. 2.33; different colors correspond to the different regions of the Crab PWN). They found a strong anticorrela- tion between the photon index and surface brightness for the umbrella-shaped northwest region and fainter peripheral region of the Crab PWN (Fig. 2.33). The X-ray morphologies of the Vela and Crab PWN show both remarkable sim- ilarities and noticeable distinctions. The main distinction between the two PWNe is in their sizes and energetics. In particular, the physical size of the bright Vela PWN, ∼ 0.1 pc at d = 300 pc, is an order of magnitude smaller than that of the Crab PWN, in ˙ 1/2 rough correspondence with the scaling, rs ∝ E , for the shock radius in an ambient medium with a given pressure. This correspondence indicates that typical pressures, ˙ 2 −9 −3 p ∼ E/4πcrs ∼ 10 erg cm , are of the same order of magnitude, which is in agree- ment with the close values of their equipartition magnetic fields, B ∼ 10−4 G (Kargaltsev et al. 2002; see also §2.4.3.4). The similarity of physical parameters of the relativistic

28Due to a different observation setup, these data are less affected by the pile-up than the data used by Weisskopf et al. (2000) 82

Figure 2.31 Photon index maps (40.2 × 40.2 – top panel; 10 × 10 – bottom panel) with X-ray contours overlayed. In the top panel, black color corresponds to the pixels with low S/N ratio for which the spectral index is not calculated. 83

Figure 2.32 Chandra ACIS images of the Crab (200. 7 × 200. 7; left) and Vela (30 × 30; right) PWNe.

plasmas in the two PWNe suggests that typical velocities of MHD waves, presumably responsible for some of the observed variabilities, are also similar. If one leaves aside the different sizes of the PWNe, the apparent similarities in spatial structure are obvious from Figure 2.32. Both PWNe exhibit toroidal structures, although in the Crab PWN only inner ring (perhaps, an analog of the inner arc in the Vela PWN) clearly stands out from the more diffused emission, whereas in Vela PWN both inner and outer arcs are easily identified and have comparable sizes and brightnesses. As the Vela PWN, the Crab PWN exhibits variable jets (Hester et al. 2003), with flow speeds similar to those inferred for the outer jet of the Vela PWN (§2.4.3.1). The Crab and Vela PWNe both exhibit correlation between the spectral and spa- tial structure which, however, is somewhat different for the two PWNe. For the Vela PWN we produced a plot similar to that shown in Fig. 2.33 for the Crab PWN. For spectral extraction we used the same spatial cells as for the photon map calculations (§2.4.4.2). In Figure 2.34 we plot the photon index versus PWN surface brightness in the individual cells (top panel of Fig. 2.34) in different colors corresponding to different regions of the PWN (shown in the bottom panel of Fig. 2.34). We see a hint of anticor- relation between the photon index and surface brightness for the inner arc and fainter soft-shell region (such a trend is more prominent in the Crab PWN; see Fig. 2.33 from Mori et al. 2004). This could be a signature of a expanding and cooling equatorial outflow since fainter emission comes from the regions located further away from the pulsar(s). The inner arc (light blue color in Fig. 2.34) spectrum is on average harder than that of the outer arc (yellow color in Fig. 2.34). As we already mentioned, the diffuse emission SW of the pulsar (dark blue color in Fig. 2.34) has on average a harder spectrum than the “soft shell” which is closer to the pulsar (nothing similar seen in the Crab PWN). The same is true for the region NE of the Vela pulsar (green color in Fig. 2.34). 84

Figure 2.33 Spectral morphology of the Crab PWN (from Mori et al. 2004; see text for details). 85

Figure 2.34 Top: Photon index versus surface brightness for different Vela PWN regions. Bottom: Shows color coding that is used in the upper panel to distinguish different PWN regions. 86

2.5 Vela PWN in radio and optical: The multiwavelength picture.

The X-ray spectrum of the Vela PWN can be described by a power law with an average spectral (energy) index α ∼ 0.5 (e.g., Fig. 2.31), which can be interpreted as synchrotron emission of relativistic electrons and/or positrons. The same electron distributions should emit optical and radio synchrotron radiation, provided that the 1/2 −1/2 electron power-law spectrum extends down to sufficiently low energies, ∼< 300ν14 B−4 14 −4 GeV (where ν = 10 ν14 Hz is the radiation frequency, and B = 10 B−4 G is the magnetic field), and synchrotron self-absorption plays no role.

2.5.1 Radio PWN The highly polarized (≈ 60% at 5.2 GHz) extended radio emission has been recently detected around the Vela pulsar (Lewis et al. 2002; Dodson et al. 2003), covering a region ∼ 4 times larger than the X-ray PWN, as observed in the case of the Crab. Most of the diffuse radio emission comes from two lobes (see Figs. 2–4 in Dodson et al. 2 2003; also Fig. 2.35) — the southeast lobe of an area of 18 arcmin (Fν = 760 ± 100 2 mJy at 5.2 GHz) and a brighter northeast lobe of an area of 5.3 arcmin (Fν = 290 ± 50 mJy at 5.2 GHz). Search for radio emission from the X-ray-bright compact nebula was hampered by the brightness of the pulsar. Although some emission was detected (e.g, about 30 mJy at ν = 2.4 GHz, in a 0.73 arcmin2 area around the pulsar), it can well be an unsubtracted pulsar contribution and should be considered as an upper limit on the compact PWN emission.

2.5.2 Comparison between the radio and X-ray PWNe morphologies. In the radio images of the Vela PWN the emission mostly comes from two lobes of different sizes and brightnesses (Dodson et al. 2003b). This structure is also seen at lower resolution in earlier VLA image of the Vela PWN region (Bock 1999; also right panel in Fig. 2.30). Overlaying the X-ray contours on top of the radio image (from Dodson et al. 2003b), we find that the outer contours (corresponding to lower X-ray brightness) are well correlated with the shape of the radio PWN (Fig. 2.35). This suggests that the X-ray and radio emitting electrons are carried with the same outflow which is mostly confined to a low-latitude (equatorial) region. In terms of relative brightness, the radio emission is brighter further away from the pulsar while the X-ray emission is the brightest close to the pulsar. Such a picture could be explained by the synchrotron and expansion losses incurred by energetic particles as they travel away from the pulsar.

2.5.3 Search for a compact optical nebula Since the Vela PWN has been detected in X-rays and radio, one would also ex- pect to find an optical nebula around the Vela pulsar. So far searches for the optical counterpart have been inconclusive. The only marginal detection of the optical PWN was reported by Ogelman¨ et al. (1989), who observed the Vela pulsar field in the V and B bands with the ESO 2.2 m telescope. These authors found evidence for optical diffuse emission (typical size ∼ 20), with an average surface brightness of about 26 mag arcsec−2. 87

Figure 2.35 8.5 GHz image with the X-ray contours overlayed.

However, the presence of bright filaments from the host SNR, as well as of several bright stars in the field, made it difficult to assess the reality of the putative optical nebula. The increase in sensitivity and angular resolution provided by the HST prompted us to carry out a new optical investigation of the Vela pulsar region. We also searched for spatial correlations between the Chandra ACIS images (Pavlov et al. 2001b; Pavlov et al. 2003) and the optical ones collected by both the HST WFPC2 (Mignani and Caraveo 2001; Caraveo et al. 2001a) and ESO NTT (Nasuti et al. 1997) and VLT. Optical observations of the Vela pulsar field were collected at different epochs using different telescopes, instrumentation, observational set-ups, and filters. Table 2.7 gives summary of the available observations (see also Mignani, De Luca, Kargaltsev et al. 2003 for details). The direct comparison of images taken in different energy bands (e.g., optical and X-rays) can be achieved through accurate image superposition. Following the approach used by Caraveo et al. (2001b), we superimposed the X-ray Chandra image onto the op- tical ones with respect to the absolute (α,δ) reference frame, relying on the astrometric solution of each image. The absolute frame registration between the optical and X-ray images turned out to be accurate within ≈ 100, i.e., compatible with the overall uncer- tainties of the absolute astrometry of each frame (see also Mignani, De Luca, Kargaltsev et al. 2003 for details). As a first step, the central part of the X-ray PWN field (corresponding to the inner nebula and the outer nebula) was inspected to search for optical counterparts of the complex structures seen with Chandra. The starting point was the combined WFPC2 555W image, which is by far the deepest optical image of the Vela pulsar field. The final image is shown in Figure 2.36, where we superimposed the X-ray contour map 88

Table 2.7. Available optical datasets for the Vela pulsar field.

Date Telescope Instr. Filter λ (∆λ) Exp. Ref.

Jan 1995 NTT EMMI-B U 3542A˚ (542A)˚ 4800 (1) Jan 1995 NTT EMMI-B B 4223A˚ (941A)˚ 1800 (1) Jan 1995 NTT EMMI-R V 5426A˚ (1044A)˚ 1200 (1) Jan 1995 NTT EMMI-R R 6410A˚ (1540A)˚ 900 (1) June 1997 HST WFPC2 555W 5500A˚ (1200A)˚ 2600 (2) Jan 1998 HST WFPC2 555W - 2000 (2) June 1999 HST WFPC2 555W - 2000 (2) Jan 2000 HST WFPC2 555W - 2600 (2) Jul 2000 HST WFPC2 555W - 2600 (2) Mar 2000 HST WFPC2 675W 6717A˚ (1536A)˚ 2600 (3) Mar 2000 HST WFPC2 814W 7995A˚ (1292A)˚ 2600 (3) Apr 1999 VLT FORS1 R 6750A˚ (1500A)˚ 300 Apr 1999 VLT FORS1 I 7680A˚ (1380A)˚ 300 Apr 1999 2.2m WFI Hα 6588A˚ (74.3A)˚ 3600

Note. — First column lists the epoch of observation. Second and third columns show the telescope and the detector used for the observations, re- spectively. The filter names are listed in column four, with their pivot wave- lengths and widths in column five. The total integration time per observation (in seconds) is given in column six. The last column provides the references: (1) Nasuti et al. 1997; (2) Caraveo et al. (2001a); (3) Mignani & Caraveo (2001). 89 obtained from the combined Chandra ACIS exposure of the region. Although a number of complicated patterns of diffuse emission are present in the ≈ 30 × 30 field of view, no optical counterparts of the X-ray features seen in right panel of Figure 2.32 can be identified, nor any other structure symmetric with respect to the axis of symmetry of the X-ray PWN. We thus conclude that the PWN is undetected in the optical. To compute the upper limit on the optical surface brightness of the PWN, an accurate mapping of the background is required. This is complicated by the presence of diffuse, non-uniform emission patterns which show sharp surface brightness variations on angular scales as small as ≈ 5 arcsec. For this reason, we evaluated the background level in ≈ 200 cells of 1 arcsec2 each, selected in a number of star-free regions across the whole image. Statistical errors on the number of counts per cell were of the order of 0.3%. The background level, ≈ 22.3 ST magnitudes29 arcsec−2 on average, was found to vary typically by 4%–5% across the whole field, with a maximum variation of ≈ 7%. For an extended source, the upper limits on the surface brightness scale with the detection area A as A−1/2. An optimally chosen area should be large enough to reduce the statistical errors due to the background fluctuations but it should be smaller than the scale of sharp background variations. According to our mapping of the background, a detection area of 10 arcsec2 represents a reasonable optimization. For the area chosen, the measured background variations affect the upper limit on the flux of an extended source (at a 3 σ level) by no more than ≈3%, corresponding to surface brightness variations below 0.1 magnitudes arcsec−2. While variations in the sky background across the image play a minor role, we found that the derived surface brightness upper limits are different in different regions of the image. This is mainly due to the non-uniform coverage of the field performed by the WFPC2. First, because of the intrinsic differences in the pixel size and in the physical characteristics of the CCDs, the PC and the WFC chips contribute differently to the instrumental background per unit area. In addition, since the five WFPC2 555W observations listed in Table 2.7 were executed at different epochs and with different telescope roll angles, the exposure map varies across the field. For instance, the central region of the field, which is covered by the PC (3500 × 3500), reaches an integration time of 11 800 s, while the outer regions, covered by the three WFC chips, have integration times varying between 4 600 and 11 800 s. Both effects clearly affect the evaluation of the surface brightness upper limits in different regions of the PWN, as they are covered differently by the four WFPC2 chips. As it is seen from Figure 2.36, some regions of the inner nebula (inner arc, jet, and counter-jet) fall entirely within the PC, while the outer arc is coincident with the inter-chip gaps and is covered partially by the PC and partially by the WFC chips. On the other hand, the outer nebula is entirely covered by the WFC chips. Taking all these effects into account, we have computed the 3σ upper limits on the optical surface brightness of both the inner nebula (inner arc, jet, counter-jet, outer arc) and the outer nebula. We note that although our upper limits have been computed for a detection area of 10 arcsec2, they can be easily rescaled to any other area.

29STScI magnitude is defined in such way that an object with constant flux per unit wavelength interval has zero color; STmag =−2.5 log Fλ − 21.10. 90

Figure 2.36 Image of the Vela pulsar field obtained by combining all the WFPC2 555W observations listed in Table 2.7 (North to the top, East to the left). The gaps among different CCD chips are evident. The overall integration time on the central part, cor- responding to the PC field of view, is 11 800 s (see text). The overlayed contours (loga- rithmic scale) correspond to the X-ray intensity maps obtained from the Chandra ACIS image of the field in the energy band 1–8 keV. The point source within the innermost X-ray contour is the optical counterpart of the Vela pulsar. 91

Figure 2.37 The upper panel shows the combined UBVR image of the Vela pulsar field obtained from the NTT/EMMI observations listed in Table 2.7. The lower panel shows 0 0 the ESO/2.2m Hα image. In both cases the image size is ≈ 4 × 4 . North is up, East to the left. The X-ray contour plots of the Vela PWN derived from the ACIS observations (§2.4.1) are overlayed. 92

Using the HST pipeline photometric calibration, we computed an upper limit of 28.1 and 28.0–28.5 ST magnitudes arcsec−2 for the inner nebula and for the outer nebula, respectively. As we mentioned before, because of the non-uniformity of the exposure map the upper limit for the outer nebula turned out to be slightly position-dependent. To correct these limits for the interstellar reddening, we use the extinction AV = 0.2, consistent with the hydrogen column density estimated from the X-ray observations of the Vela pulsar (§2.2.2). The corrected limits are 27.9 and 27.8–28.3 ST magnitudes arcsec−2. The same analysis was then repeated for the other available WFPC2 images (675W and 814W ) as well as for the NTT (UBVR) and VLT (VI) ones (see Table 2.7) but no evidence for a compact optical nebula was found in either of these datasets. The computed upper limits are summarized in Table 2.8.

2.5.4 Search for an extended nebula Since the emission from the PWN could, in principle, be visible at optical wave- lengths on larger angular scales with respect to the X-rays, as it has been observed in radio (see §2.5.1), we took advantage of the larger field of view provided by the NTT images to search for extended features up to distances of ≈ 3 arcmin. In particular, we searched for diffuse optical emission at the position of the southwest extension of the X-ray nebula (see Fig. 2.32, right panel). To go as deep as possible, we have combined all the available NTT UBVR band images (Fig. 2.37, upper panel). The combined image shows many different enhancements in the background, with a rather complex spatial distribution. However, none of them can be firmly correlated with the known X-ray fea- tures. In addition, we note that almost all the diffuse emission patterns seen in the NTT UBVR image can be also identified in the ESO/2.2m Hα (Fig. 2.37, lower panel). This suggests that they are most likely associated with the bright filaments of the Vela super- nova remnant. We note that the computed NTT upper limits on the optical emission of the compact X-ray nebula can be applied also at larger distances from the pulsar. The maximum variation in surface brightness for source-free regions, due to the complicated distribution of diffuse emission, is found to be of order 7% even in the outer regions of the NTT field, which corresponds to < 0.1 magnitudes arcsec−2 variations of the upper limit across the field. We note that for the NTT images the measured upper limits in the U and B bands do not apply to the region ≈ 2.5 arcmin southwest of the pulsar position, close to the southwest edge of the extended X-ray nebula. The background in this region is heavily polluted by the presence of a bright (B ≈9) B star that is not visible in the V and R band images because of the slightly narrower field of view.

2.5.4.1 Implications of non-detection of optical PWN. It is interesting to compare the measured upper limits on the optical brightness of the Vela PWN with the X-ray and radio observations. The observed X-ray spectra of the Vela PWN are described by a power law with spectral indices α ≈ 0.3–0.4 and α ≈ 0.4– 0.5, for the arcs and the extended diffuse emission southwest of the pulsar, respectively −α (Fν ∝ ν ; §2.4.4.2). The X-ray and radio surface brightness spectra, together with the optical upper limits, are shown in Figure 2.38 for the outer arc (upper panel) and the 93

Table 2.8. 3σ upper limits to the surface optical brightness of the X-ray PWN structures.

Observed Extinction-corrected1

Telescope Instrument Filter mag arcsec−2 Flux2 mag arcsec−2 Flux2

HST WFPC2 555W 28.1 0.21 27.9 0.25 28.5–28.0 0.15–0.23 28.3–27.8 0.18–0.28 WFPC2 675W 27.5 0.55 27.3 0.66 27.9 0.38 27.7 0.46 WFPC2 814W 27.7 0.65 27.6 0.71 28.1 0.45 28.0 0.49 NTT EMMI-B U 26.4 0.52 26.1 0.69 B 27.4 0.47 27.1 0.62 EMMI-R V 27.1 0.53 26.9 0.64 R 26.7 0.59 26.5 0.71 VLT FORS1 R 27.0 0.45 26.8 0.54 I 26.1 0.81 26.0 0.90

1 for AV = 0.2 2flux values are in units of 10−30 ergs cm−2 s−1 Hz−1 arcsec−2

Note. — The upper limits are computed for an area of 10 arcsec2. For the HST results, the first and second rows, for a given filter, are the upper limits measured in the PC and WFC chips, respectively. Due to the uneven exposure map of the combined WFPC2 555W image (Fig. 2.36), slightly different upper limits are derived across the WFC field. For both the NTT and VLT, the upper limits apply to the overall X-ray nebula. 94

-28 Outer Arc

-30

-32

-34 Log Spectral Brightness

-28 SW lobe

-30

-32

-34 Log Spectral Brightness

8 10 12 14 16 18 20 Log Frequency (Hz)

Figure 2.38 Spectra of surface brightness (in erg cm−2 s−1 Hz−1 arcsec−2) in X-rays (solid lines) and radio (points), together with the optical upper limits, for the inner/outer arc (upper panel) and diffuse emission southwest of the pulsar (lower panel). Expected brightness levels in optical, based on extrapolations of the X-ray and radio data, are shown with dashed lines. 95 diffuse emission southwest of the pulsar (lower panel). Since the inner PWN structures were not resolved in the radio, only radio upper limits are plotted in the upper panel. From the plot we see that both the optical and radio upper limits for the outer arc are within the uncertainty of the extrapolation of the X-ray spectrum towards lower frequencies. In the case of the southwest diffuse emission, we note that the X-ray-to-radio extrapolation is well below the measured radio brightness values. This apparent in- consistency can be explained by the fact that the radio and X-ray brightnesses were measured in different areas (the X-ray image is substantially smaller than the radio im- age). Moreover, even within the smaller X-ray field-of-view, it is seen that the X-ray brightness of the southwest diffuse emission fades towards the region of maximum radio brightness (which is outside the X-ray field of view). Such behavior can be explained by radiative (synchrotron) and adiabatic cooling of the expanding cloud of relativistic electrons, which can result not only in the increase of the spectral index, but also in the shift of the energy boundaries of the power-law spectrum towards lower energies (see also §2.5.5). Therefore, we can expect maximum optical brightness to be observed in between the regions of the X-ray and radio maximum brightnesses. Although the X-ray and radio spectra in the lower panel of Figure 2.38 cannot be directly compared with each other, a crude estimate of the expected optical brightness can be obtained by connecting the radio and X-ray points. This yields ∼ 3 × 10−32 erg cm−2 s−1 Hz−1 arcsec−2, i.e., about 3 magnitudes below our measured optical upper limit.

2.5.5 Multiwavelength spectrum of the Vela PWN Figure 2.39 shows spatially integrated multiwavelengths (radio to gamma-ray) spectrum of the Vela PWN (cf. Crab PWN spectrum in Fig. 2.40 from Atoyan 1999). The radio points are from Dodson et al. 2003 (§2.5.1), optical upper limits are from §2.5.3, X-ray data points are from the ACIS data described above (§2.4) and from the previous X-ray missions (see de Jager et al. 1996 for details). The EGRET upper limits (in the lower panel of Fig. 2.39) are from Kanbach et al. (1994). The CGRO/OSSE observations (de Jager et al. 1996) do not show substantial change of the spectral slope in the 44−380 keV energy range, while no unpulsed radiation was detected with the CGRO/EGRET in the 60 MeV – 10 GeV range (Kanbach et al. 1994). Since the extrapolation of the ACIS PWN spectrum (OSSE spectrum has a large associated uncertainty, which makes the extrapolation inconclusive) to the EGRET range (Fig. 2.39) lies above the upper limits on the unpulsed PWN spectrum, we can assume that the PWN spectrum experiences a break or a cutoff between 0.4 and 60 MeV, which translates to an upper energy of 10 11 −1/2 electron injection spectrum γmax ∼ (10 − 10 )(B/100µG) . Similar high-energy break is seen in the Crab PWN spectrum above 1 MeV (Fig. 2.40). To explain the deficit of radio emission at 8.5 GHz in the region around the pulsar (i.e. the region of the bright X-ray PWN; Dodson et al. 2003), one could assume that 4 −1/2 the lower energy of electron injection spectrum is such that γmin ∼> 10 (B/100µG) (corresponding to synchrotron frequencies νsyn ∼> 14 GHz). The bulk of radio emission comes from two lobes located further away (at about 6 × 1017 cm) from the pulsar and positioned symmetrically with respect to the pulsar spin axis (Fig. 2.35; Dodson et al. 96

) -22 -1 ROSAT EINSTEIN Hz -24 OSSE

-1 SpaceLab2 Chandra ACIS s -2 -26

-28

-30

-32 Log Flux (erg cm 8 10 12 14 16 18 20 Log Frequency, Hz

Figure 2.39 Top: The spatially integrated spectrum of the Vela PWN. Bottom: The EGRET upper limits on the unpulsed GeV emission from the Vela PWN. The solid line shows the extrapolation of ACIS spectrum with associated uncertainties (the dashed lines). 97

Figure 2.40 Multiwavelengths spectrum of the Crab PWN (from Atoyan 1999).

2003). If the low-energy (i.e. radio emitting) electrons are absent in the initial injection spectrum, one should assume the electrons with higher energies cool sufficiently by the time they reach the lobe regions, to produce the observed radio emission. This, however, seems unlikely because for electrons emitting at λ = 6 cm the synchrotron cooling time, 5 −3/2 −1/2 τsyn ≈ 5.1 × 10 B−4 ν9 yrs, is much greater than the age of the Vela SNR (∼ 10 − 20 kyrs). Therefore, unless the cooling is much more efficient (e.g., due to the expansion losses), it is likely that radio-emitting electrons with γ ∼ 104 are present in the injection spectrum. The peak in the surface brightness of the emission produced by uncooled electrons is attained at the distance r? where the magnetic field reaches its maximum −1/2 value (r? ≈ rs(3σ) ; rs cm is the shock radius; σ the flow magnetization parameter; see Kennel & Coroniti 1984 for details). Assuming that in the Vela PWN the shock radius 16 is approximately equal to the distance from the pulsar to the inner arc (i.e. rs ∼ 5×10 16 cm) and r? ≈ 6 × 10 cm (see above) we can estimate the pre-shock magnetization parameter σ ∼ 0.002. More energetic electrons, which emit X-rays, suffer substantial radiation losses before they reach r?. Therefore, the X-ray surface brightness peaks at the distance which these electrons reach before their characteristic synchrotron frequency (or, more precisely, high-frequency boundary of the power-law spectrum) moves out of the X-ray band (0.5 − 8.0 keV in Chandra images) toward lower frequencies due to the efficient cooling. If radio-emitting electrons are present in the particle injection spectrum (i.e. just downstream of the shock), then the spectrum of energies of the electrons in the pulsar wind should span 6–7 orders of magnitude. Therefore, whatever acceleration mechanism operates at the shock (or upstream of the shock), it should be able to produce such wide range of electron energies. The detailed analytical modeling (currently under development) is required to determine the effects of cooling on the surface brightness of the PWN emission, to confront the modeled surface brightness distribution with the one observed at different frequencies and derive physical parameters of the pulsar wind. 98

2.6 Observational perspectives. Optical, X-ray and radio polarimetry.

Despite the multiple observations carried out in different bands, our understanding of the structure and physics the Vela PWN (and PWNe in general; see next Chapter) is far from being complete. The non-detection of the optical PWN (§2.5.3 and 2.5.4) is intriguing. Since we know very little about the optical properties of PWNe (only three PWNe have been detected in the optical continuum emission; §1.1.3), one could speculate that in the Vela PWN radio and X-ray emission are produced by different electron populations (as it has been suggested for the Crab PWN, e.g., Atoyan 1999) whose energy distributions do not extend to the energy range responsible for the optical synchrotron emission. More likely, the obtained optical limits in Table 2.8 are only slightly above the actual PWN surface brightness. Therefore, just a slightly deeper optical observation may allow one to detect the outer/inner arc (and other bright elements of the inner PWN), while much deeper optical observations are needed to detect the emission from the extended Vela PWN. However, owing to the presence of background/foreground emission from the SNR as well as numerous bright stars in the field, even longer exposures would hardly help to detect the optical PWN — neither its X-ray-bright central part nor the radio-bright outskirts. To get rid of the contaminating emission, one could observe the field at UV wavelengths, where most of the field stars should be much dimmer. However, the appreciable extinction toward the Vela PWN (AV ≈ 0.17) would still require a long exposure30. Observing in polarized optical light can be more promising. Since the synchrotron emission from the PWN should be highly polarized (as confirmed by the radio observations), polarimetry observations would allow one to minimize the contamination from field sources and provide a clean image of the PWN. Polarimetry observations of the Vela pulsar field have been recently obtained by Wagner and Seifert (2000), but they did not yield a conclusive result. Deeper, higher-resolution, observations are needed to unveil extended polarized emission from the PWN. As for the X-ray observations, there are several promising directions that one could pursue. It is interesting to investigate the connection between the Vela PWN and radio bright Vela-X region (which once thought to be due to the jet of the Vela pulsar) by mapping the brightness distribution and spectral properties of the emission from Vela-X region and the region between the PWN and the radio bright filament of Vela X (§2.4.4.1). This could be done with Chandra ACIS-I which offers a larger field-of-view than ACIS-S and good spatial and spectral resolution or with XMM EPIC. Deep observations (∼ 500 ks) of the Vela PWN with Chandra ACIS would allow us to trace spectral changes along the outer jet and resolve the structure of a fainter and more diffuse outer counter-jet (§2.4.3). With such a long exposure it would become possible to measure the blob speeds in the outer counter-jet and better constrain the orientation of the jets and the flow speed(s). Finally, along with the Crab PWN, the Vela PWN is one of the best targets for future X-ray polarimetry missions.

30Current limit on the PWN surface brightness in NUV is 0.8 µJy arcsec−2 at 2300 A˚ (achieved in a short 6 ks exposure; §2.3.1.1). 99

Chapter 3

Chandra observations of pulsars and PWNe.

Thanks to Chandra and XMM, more than 30 PWNe have been detected in X-rays (as of March 2004; e.g., Kaspi, Roberts & Harding 2004). The number of pulsars with associated PWNe has finally become sufficiently large to permit the statistical analysis of their X-ray properties. Instead of using various published results on PWNe observed with different X-ray telescopes (e.g., Possenti et al. 2001), we retrieved the data on 35 pulsars/PWNe (see ) from the Chandra archive and reduced the data following the same procedure in each case. This uniformly analyzed sample of PSRs/PWNe, each of which was observed with the same detector (i.e. Chandra ACIS), should provide more accurate relations between the pulsar and PWNe properties than the previously obtained relations (e.g., Possenti et al. 2001, Gotthelf 2003, and references therein). In this chapter we report the results of such analysis and systematize our current empirical knowledge about the X-ray properties of PWNe and powering them pulsars.

3.1 Overview of the observations. Data reduction.

Table 3.1 shows the summary of PSR/PWNe observations that have been re- trieved from the Chandra archive to perform a uniform comparative analysis. In addi- tion to PSRs/PWNe, we also used the described above results on the Vela PSR/PWN and numerous published Chandra results on the Crab PSR/PWN (e.g., Mori et al. 2004, and references therein).

3.1.1 Images. The diversity of PWN morphologies is demonstrated in Figure 1.4 which shows adaptively smoothed ACIS images of 20 selected PWNe. We see that some PWNe exhibit already familiar arc-like (or toroidal) structure(s) (panels 1,2,3,4,5,6,9 and 11), others have elongated morphology (presumably stretched along the direction of the pulsar proper motion), while the rest show more complex structure (8,12,16 and 20). The jets appear to be a common PWN element (1,2,3,4,6,9,11,15 and 17). We measured count rates of PWNe/PSRs listed in Table 3.1 and plotted the PWN/PSR count rates versus each other and each of them versus pulsar spin-down power E˙ (Figs. 3.1–3.3). The pulsar extraction region is defined as a circle that contains 90% of pulsar counts at 1 keV. The background for the pulsar spectrum is taken from an annulus surrounding the pulsar extraction region. The PWN region has been defined as a region where the PWN emission noticeably brighter than the underlaying background. Note, that such simplistic definition may lead to inaccurate estimate of the PWN flux (only part of the 100 62 56 PWN − − ray src. α γ -ray src. -ray src. -ray src. γ γ γ Comment a 8 3C396 kpc 1 − ˙ E d erg s 34 ) ˙ P 2 P/ Age ( s kyrs 10 P c 5 6 0.089 153 51 3.8 5 MSH 15 5 0.406 1.6 230 6 5 0.682 1114 0.12 1.8 Guitar, H . 2. 0.016 5.0 48000 49.4 3 0.143 618 4.92 0.151 1.2 1.5 1800 4.2 70 0.050 1.6 15000 49.4 4 0.197 536 3.0 0.73 5 . 6 0.385 111 3.81 0.288 . 1 0.066. 2 5.4 0.039 107 2700 3.2 374 3.1 3C58 CTB80, 3 IC443 1 b 51 0.135 0.137 2.9 2.9 1200 1200 6 5 1 1.244 2770 0.015 1.4 not PSR? 21 0.1025 0.125 17.4 0.154 15.5 113 340 260 23 2.3 1 5.11 2 1.36 Duck PWN 0.069 not PSR? 8.1 1600 6.5 near RCW103 3 0.065 23.4 640 5 1 31 0.096 33.7 200 6.2 MSH 11 1 0.387 2993 0.14 2.4 11 0.2670 0.101 20.3 21.3 43 280 3 3.9 W44 2 0.3240 0.72 830 21 Kes75 0 10 EGRET src. 3(?) 15 0.036 168 290 4.5 . − . . ± ± ± ± ± ± ± ± ± ± 1(?) 0 ± ± ± ± ± ± ± ± ± ± ± ± ± 0 0 ± ± ± ± ± ± ± ± PSR 5 6 . ± 3 4 7 9 6 . C < ± . . . . < 4 cts ks . 5 7 6 1 7 127 . . . 3 65 5 150 77 107 9 2 17 70 1490 174 189 8 4 69 3 221 3 13 1 b 1 5 124 1 21 2 37 0 1 9 5 5 3 11 1 2 5 1 19 1 2 1500 70 − ± ± ± ± ± ± ± ± ± ± ± d 10 keV band ± ± ± ± ± ± ± ± ± ± ± ± PWN − 9 9 − . . Chandra C cts ks 1.2 962 1.1 143 0.5 21 1.8 8 0.1 130 0.4 16 0.90.3 2485 668 0.3 27 0.3 126 − − − − − − − − − − ACIS count rate in 0.1 3613 – 4 2858 – G320.4 11 24 3 44 26 69 2715 52 – 684 5916 G292.0+1.8 300 69105850 N157B 661 – 2 5055 – 84 0258 G29.7 1925 G11.2 6127 G292.2 0604 – 13 − − − − − − − − − − − − − − − − Chandra 126 J1124 754760 B1509 G189.1+3.0 273 753 B1757 123 J1617 757 B1706 748 J1846 752 B1055 780 J1811 755 J2225+6535 – 1 19831958 J1930+1852 J1856+0113 G54.1+0.3 G34.7 279 2011 B1813 2830278335133854 B1823 J0537 J1509 J1913+1011 – 27962010 J0538+2817 B0628 15 19552787 J2229+6114 G327.1 25 1989 J1740+1000 – 34 1740 B0540 3693 G21.5 1988 G39.2 10362833 J1119 19652800 G0.9+0.1 B0656+14 22 G326.3 – 112 4382 J0205+6449 G130.7+3.1 382 2782 G291.0 2764 3EG J1835+59181984 B1951+321037 G69.0+2.71986 505 – J1837 G74.9+1.2 47 ObsID PSR SNR – observed – no PWN is seen or it is so small and faint that can hardly be discernable from the pulsar emission; correspondingly, the PWN – distance (as estimated from parallax, PSR dispersion measure etc.) – the pulsar within PWN is hardly discernable, or there are multiple candidates Table 3.1 Pulsars and PWNe observed with a b c d count rate (flux) cannot be accurately measured with the data available. 101

PWN flux is accounted for) for the cases when the PWN is faint and there is a bright underlaying background from the host SNR.

Figure 3.1 PWN count rate (in the 0.1−10 keV band; Table 3.1) versus pulsar spin-down flux E/˙ 4πd2.

Although these empirical plots may not carry obvious physical information (cf. other plots below), they can be used by the observers to get a rough estimate of count rates expected from other PSRs/PWNe, when E˙ is known from pulsar observations in radio or when only one of the count rates (PSR or PWN) is known. Note that although the correlations are obvious in these plots, each of the plots shows a large dispersion with several outstanding data points. For instance, the PWN in G29.7-0.3 (Fig. 3.1) and the associated PSR J0538+2817 (Fig. 3.2) are outstandingly bright if the assumed distance to the objects is correct. However, since the distance is very uncertain (this uncertainty is not included in the error bars shown in the figures), decreasing it by a factor of 2 − 3 would bring these outstanding data points closer to the rest of the data points. There are also several pulsars that are underluminous in X-rays (e.g. B1813−36 and J1913+1011; shown by the upper limits in Fig. 3.2), perhaps due to unfavorable orientation of the emission beam with respect to the observer. Another unaccounted factor that contributes to the dispersion of the data points in Figs. 3.1–3.3 is the different amount of interstellar absorption for different objects. 102

Figure 3.2 Pulsar count rate (in the 0.1−10 keV band; Table 3.1) versus pulsar spin-down flux E/˙ 4πd2. 103

Figure 3.3 Pulsar count rate versus PWN count rates (in the 0.1−10 keV band).

3.1.2 Spectra. To account for varying absorption and extract more physical parameters for the objects in Table 3.1, we extracted spectra for PSR and PWN components (separately) and performed spectral fits for each object in Table 3.1. To automatize this procedure, a set of TCL and UNIX shell scripts was developed and run on each ObsID from Ta- ble 3.1. These scripts made extensive use of CIAO v.2.2.1 and XSPEC v.11.2. The data reduction included the correction of the ACIS data for charge transfer inefficiency with tools provided by the ACIS Instrument Team of Penn State University (Townsley et al. 2000). The gain-map calibration was re-applied according to standard CIAO version 2.2.1 processing procedures (using ver. 2.10 of the CALDB calibration files), and only events with standard ASCA grades (02346) were retained. Before fitting models to the spectral data with XSPEC 11.2, the ACIS ABS correction was applied to account for the continuing decrease in low-energy sensitivity of the ACIS detectors due to contamination buildup on the ACIS filters 1. The spectral fits with the absorbed PL model were carried out in several energy bands: 0.5 − 8 keV (nH is allowed to be a free parameter) and 2 − 8 keV (or 3 − 8 22 −2 keV) with nH being frozen at 10 cm . The advantage of the first energy band is a large number of counts available for the fit while the disadvantage is the wrong best fit values for the absorbed PL model when a soft thermal component (which is currently

1see http://heasarc.gsfc.nasa.gov/docs/software/lheasoft/xanadu/xspec/models/acisabs.html 104 not subtracted) is present in the pulsar spectrum or the amount of absorption varies across the PWN image2. In the other band the fit is not sensitive to the actual (often 23 −2 unknown) value of nH (unless nH ∼> 10 cm ) and to the presence of the thermal component. Naturally, this comes at a price of smaller number of counts available for fitting than in the 0.5 − 8 keV band and hence the number of objects that are bright enough to permit spectral fitting drops down. Therefore, it is important to expand the sample of X-ray bright PWNe by observing SNRs with plerionic radio morphologies (see §1.1.3 and Fig. 1.3 from Chapter 1).

3.2 Correlations between pulsar and PWNe properties.

The results of the spectral fits are summarized in Figures 3.4–3.10. Here we un- derline several interesting points that follow from these figures. For instance, Figures 3.4 and 3.5 show a strong correlation between the PWN X-ray luminosity and pulsar spin- down power. Such a correlation was first found by Seward & Wang (1998) based on the Einstein Observatory data (§1.2.2). The superior quality of the Chandra data allows us to determine the correlation law much more accurately. The slope of the observed correlation is steeper than it follows from a simple one-zone (isotropic, no cooling) wind models (ΓPWN = ΓPSR/2; Chevalier 2000). Even stronger correlation is observed between the PWN luminosity and pulsar luminosity (Fig. 3.6). The precise luminosity measurements accounting for the faint PWN emission blended with the SNR background and spatially resolved spectroscopy of PWNe can help to develop more realistic PWN models which would account for particle energy losses and anisotropy of the pulsar wind and evaluate particle injection rates. Analyzing the spectra of nine pulsar/PWN systems, Gotthelf (2003) reported a correlation between the slope of the non-thermal component in the pulsar spectrum and the slope of the synchrotron spectrum emitted by the PWN. Using a different data reduction and extraction technique (e.g., different energy bands, region definitions) and expanding the pulsar/PWN sample, we confirm such a correlation (see Fig. 3.7) but find a correlation law different from that reported by Gotthelf (2003). This can be due to a different choice of the source and background regions, energy bands, spectral binning, and still imperfect “pile-up” correction algorithms. We find that, on average, the PWN and PSR spectral indices are closer to each other than suggested by Gotthelf (2003). Determining the functional form of the correlation can put strong constraints on the poorly understood mechanisms of particle acceleration in the pulsar wind. For instance, the stochastic acceleration by magnetosonic waves (Achterberg 1991) would preserve the slope of the injected particles spectrum, which could explain the observed correlation. Our analysis does not confirm the reported correlation (Gotthelf 2003) between the PSR spectral index and E˙ (cf. Fig. 3.8 and Fig. 2 from Gotthelf 2003). We also calculated the luminosities of the pulsars from Table 3.1 and plotted them versus the pulsar’s E˙ (Figures 3.9 and 3.10). The slope of the correlation in Figure 3.9 (where the pulsar’s luminosity is calculated in the 0.5 − 8.0 keV band) is similar to

2In these cases fits with two- or more component models are required and hence in each case the data should be individually (manually) investigated. 105

Figure 3.4 PWN luminosity (3 − 8 keV) versus E˙ .

Figure 3.5 PWN luminosity (0.5 − 8.0 keV) versus E˙ . 106

Figure 3.6 PWN luminosity (3 − 8 keV) versus pulsar luminosity (3 − 8 keV).

Figure 3.7 Pulsar photon index versus PWN photon index. 107

Figure 3.8 The lack of correlation between the pulsar photon index and E˙ .

that reported by Becker & Trumper (1997; shown by the solid line in Fig. 3.9). In this case the luminosity includes the contribution of the thermal spectral component emitted from the NS surface (see §1.1.1 and 1.2.3). When the pulsar luminosity is calculated for the 2 − 8 keV band (Fig. 3.10), the slope of the correlation is significantly steeper than that in Figure 3.9. This may reflect different dependencies for thermal and non-thermal pulsar luminosities on pulsar’s E˙ . The results reported in this Chapter are preliminary. It is imperative to further expand the PWN sample and look for correlations between other parameters (e.g., PWN X-ray luminosity vs. pulsar age, period and period derivative) and connections between the PWN spatial structure and the host SNR morphology. When available, the results obtained from Chandra and XMM data should be compared. To improve the quality and significance of the results, a more carefull evaluation of numerous selection and systematic effects (e.g., uncertainties in pulsar distances and NH values, pile-up in bright pulsars, nonuniform SNR background, faint PWN emission, etc.) should be carried out. 108

Figure 3.9 Pulsar luminosity (0.5 − 8.0 keV) versus E˙ .

Figure 3.10 Pulsar luminosity (2 − 8 keV) versus E˙ . Part II

Thermal and magnetospheric emission from neutron stars.

109 110

In Part II of this thesis I describe observations of two middle-aged pulsars (Geminga and B0656+14; Chapters 4 and 5) and an old millisecond pulsar J0437-4715 (Chapter 6). These objects exhibit quite different X-ray and optical properties (e.g., spectra and pulse profiles). Spin-powered pulsars show highly pulsed emission from the radio to γ-rays, arising from narrow acceleration zones in their active magnetospheres. Measuring the slope of the non-thermal spectrum and non-thermal pulsations from optical to X-rays improves our understanding of pulsar magnetospheres. In the UV to soft X-ray band, however, thermal emission from the surface can contribute significantly for middle-aged pulsars, whose characteristic ages are in the range of 104—106 yr. Spectral and timing measurements can isolate these two components, allowing a measure of the surface spec- trum and thermal luminosity. Such measurements can constrain the surface composition and, by measuring thermal emission as a function of age, can probe the equation of state of matter at supranuclear densities in the neutron star (NS) core. I also describe the Chandra ACIS observation of the enigmatic central source RX J0852.0–4622 in the Supernova Remnant G266.2−1.2 (Chapter 7). This object appears to be a close relative of another CCO in the Supernova Remnant Cas A. Currently, there is no agreement on the nature of CCOs (see §1.3.4). Therefore, it is important to increase the small number of known CCOs and thoroughly study the X-properties of the brightest candidates, one of which is RX J0852.0–4622. 111

Chapter 4

HST and XMM observations of the Geminga pulsar.

In this Chapter we describe the results of HST and XMM observations of the famous Geminga pulsar. We provide a detailed description of the data reduction tech- nique which is also used to analyze the data from similar observations of the Vela and B0656+14 pulsars (see §2.3.1 and §5.2).

4.1 Introduction.

Observations of spin-powered pulsars with the Chandra and XMM-Newton X-ray observatories have begun to reveal much about the thermal component (see Pavlov, Za- vlin, & Sanwal 2002 and Kaspi, Roberts, & Harding 2004 for recent reviews). However, since typical effective temperatures of middle-aged pulsars are as low as ∼ 20–100 eV, and interstellar absorption severely attenuates the flux below ∼ 0.1 keV, the X-ray obser- vations of these objects lie well out on the Wein tail of a surface thermal spectrum. Two issues then complicate the interpretation. First, surface composition can dramatically affect the X-ray flux (Romani 1987; Zavlin & Pavlov 2002) with light element atmosphere leading to a large Wien excess. Second, any surface temperture inhomogeneities will also complicate the spectrum, with hot spots disproportionally important in the high energy (X-ray) tail. For these reasons, comparison of the X-ray results with UV emission from the Rayleigh-Jeans side of the thermal bump is particularly valuable.

4.2 Previous observations of Geminga.

Discovered in 1972 by the SAS-2 satellite (Fichtel et al. 1975), this object had been known only as a γ-ray source until it was detected in X-rays by the Einstein observatory (Bignami, Caraveo, & Lamb 1983) and associated with a faint (V ≈ 25.5) optical counterpart (Bignami et al. 1987, 1988; Halpern & Tytler 1988). The discovery of a period P = 237 ms in X-rays with ROSAT (Halpern & Holt 1992) and γ-rays with Compton Gamma-ray Observatory (Bertch et al. 1992) proved the source to be a spin- powered pulsar, with a characteristic age τ ≡ P/(2P˙ ) = 342 kyr and spin-down energy loss rate E˙ = 3.3 × 1034 erg s−1. Contrary to most spin-powered pulsars, Geminga is not a strong radio source. Detection of pulsed radio emission at 102 MHz was claimed by Malofeev & Malov (1997), Kuz’min & Losovskii (1997) and Shitov & Pugachev (1997), but the pulsar has not been detected at other frequencies (e.g., McLaughlin et al. 1999). ROSAT, EUVE, and ASCA observations have established that the X-ray spec- trum of Geminga consists of a soft thermal component, emitted from the NS surface, and a nonthermal component, presumably generated in the pulsar magnetosphere (Halpern & Wang 1997; Jackson et al. 2002). Recent observation of Geminga with XMM-Newton 112 have shown an extended emission resembling a bow-shock nebula (Caraveo et al. 2003). From a two-component, blackbody (BB) plus power-law (PL), fit of the phase-integrated XMM-Newton spectrum, Zavlin & Pavlov (2004) found a temperature Tbb ≈ 0.5 MK for the thermal component and a photon index Γ ≈ 2 for the magnetospheric component. The X-ray pulse profile shows a strong dependence on energy, changing from a single broad peak at E ∼< 0.8 keV to a double-peak structure at E ∼> 2 keV. The shape of the Geminga’s optical spectrum remains controversial. Based on photometry with a few broad-band filters, Bignami et al. (1996) proposed a broad emis- sion feature around λ ∼ 5000 A,˚ superimposed on a Rayleigh-Jeans thermal spectrum (see also Mignani, Caraveo, & Bignami 1998), and interpreted the feature as an ion cy- clotron line emitted from the NS atmosphere. Martin, Halpern, & Schiminovich (1998) reported a possible broad dip over 6300–6500 A˚ in a flat (Γ ≈ 1.8) spectrum spanning 3700–8000 A,˚ but the spectrum was severely contaminated by the sky background. Har- low, Pavlov, & Halpern (1998) detected Geminga in two near-IR bands, which proved that the spectrum grows toward lower frequencies, similar to another midlle-aged pul- sar B0656+14 (Koptsevich et al. 2001). Overall, it is clear that the optical spectrum is predominantly nonthermal, perhaps with a hint of a Rayleigh-Jeans component at ˚ λ ∼< 3000 A. Optical pulsations of Geminga were (marginally) detected in the B band only (Shearer et al. 1998). The similarity between the optical and γ-ray pulse shapes supports the conclusion on the nonthermal origin of the optical emission. Based on three HST WFPC2 observations, Caraveo et al. (1996) found Geminga’s parallax of 6.4 ± 1.7 mas, corresponding to d ≈ 160 pc. The reanalysis of these data together with fourth WFPC2 observation shows that the result is not reliable because the exposures were too short to determine the Geminga’s positions with a needed accuracy (Pavlov et al. 2004, in preparation). Therefore, the distance to Geminga is currently unknown; we can only crudely estimate the range of possible distances, d ≈ 100–400 pc, with the upper limit determined from the requirement that the optical through γ- ray luminosity of the nonthermal radiation does not exceed the spin-down power E˙ (cf. Halpern & Ruderman 1993). In this paper we will scale the distance to d = 200 pc. Geminga has not been observed in the far-UV range where one could expect ther- mal radiation from the NS surface to take over the apparently nonthermal radiation that prevails in the optical. Moreover, pulsations of Geminga have not been observed shortward of ∼ 4000 A,˚ while such an observation would allow one to study the transfor- mation of the pulse profile in the transition from the nonthermal to thermal regime and elucidate the nature of the Geminga’s radiation in the optical-UV range. To measure the spectrum and pulsations in the ultraviolet, we carried out an imaging observation with NUV-MAMA and a spectral observation with FUV-MAMA, both in TIME-TAG mode.

4.3 Optical/UV observations with HST

4.3.1 Photometry with STIS/NUV-MAMA. Geminga was observed with the STIS NUV-MAMA on 2002 February 27 (start date is 52, 332.4340 MJD UT). The broad-band filter F25SRF2 (pivot wavelength 2299 113

A,˚ FWHM 1128 A)˚ was used in this imaging observation to minimize the contribution of geocoronal lines. The data were taken during four consecutive orbits. To avoid possible additional errors associated with the pipeline subtraction of the strong dark current background (see § 7.4.2 of the STIS Instrument Handbook [IHB]1), we reprocessed the “raw” NUV-MAMA images repeating all standard calibration pipeline steps except for this subtraction. As an output, we obtained four flat-fielded “low- resolution” images (1024 × 1024 pixels; plate scale 000. 0244 pixel−1). The target was detected in each of the four exposures. To increase the signal-to-noise ratio, S/N, we combined the images from the four exposures into a single image using the STSDAS2 task “mscombine”. From the sharpness of the source counts distributions for the two point sources detected, Geminga and star G (see Fig. 4.1) we conclude that the images are aligned well enough for photometric purposes. (Slight apparent elongations of the images of the two point sources, in different directions for Geminga and star G, are likely caused by nonuniformity of the background.) We measure the background, which is dominated by the detector dark current, in the annulus with the inner radius of 40 pixels and outer radius of 55 pixels, centered on the source (X = 539.5 pixels, Y = 540.5 pixels). The mean background count rate within the annulus is 1.59 × 10−3 counts s−1 pixel−1. To find an optimal aperture radius, we measured the number of source counts, Ns = Nt − Nb (where Nt is the total number of counts, and Nb is the number of back- ground counts estimated by scaling the mean background in the annulus to the aperture area), and its uncertainty, δNs, in apertures with radii of about 2, 3, 4, 5, 6, and 7 pixels (see Table 4.1). To evaluate the background uncertainty needed for calculating δNs, we put each of the apertures at 15 positions randomly distributed over the annulus, measured the number of background counts within the aperture for each position, and calculated the root-mean-square, δNb, of the differences between this number and the mean background scaled to the aperture area. The uncertainty of the source counts can 2 1/2 then be calculated as δNs = [Ns + δNb (1 + 1/15)] for each of the apertures. From Table 4.1 we see that the dependence of S/N (= Ns/δNs) on aperture radius has a flat maximum at a level of S/N ≈ 35 at r ≈ 3–6 pixels. We also measured the numbers of counts in the image combined from the au- tomatically processed images (with the dark current subtracted), performing standard aperture photometry with the IRAF task “phot” from the “digiphot” package3. A good agreement with the results obtained with the direct measurements of the total (dark current plus sky) background (e.g., Ns ± δNs = 1821 ± 51 vs. 1808 ± 50, for the 4- pixel-radius aperture) shows that the pipeline subtraction of the dark current does not introduce substantial errors in this case.

1http://www.stsci.edu/hst/stis/documents/handbooks/currentIHB/stis ihbTOC.html 2Space Telescope Data Analysis System; http://www.stsci.edu/resources/software hardware/stsdas 3http://stsdas.stsci.edu/gethelp/pkgindex noao.html 114

Figure 4.1 NUV-MAMA image of the field around the Geminga pulsar (at the center of the image). The only other point source in the field is “star G” (e.g., Halpern, Grindlay, & Tytler 1985) used for acquisition. The inset shows brightness contours in the 200. 4×200. 4 region centered on Geminga.

Table 4.1 Numbers of NUV counts for different extraction aperture sizes

a b c ¯ d d rs Nt Nb δNb Ns δNs S/N² ¯ C Fλ hFλi 1.95 1464.65 215.426 40.2 1249.23 54.54 22.90 0.496 0.222 1.26 1.33 2.99 2119.58 502.660 21.8 1616.92 46.08 35.08 0.566 0.251 1.45 1.50 3.95 2688.26 879.655 26.1 1808.61 50.35 35.92 0.628 0.253 1.47 1.51 4.98 3357.36 1400.27 35.2 1957.10 57.26 34.18 0.691 0.249 1.46 1.49 5.97 4115.12 2010.64 35.4 2104.48 58.66 35.87 0.716 0.259 1.51 1.55 7.02 4950.36 2782.58 51.2 2167.78 70.45 30.77 0.741 0.257 1.50 1.53

aRadius of the extraction aperture in pixels. bNumber of background counts within the extraction aperture. cSource count rate corrected for the finite aperture in counts s−1. dMean spectral flux (see eqs. 4.2 and 4.3) in units of 10−18 ergs cm−2 s−1 A˚−1. 115

The source spectral flux Fλ is connected with the number of source counts in a given aperture by the integral relation Z

Ns = t RλλFλ²λ dλ , (4.1) where t is the exposure time, Rλ is the integrated system throughput, including the 4 Optical Telescope Assembly and filter throughputs , and ²λ is the wavelength-dependent encircled energy fraction. One can estimate an average flux in the filter passband defined as either ¯ Ns Fλ = R (4.2) t Rλλ²λ dλ or Ns hFλi = R , (4.3) t²¯ Rλλ dλ where² ¯ is in average encircled energy fraction in the filter passband, and Ns/(t²¯) = C is the source count rate corrected for the finite aperture. We calculated the average spectral fluxes in both ways (see Table 4.1) using the ²λ values measured by Proffitt et al. (2003) ¯ −18 for several aperture radii. We see that the mean fluxes, Fλ ' hFλi ' 1.5 × 10 ergs −2 −1 ˚−1 cm s A are close to each other for r ∼> 3 pixels. The uncertainty of these values, ∼ 10%, is mostly due to systematic errors in the encircled energy fraction. Another way to evaluate the flux is to assume some form for the spectral flux Fλ and determine its normalization using equation 4.1. We approximate the spectral flux in −α −0.4A(λ)E(B−V ) the F25SRF2 passband as an absorbed power law: Fλ = F2299(λ/2299 A)˚ 10 , where F2229 is the intrinsic source spectral flux at the pivot wavelength [it coincides with ¯ Fλ in the special case α = 0, E(B−V)=0], and A(λ) is the ultraviolet extinction curve (Seaton 1979). The color index, E(B−V) is poorly known. An estimate based on the hydrogen column density found from the X-ray fits gives E(B−V)' 0.03; below we will adopt E(B−V)=0.01–0.07 as a plausible range. We calculated the dependencies of F2299 on the spectral slope α in a reasonable range 0 ≤ α ≤ 4 for several values of E(B−V), based on the Ns values measured in the 4-pixel radius aperture. (see Fig.4.2). We see that, at given E(B−V), F2299 varies with α by up to 20%. We estimate the uncertainty of the F2299 values at given α and E(B−V) as ≈ 8%–10%, mostly associated with unpre- dictable changes of the MAMA imaging PSF between individual observations that cause systematic uncertainties of ²λ (see Profitt et al. 2003 and §16.1 of IHB).

4.3.2 FUV Spectrum. Geminga was observed with the STIS FUV-MAMA on 2002 February 26 (start date is 52, 331.2391 MJD UT). The low-resolution grating G140L (which covers the wavelength interval ≈ 1150–1700 A)˚ with the 5200 × 000. 5 slit was used. The data were taken during four consecutive orbits (including the target acquisition). We used a nearby field star G (V=21.3; Fig. 4.1) as the acquisition target and applied a 400. 9 offset, deduced

4We corrected the throughputs supplied with the data for the time-dependent sensitivity loss (see http://www.stsci.edu/hst/stis/calibration/reference files/tds.html). 116

Figure 4.2 Model flux F2299 (see text) versus PL index for different values of E(B-V). 117 from the positions of Geminga and the acquisition star measured in the archival HST images, which places Geminga within 000. 1 of the slit center. The total scientific exposure time was 10,674 s. For each exposure, we processed the raw “high-resolution” images (2048 × 2048 pixels; plate scale of 000. 0122 per pixel — see §11 of the STIS IHB) using the calibration files available on 2003 July 1. As an output, we obtained flat-fielded low-resolution (1024×1024 pixels; plate scale 000. 0244 pixel−1; spectral resolution 0.58 A˚ pixel−1) images and used them for the spectral analysis. The processed images show a nonuniform detector background that consists of a flat (constant) component and the so-called “thermal glow” component (Landsman 1998) that dominates over most of the detector area and grows with increasing the FUV- MAMA low-voltage power supply (LVPS) temperature (the average LVPS temperatures were 38.45, 39.67, 40.89, and 41.62 C in the four consecutive orbits of our observation). The thermal glow is the strongest in the upper-left quadrant of the detector, where the dark count rate can exceed the nominal value, 6 × 10−6 counts s−1 pixel−1, by a factor of 20. To reduce the contamination due to the thermal glow background, the source was placed close to the bottom edge of the detector (see Fig. 4.3).

Figure 4.3 Raw Geminga FUV spectrum. Boxes show approximate regions for the source and background extraction used in spectral analysis.

We find the spectrum centered at Y = 105 ± 2 pixels in each of the flat-fielded images (the centroid slightly varies with X), where X and Y are the image coordinates along the dispersion and spatial axes, respectively. Even at this location on the detector the background still exceeds the nominal value by a factor of 1.5–5, depending on the position along the dispersion axis. To improve S/N, we combined the images from four exposures into a single image using the STSDAS task mscombine. The Y -positions of the centroids differ by less than 3 pixels for different exposures and different wavelengths (X-positions). Accurate subtraction of the enhanced, nonuniform background (typical values are 1–3 ×10−5 counts s−1 pixel−1) is crucial to measure the spectrum of our faint tar- get. The spectral extraction algorithm implemented in the standard STIS pipeline (task X1D) does not adequately correct for the nonuniform background while extracting the spectrum of such a faint source and does not allow varying extraction box size with the position along the dispersion axis. Therefore, we used an IDL routine with additional capabilities of grouping and fitting the background and selecting an optimal extraction box size depending on the position along the dispersion axis (see Kargaltsev, Pavlov, & Romani 2004). 118

Table 4.2 FUV-MAMA counts and fluxes in λ-bins

a b λ-bin (A)˚ As Nt Nb δNb Ns δNs S/N hFλi ± δhFλi 1155−1187 9 238.321 157.25 17.15 81.07 19.9 4.1 13.8 ± 3.4 1248−1259 9 130.662 63.59 5.386 67.07 9.9 6.8 9.5 ± 1.4 1260−1270 9 110.939 50.73 5.234 60.20 9.5 6.4 7.6 ± 1.2 1271−1283 9 132.926 54.04 4.973 78.89 10.3 7.7 9.8 ± 1.3 1316−1332 7 130.296 57.19 8.140 73.11 12.0 6.1 7.1 ± 1.2 1333−1347 11 145.756 67.47 8.656 78.29 12.6 6.2 8.2 ± 1.3 1365−1378 11 96.5546 49.30 7.114 47.26 10.1 4.7 5.3 ± 1.1 1385−1402 11 123.641 62.01 4.823 61.63 9.3 6.6 6.8 ± 1.0 1403−1431 5 112.469 42.59 6.347 69.88 10.6 6.6 6.3 ± 1.0 1432−1471 5 155.827 53.05 6.981 102.8 12.4 8.3 7.7 ± 0.9 1472−1525 5 140.148 61.29 8.012 78.85 12.1 6.5 6.0 ± 0.9 1526−1702 5 258.505 155.07 9.386 103.44 14.0 7.4 5.1 ± 0.7 Summedc ... 1776.04 873.575 28.8 902.49 42.3d 20.9 6.76 ± 0.43e

aHeight of extraction box, in pixels. bAverage spectral flux and its statistical error, in units of 10−18 erg s−1 cm−2 A˚−1, corrected for the finite aperture. cValues for summed λ-bins. P dDefined as [ (δN )2]1/2. · i s,i ¸ P ³P ´1/2 ¡P ¢ eDefined as hF i ∆λ ± hδF i2∆λ2 ∆λ −1. i λ i i i λ i i i i 119

Since the source spectrum occupies only a small region on the detector, we do not attempt to subtract the background globally. Instead, we scan the count distribution within two strips, 36 ≤ Y ≤ 95 and 116 ≤ Y ≤ 175, adjacent to the source region, 96 ≤ Y ≤ 115. To obtain the spectrum with a sufficiently high S/N, we have to bin the spectrum heavily; after some experimenting, we chose 12 spectral bins (λ-bins; see Table 4.2). The bins chosen exclude the regions contaminated by the geocoronal emission (Lyα line and OI lines at 1304 A˚ and 1356 A)˚ and by an artificial background structure at λ ≈ 1379–1384 A,˚ Y ≈ 96–103. The bins outside the contaminated regions were chosen to have comparable S/N (≈ 6–8), whenever possible. For each of the λ-bins, we calculate the total number of counts, Nt, within the extraction boxes of different heights (one-dimensional apertures): As = 3, 5, 7, 9, 11, 13, 15, and 17 pixels, centered at Y = 106 for the first two λ-bins and at Y = 105 for the rest of the λ-bins. To evaluate the background, we first clean the background strips (see above) from outstanding (> 10−3 cts s−1 pixel−1) values (“bad pixels”) by setting them to local average values. Then, for each of the λ-bins, we fit the Y -distribution of the background counts with a first-order polynomial (interpolating across the source region), estimate the number Nb of background counts within the source extraction aperture As, and evaluate the number of source counts, Ns = Nt − Nb (Table 4.2). 2 The uncertainty δNs of the source counts can be evaluated as δNs = [Ns+δNb (1+ 1/2 As/Ab)] , where δNb is the background uncertainty in the source aperture. We binned the distribution of background counts along the Y -axis with the bin sizes equal to As and calculated δNb as the root-mean-square of the differences between the actual numbers of background counts in the bins and those obtained from the fit to the background. We calculated δNs and S/N for various extraction box heights and found the As values maximizing S/N for each λ-bin (see Table 4.2). We calculated the average spectral fluxes in the λ-bins defined as (cf. eq. 4.3) R Rλλ Fλ dλ C hF i = ∆Rλi = R i , (4.4) λ i R λ dλ R λ dλ ∆λi λ ∆λi λ where Ci is the source count rate in the i-th λ-bin corrected for the finite size of the source extraction aperture, and Rλ is the system response that includes the Optical Telescope Assembly throughput and accounts for the grating and slit losses and time-dependent sensitivity losses (Bohlin, 1999; see also §3.4.12 of the HST Data Handbook for STIS5 for details). The resulting flux values are given in Table 4.2, while the spectrum is shown in Figure 4.4. The total flux in the 1155–1702 A˚ range (∆λ = 547 A),˚ can be estimated as P P −1 −15 −1 −2 F ' ∆λ ( ihFλii∆λi)( i ∆λi) ' (3.72 ± 0.24) × 10 erg s cm , corresponding 2 28 2 −1 to the luminosity LFUV = 4πd F = (1.78 ± 0.11) × 10 d200 erg s . αλ We fit the spectrum with the absorbed power-law model, Fλ = F1500 (λ/1500 A)˚ × 10−0.4A(λ) E(B−V ). For plausible values E(B − V ) = 0.01, 0.03, 0.05 and 0.07, we found the power-law indices αλ = −3.29 ± 0.53, −3.43 ± 0.53, −3.56 ± 0.54 and −3.69 ± 0.54, −18 and the normalizations F1500 = 5.38±0.33, 6.25±0.38, 7.26±0.37 and 8.44±0.52×10

5http://www.stsci.edu/hst/stis/documents/handbooks/currentDHB/STIS longdhbTOC.html 120

Figure 4.4 The measured (absorbed) FUV spectrum of Geminga pulsar. The dashed line shows the best-fit absorbed BB model (T = 0.31 MK; R = 13d200 km; E(B-V)=0.03). 121

−2 −1 ˚−1 2 erg cm s A , respectively (Fig. 4.5); the corresponding χν values are 0.80, 0.81, 0.81, 0.82, and 0.83, for 10 degrees of freedom (d.o.f.). −4 The inferred slope αλ is close to that of the Rayleigh-Jeans spectrum, Fλ ∝ λ , suggesting that the observed radiation is thermal radiation from the NS surface. To esti- mate the NS surface temperature, we fit the absorbed blackbody model to the observed spectrum. Since the FUV fluxes are in the Rayleigh-Jeans part of the spectrum, the tem- perature values are strongly correlated with the radius-to-distance ratio (approximately, T ∝ d2/R2), as demonstrated by the confidence contours in the T -R plane (Fig. 4.6) For a typical NS radius R = 13 km and the assumed distance d = 200 pc, the inferred surface temperatures are 0.27 ± 0.02, 0.31 ± 0.02, 0.35 ± 0.02,. and 0.41 ± 0.02 MK, for 2 E(B − V ) = 0.01, 0.03, 0.05, and 0.07, respectively; the corresponding χν values are 0.90, 0.87, 0.85, and 0.85, for 10 d.o.f. An example of best-fit blackbody spectrum is shown in Figure 4.4, for E(B−V)=0.03 and E(B−V)=0.07.

4.3.3 NIR through FUV spectrum To compare the UV emission of Geminga with its NIR-optical emission, we plotted in Figure 4.7 the FUV-MAMA and NUV-MAMA spectral fluxes hFνi togeter with the fluxes at lower frequencies measured in eight broad passbands. Seven of these fluxes have been published previously (see caption to Fig. 4.7 for references), while the flux marked ‘555W’ in Figure 4.7 was measured in this work from a recent observation of Geminga with the HST Advanced Camera for Surveys (ACS). Geminga was observed with the Wide Field Channel (WFC) of the ACS on 2003 October 7 for 6296 s total exposure (3 HST orbits, two dither positions per orbit, two exposures per dither position) in the F555W filter (ACS ‘V filter’; pivot wavelength 5358 A,˚ FWHM 1235 A).˚ We combined the aligned, pipeline calibrated images from the three orbits into a single image and performed aperture photometry using the phot task from the IRAF apphot package. To extract the source counts, we used a circular aperture with a radius of 000. 15 (3 WFC pixels) which provides an optimal S/N≈ 36. For this aperture, the encircled energy fraction of 0.82 ± 0.04 was determined from the empirical PSF measured for six field stars with apertures varying from 2 to 25 WFC pixels. The source count rate was corrected for the finite aperture size and converted to average spectral flux using the conversion factor (inverse sensitivity), 1.974 × 10−19 erg cm−2 A˚−1 per count, for this observing mode6. The accuracy of the flux measurement, about 10%, is limited by the uncertainty in the encircled energy fraction and various systematic uncertainties. The flux we measured, hFνi = 0.17±0.02 µJy, is a factor of 1.6 lower than that measured by Bignami et al. (1996) from the HST WFPC2 observation of 1994 September 23 with a similar filter. We remeasured the WFPC2/F555W flux and obtained a value consistent with our ACS result within the uncertainties. With the new value for the F555W flux and the other NIR-optical fluxes, it is finally clear that the “cyclotron feature” in the Geminga’s spectrum (Bignami et al. 1996; Mignani et al. 1997) was likely a result of inaccurate photometry.

6see http://www.stsci.edu/hst/acs/documents/handbooks/DataHandbookv2/intro ch34.html#1896082 122

Figure 4.5 Confidence levels (67% and 90%) for the absorbed power-law model fit, for E(B-V)=0.01, 0.03, 0.05 and 0.07. 123

Figure 4.6 Confidence levels (67% and 90%) for the absorbed black-body model fit, for E(B-V)=0.03 and E(B-V)=0.07. 124

Figure 4.7 NIR through FUV spectrum of Geminga. The broadband fluxes were mea- sured with the HST NICMOS (F110W and F160W; Koptsevich et al. 2001), Subaru SuprimeCam (Ic and Rc; Komarova et al. 2003), HST ACS/WFC (F555W; this work), and HST FOC (F430W, F342W, and F195W; Bignami et al. 1996 and Mignani et al. 1997). The solid and dash-dotted lines show the fits with the absorbed blackbody + power-law model for E(B−V)=0.03 and 0.07, respectively. The model components are shown by the dashed and dotted lines (see text for details). 125

It is obvious from Figure 4.7 that the NIR through FUV spectrum of Geminga cannot be be described by a simple power-law model. We fit this spectrum with a two- component, power-law plus blackbody, model. Since the temperature and the radius-to- distance ratio of the blackbody component are strongly correlated in the Rayleigh-Jeans regime (TR2/d2 ≈ const), we have to fix one of these parameters in the fit. For the fixed R/d = 13 km/200 pc, we obtained T = 0.30 ± 0.02 MK, αν = −0.46 ± 0.12, F0 = 0.11 ± 0.02 µJy for E(B−V)=0.03, and T = 0.41 ± 0.02 MK, αν = −0.41 ± 0.13, 2 F0 = 0.12 ± 0.02, µJy for E(B−V)=0.07 (χν = 1.5 for 18 d.o.f. for each of the fits), where αν and F0 are the parameters of the power-law component: Fν = F0 (ν/1 × 1015 Hz)αν . Notice that the parameters of the blackbody component are virtually the same as obtained from the FUV-MAMA spectrum alone. The best-fit spectra and their components are shown in Figure 4.7. We see that the blackbody emission dominates 15 ˚ at ν ∼> 1 × 10 Hz (λ ∼< 3000 A), while the power-law (presumably magnetospheric) emission dominates at longer wavelengths.

4.3.4 Timing analysis of NUV and FUV data. For the timing analysis of the NUV-MAMA and FUV-MAMA data, we used the so-called TIME-TAG data files that contain the photon arrival times, recorded at a 125 µs time resolution, and high-resolution detector coordinates (see §4.3.2) associated with each of the events. We use 2688 NUV-MAMA events extracted from an aperture of 8 high-resolution pixels radius (includes 66% of source counts) and 1939 FUV-MAMA events extracted from the above-defined λ-bins with heights of extraction box varying from 14 to 22 high-resolution pixels (includes 46% of source counts). The arrival times are corrected for the Earth and spacecraft motions and transformed to barycentric dynamical times (TDB) at the solar system barycenter, using the STSDAS task “odelaytime”. The time spans of the FUV-MAMA and NUV-MAMA observations are 19,181 s and 19,785 s, respectively, with a gap of 84,041 s between the last FUV-MAMA event and the first NUV-MAMA event. The expected frequency of Geminga’s pulsations at the epoch of our observation, around 52,332 MJD, can be estimated from the previous timing observations in γ-rays and X-rays. The most recent ephemerides of Geminga were published by Jackson et al. (2002; J02 hereafter). These authors found a small glitch in the Geminga’s timing history and presented post-glitch ephemeris for a time interval of 50,382–51,673 MJD. Although our observation was taken 659 days after the end of that interval, extrapolation of this ephemeris to 52,332 MJD predicts the frequency, fJ02 = 4, 217, 608.6953 µHz, with a formal uncertainty of ±0.0013 µHz, that is about three orders of magnitude smaller than we can achieve in our relatively short observation (see below). Therefore, we adopt fJ02 as an estimate of expected frequency and look for pulsations in its vicinity, in a −1 fJ02 ± (2Tspan) frequency range. Since the longer time span, Tspan = 123, 005 s, of the joint FUV+NUV data set allows a tighter constraint on the pulsation frequency, we start from the analysis 2 of this data set. First, we apply the Zn test (Buccheri et al. 1983), calculating the 2 Zn statistic as a function of trial frequency in the range of fJ02 ± 4 µHz for n = 1 through 8, where n is the number of harmonics included. For each of the n values 126

2 examined, we found statistically significant pulsations, with frequencies of Zn maxima within (−0.3,+0.7) µHz around fJ02. The most significant result is obtained for n = 6: 2 maximum Z6 = 53.1 at f = 4, 217, 608.8 µHz; the probability to obtain this value by chance is 4 × 10−7. To better estimate the uncertainty of pulsation frequency, we also applied the odds-ratio method of Gregory & Loredo (1992; see also Zavlin, Pavlov, & Sanwal 2004) and found f = 4, 217, 608.3 (−0.9, +0.7) µHz for the median frequency and 68% uncertainties, and f = 4, 217, 608.8 ± 1.2 µHz for the mean frequency and standard deviation. Within the uncertainties, these frequencies virtually coincide with the frequency predicted by the J02 ephemeris. The expected frequency shift during ˙ the FUV+NUV observation, fTspan = 0.024 µHz, is much smaller than the frequency uncertainties in our measurement, which means that this observation is not sensitive to frequency derivative f˙. Since our spectral analysis has shown that the FUV radiation is predominantly thermal while NUV the radiation has a significant contribution from the magnetospheric component (see §4.3.3 and Fig. 4.7), one can expect different strength and shape of pulsations in the FUV and NUV bands. Therefore, we analyzed these two data sets separately. Since the frequency we measured from the FUV+NUV data is consistent with the J02 ephemeris, and an XMM-Newton observation taken 37 days later also suggests that the ephemeris may still be valid (see §4.4.2), we folded the times of arrival with the J02 ephemeris, choosing the same zero-phase epoch, 50,382.999999364 MJD. The folded (source plus background) light curve in the NUV-MAMA band, plotted in the upper panel of Figure 4.8, shows one broad (FWHM ≈ 0.8 in phase), flat-top peak per period, centered at φ ≈ 1.0. The most notable feature of the pulse profile 2 is the narrow dip at φ ≈ 0.45. The Zn test shows that the pulsations are statistically quite significant, with the main contribution coming from the fundamental frequency: 2 −5 Z1 = 22.3 corresponds to 1×10 probability of false result. The pulsed fraction, defined as the ratio of the number of counts above the minimum level to the total number of counts in the light curve, is about 28%, which corresponds to the intrinsic source pulsed fraction fp ≈ 40%. 2 The Zn test for the FUV-MAMA data set shows most significant pulsations for 2 n = 4: Z4 = 25.08 corresponds to 99.84% (3.2 σ) significance. The lower significance of the FUV pulsations, compared to the NUV pulsations, can be caused by a higher background in the spectroscopic mode. Since the thermal-glow background was growing with increasing the LVPS temperature in the course of our observation (see §4.3.2), we performed the timing analysis for various combinations of orbits and found that indeed the pulsations were more significant in earlier orbits. For instance, in the first two orbits 2 (Tspan = 7638 s, N = 844 counts) the most significant Z2 = 23.46 corresponds to 99.990% (3.9σ) significance. The four-orbit and two-orbit FUV-MAMA light curves are shown in the middle and lower panels of Figure 4.8. In the same panels we show the light curves for the background counts extracted from two boxes centered at Y = 180 and Y = 240 high- resolution pixels, with the same heights as used for extraction of the source events. The background light curves do not show statistically significant pulsations. Both the four- orbit and two-orbit source-plus-background light curves show a sharp, asymmetric dip at approximately the same phase as the NUV-MAMA light curve. A hint of a shallower dip, 127

Figure 4.8 UV light curves of Geminga plotted folded with the J02 ephemeris. Top: NUV-MAMA light curve, obtained using the data from all four orbits. The estimated average background level in the 20-bin light curve is 44.3 counts per phase bin. Middle: FUV-MAMA light curve, obtained using the data from all four orbits. Bottom: FUV- MAMA light curve, obtained using only the data from the first two orbits. The dashed lines with associated errorbars shows the corresponding background light curves (see text). 128 better pronounced in the two-orbit light curve, is seen at φ ≈ 0.95. The pulsed fraction in the observed (source + background) radiation is about 35% and 45% for the four orbits and first two orbits, respectively. The corresponding intrinsic pulsed fractions are rather high, about 60%–70%. It should be noted, however, that these values are rather uncertain because of the large statistical error of the minimum level.

4.4 X-ray spectrum and pulsations of Geminga

To better understand the UV spectrum and pulsations of Geminga, observations at X-ray wavelengths are particularly useful. The deepest observation of Geminga in X-rays was carried out with the XMM-Newton observatory on 2002 April 4–5 (orbit 425). The EPIC7-MOS and EPIC-pn instruments observed the pulsar for 101.4 and 71.4 ks of effective exposures, respectively. Two EPIC-MOS detectors were operated with Medium filters in Full Frame mode providing an image of a large area, r ∼ 140, with time resolution of 2.6 s. EPIC-pn was used in combination with Thin filter in Small Window mode which covers a 40.37 × 40.37 region and provides a 5.7 ms time resolution. First results of this observation have been reported by Zavlin & Pavlov (2004) and Caraveo et al. (2003, 2004). Here we briefly describe the X-ray spectrum and pulsations of Geminga, with emphasis on the properties most useful for the comparison with the optical-UV data.

4.4.1 X-ray spectrum The most detailed X-ray spectrum of Geminga was obtained with the EPIC-pn instrument. The EPIC-pn data, processed with the SAS package8 (v. 6.0.0), were used for the spectral and timing analysis. We extracted the source (plus background) pho- tons from a 4000-radius circle centered at the pulsar position, which contains about 88% of source counts. The estimated total source count rate (corrected for finite extrac- tion radius) is 0.813 ± 0.004 counts s−1 in the 0.2–10 keV range for single and double events (with photon-induced charge detected in a single CCD pixel and two adjacent pixels). The 0.2–10 keV phase-integrated spectrum was binned in 222 spectral bins with at least 40 source counts per bin. The detector response matrix and effective area were generated with the rmfgen and arfgen tools, respectively. Fitting this spectrum with a two-component, blackbody (BB) + power-law (PL), model, we find the blackbody tem- perature Tbb = 0.47 ± 0.02 MK and radius R = (17.0 ± 2.5) d200 km, which suggests that the thermal component originates from the NS surface. The PL component, with a pho- ton index Γ = 2.02 ± 0.05 dominates at energies E ∼> 0.6 keV and contains about 10% of pl 30 2 −1 the total luminosity in the 0.2–10 keV band, L0.2−10 keV = (2.6±0.1)×10 d200 ergs s ' −5 2 ˙ 7 × 10 d200E. Extrapolated into the optical domain, the PL component exceeds the observed optical fluxes by a factor of 100–500, which might be interpreted as a flattening of the pulsar magnetospheric spectrum at lower photon energies. The hydrogen column 20 −2 density derived from this fit is nH = (2.9 ± 0.2) × 10 cm .

7European Photon Imaging Camera. 8http://xmm.vilspa.esa.es 129

Although the two-component model cannot be rejected based on the overall fit 2 quality (χν = 1.11 for 217 d.o.f.; systematic errors in the EPIC-pn response not included), the fit residuals show some excess of observed counts over the best-fit model at higher energies, E ∼> 7 keV, indicating a harder PL spectrum. Indeed, fitting the high-energy tail (E > 2.5 keV) of the spectrum with a single PL model gives Γ = 1.56 ± 0.24, pl 30 2 −1 2 L0.2−10 keV = (2.2 ± 0.2) × 10 d200 erg s (χν = 0.98 for 30 d.o.f). The BB+PL fit with Γ fixed at this value is statistically unacceptable (χν = 2.95 for 219 d.o.f.). Therefore, we tried a three-component model consisting of soft (TS) and hard (TH) blackbody components and a PL component. With the PL parameters fixed at the values obtained from the best PL fit in the 2.5–10 keV band (Γ = 1.56, N = 5.5 × 10−5 photons cm−2 s−1 kev−1 at 1 keV), we obtain the following parameters for the thermal components: Ts = 0.49 ± 0.01 MK, Rs = (12.9 ± 1.0) d200 km, Th = 2.32 ± 0.08 MK, 20 −2 2 Rh = (46 ± 12) d200 m, and nH = (2.4 ± 0.2) × 10 cm (χν = 1.10 for 217 dof). Fitting the EPIC-MOS spectra obtained in this observations yields almost the same model parameters (discarding the EPIC-MOS events below 0.3 keV, where the responses of the MOS detectors are known very poorly). In the TS+TH+PL model the TS component can be interpreted as emission from the bulk of NS surface, the TH component can be ascribed to emission from smaller, hotter regions of the NS surface, and the PL component represents the magnetospheric radiation. Such an interpretation of the Geminga’s X-ray spectrum is in line with the re- sults obtained from Chandra and XMM-Newton observations of the other bright middle- aged pulsars, B0656+14 and B1055–52, whose X-ray spectra can also be described by the TS+TH+PL model with similar parameters (Pavlov, Zavlin & Sanwal 2002; Za- vlin & Pavlov 2004). However, the effective radius of the Geminga’s TH component is much smaller than those of B0656+14 and B1055–52 (0.5 and 0.8 km, respectively). Confidence contours for the temperature and radius of the TS component are shown in Figure 4.9. In the same figure we plotted the temperature-radius confidence contours obtained from the blackbody fit of the FUV-MAMA spectrum, for E(B−V)=0.03 and 0.07 (see §4.3.2 and Fig. 4.6). We see that at plausible values of interstellar extinction, E(B−V)∼< 0.07, the FUV contours lie at smaller radii (or much lower temperatures) than the X-ray contours. This means that the extrapolation of the thermal X-ray component into the UV-optical goes above the observed FUV flux, as demonstrated in Figure 4.10. Such behavior is in contrast to all other neutron stars observed in both X-rays and op- tical, for which such an extrapolation underpredicts the optical fluxes by a factor of 2–7 (see §4.5.1 for more discussion). If we adopt the above-described two-component (BB+PL) model, the discrepancy between the X-ray and FUV temperature/radius is even more pronounced, as demon- strated by the corresponding confidence countours in the upper left part of Figure 4.9 and the upper panel of Figure 4.10. We note, however, that the nH values correspond- ing to these contours, (2.4 ± 0.2) and (2.9 ± 0.2) × 1020 cm−2 for the TS+TH+PL and 20 −2 BB+PL models, respectively, significantly exceed the nH ' (1.1 ± 0.2) × 10 cm ob- tained from the ROSAT PSPC observations (Halpern & Wang 1997), which indicates a discrepancy between the PSPC and EPIC responses at low energies. If we fix nH at the best-fit PSPC value, the confidence contours shift to higher temperatures and lower radii (see the lower-right EPIC-pn contours in Fig. 4.9), overlapping the FUV contours. 130

Figure 4.9 Confidence contours (68%, 90% and 99%) in the temperature-radius plane ob- tained from fitting the EPIC-pn spectra (solid lines) with the TS+TH+PL and BB+PL models (labels near the contours). The TS+TH+PL contours were obtained at the fixed parameters of the PL component; nH was free for upper contours,while it was fixed at the value obtained from ROSAT data for the lower contours. All the model parameters were free for the EPIC-pn BB+PL contours. The dashed and dash-dotted lines show the confidence contours obtained from fitting the FUV-MAMA spectrum with a blackbody model for two values of the color index E(B−V). 131

For this nH, the FUV fluxes lie on the extrapolation of the best-fit X-ray TS compo- nent at E(B−V) ∼< 0.04 (see lower panel of Fig. 4.10). Since neither EPIC nor PSPC have been accurately calibrated for very soft spectra, systematic errors can substantially exceed the statistical errors, and the model parameters inferred from such fits may not be very accurate. Therefore, there still remains some uncertainty in the comparison of the X-ray (Wien) and UV (Rayleigh-Jeans) tails of the thermal spectrum. However, even with account for this uncertainty, Geminga exhibits a fainter UV-optical thermal radiation, relative to the soft X-ray radiation, than the other neutron stars for which such a comparison is possible (see §4.5.1). Figure 4.10 also shows that the continuation of the best-fit X-ray PL into the optical very strongly overpredicts the observed NIR-optical fluxes for the BB+PL model. However, the predicted and observed fluxes become marginally consistent if we use the PL component inferred from the E > 2.5 keV spectral tail.

4.4.2 X-ray pulsations

To study the X-ray pulsations of Geminga, we use the same EPIC-pn data (Tspan = 101.9 ks, epoch of the middle of the time span 52,369.2997 MJD). First, we measured 2 the pulsation frequency using the Zn and odd-ratio methods, for various energy bands and extraction radii, and found most probable frequencies in the range of 4,217,607.75– 4,217,607.96 µHz, with typical uncertainties of about 0.1 µHz for individual measure- ments. For example, the odds-ratio method applied for 42,170 events in the 0.23–4.0 keV band, extracted from 4000-radius circle, gives f = 4, 217, 607.85 ± 0.10 µHz for the mean frequency and standard deviation, and f = 4, 217, 607.86 (−0.05, +0.05; −0.16, +0.12; −0.24, +0.19) µHz for the median frequency and 68%, 90%, and 99% uncertainties. The most probable frequencies are consistently lower, by 0.1–0.3 µHz, than the frequency fJ02 = 4, 217, 608.0664 ± 0.0013 µHz predicted by the J02 ephemeris. However, since the differences do not exceed 3 σ uncertainties of our measurements, it is still possible that the J02 ephemeris is applicable at the epoch of the XMM-Newton observation. We have also directly checked the phase alignment of the light curves extracted from the XMM-Newton data with those observed by ASCA in 1999 October 5–11. The lower panel of Figure 4.11 shows the XMM-Newton light curve folded with the J02 ephemeris, in the energy band 0.5–2 keV (10,264 counts in 4000-radius aperture). The upper panel of the same figure shows the light curve obtained with the two ASCA GIS instruments (Texp = 207.8 ks, Tspan = 486.5 ks, epoch of the middle of the time span MJD 51,459.7356, 1,819 counts in 30-radius aperture) folded with the same ephemeris and in the same energy range. We see that not only the shapes of these light curves are virtually the same, but also their phases are in excellent agreement, within the phase uncertainty, ' 0.12, of the J02 timing solution propagated to the epoch of the XMM-Newton observation. Therefore, we will assume that the J02 ephemeris is still applicable in 2002 April and and use it to compare the light curves observed with different instruments. The background-subtracted light curves in the energy ranges 0.2–0.5 keV, 0.6– 1.0, and 2–8 keV are shown in Figure 4.12. In the 0.2–0.5 keV and 2–8 keV bands the radiation is dominated by the TS and PL components, respectively, while the 0.6–1.0 132

Figure 4.10 Near-infrared through X-ray spectrum of Geminga for different X-ray spectral models and different color indices. The solid lines show the best-fit (absorbed) spectra in the X-ray range and their extrapolations into the NIR-FUV range. The short-dash and dash-dot lines show the (soft) thermal and PL components, respectively, the dotted lines in three lower panels show the TH component (its contribution is negligible in the NIR- FUV range), and the long-dash lines present the unabsorbed total spectra. The crosses depict the measured NIR-FUV spectral fluxes (cf. Fig. 7). The hatched areas along the PL and thermal components in the NIR-FUV range demonstrate propagated uncer- tainties of the corresponding extrapolations. The upper panel shows a two-component (BB+PL) X-ray fit, while three lower panels show TS+TH+PL fits with fixed parame- ters of the PL component. The fit shown in the lower panel was obtained at a fixed nH value, while nH was a fitting parameter in three upper panels. (See text for more details.) 133

Figure 4.11 ASCA GIS and XMM EPIC-pn light curves in the 0.5–2 keV range folded with the J02 ephemeris. 134 keV band was chosen around the maximum of the TH component (see Fig. 4.10). The light curves were extracted from a smaller 3000-radius aperture and a shorter, 80.0 ks, time span (excluding intervals of strong background flares at the beginning and end of the observation) to reduce the background contamination and maximaze the signal- to-noise ratio. The nonthermal light curve (pulsed fraction fp = 34% ± 8%) shows two pronounced peaks per period, resembling the γ-ray light curve (albeit with smaller distance between the peaks) and a hint of a third peak, at φ ≈ 0.2. On the contrary, the TS light curve (fp = 30% ± 2%) is characterized by one broad peak per period (with small “ripples”, perhaps due to contribution from the PL and TH components). The 0.6–1.0 keV light curve shows the highest pulsed fraction, fp = 62% ± 5%, with one asymmetric peak, possibly comprised of several peaks associated with contributions from different components in this band (Fig. 4.10). The minimum of the TS light curve is approximately aligned in phase with one of the minima of the PL light curve, being shifted by ∆φ ≈ 0.1 from the sharp dips of the NUV and FUV light curves. (One should remember, however, that the shift can be caused by errors in phase alignment.) Examples of X-ray light curves for other energy ranges can be found in Zavlin & Pavlov (2004)9 and Caraveo et al. (2003, 2004). A more detailed discussion of the thermal and nonthermal light curves is presented in §4.5.1.

4.5 Discussion

The above-described results of the observations of Geminga show that both the NIR-optical-UV and X-ray emission are comprised of thermal and nonthermal compo- nents, with quite different spectra and light curves. In the following, we discuss the multiwavelength properties of these components separately.

4.5.1 Thermal component(s) of the Geminga’s spectrum It follows from §4.3.2 and §4.4.1 that thermal emission dominates in the Geminga’s spectrum at 4 eV ∼< E ∼< 0.5 keV. The observed FUV and soft X-ray spectra represent the Rayleigh-Jeans and Wien tails of the thermal spectrum emitted from the NS surface. The blackbody fits of the soft X-ray emission give the NS surface temperature in a range of 0.45–0.53 MK (≈ 39–46 eV), corresponding to effective radii of 21–8 km, at d = 200 pc (see Figs. 4.9 and 4.10). The uncertainty in these parameters is mostly due to the poorly calibrated responses of the EPIC detectors at low energies. Moreover, these temperatures are somewhat lower, and the radii larger, than those estimated from the previous ROSAT and EUVE observations (Halpern, Martin, & Marshall 1996; Halpern & Wang 1997). Since significant variations of the NS temperature and emitting area in a ten year span of these observations can hardly be expected, the discrepancy is most likely due to discrepant instrument responses at low energies. Therefore, we have to wait for more accurate EPIC (and PSPC) calibrations to measure the parameters more accurately.

9The inaccurate estimates of pulsed fractions given in Fig. 8 of Zavlin & Pavlov (2004) should be disregarded. 135

Figure 4.12 Background-subtracted light curves of Geminga in UV (NUV-MAMA + FUV-MAMA), X-rays (EPIC-pn) and γ-rays (EGRET) bands, folded with the J02 ephemeris. The γ-ray light curve is taken from J02. 136

Figure 4.13 Temperature-radius confidence contours (68%, 90%, and 99%) for the iso- lated neutron star RX J1865.5-3754 as obtained from the X-ray observations with dif- ferent instruments (solid contours) and FUV-MAMA observations (dash and dash-dot lines). 137

As we have shown in §4.4.1, the observed thermal UV spectrum of Geminga either matches the continuation of the thermal X-ray spectrum or lies somewhat below that continuation (up to about one stellar magnitude), depending on assumed extinction and X-ray spectral model. On the contrary, other NSs observed in both UV and optical show relatively brighter Rayleigh-Jeans components, well above the continuation of the X-ray thermal spectrum. To demonstrate this difference and show that it is not associated with uncertainties in instrument responses, we re-analyzed the FUV-MAMA and EPIC data on the best-studied isolated neutron star, RX J1856.5−3754 (J1856 hereafter; see Tr¨umper et al. 2004) for a recent review of its properties). We used the FUV-MAMA ob- servation of 2002 October 26 (exposure time 13,451 s), analyzed the data as described in §4.3.2, and confirmed that the spectrum follows a Rayleigh-Jeans law (Pons et al. 2002), with a total flux F = (1.89 ± 0.09) × 10−14 ergs s−1 cm−2 in the 1155–1702 A˚ range. Fit- −2 2 ting the FUV-MAMA spectrum with a blackbody model gives T = (0.45±0.02) R13 d120 −2 2 MK and (0.55 ± 0.02) R13 d120 MK, at plausible color indices E(B−V) = 0.01 and 0.03 (R13 = R/13 km, d120 = d/120 pc). The temperature-radius confidence contours of these fits are shown in Figure 4.13. We also re-analyzed the archival XMM-Newton obser- vation of 2002 April 8–9 together with the recent observation of 2004 April 17–18. In the observations of 2002 and 2004, the EPIC-pn was operated in Small Window mode with thin filter (40.0 ks effective exposure) and Timing mode with thin filter (64.1 ks effective exposure), respectively. The EPIC-MOS observations of 2004 were carried out in Full Frame mode with thin filter (the same 65.3 ks effective exposures for MOS1 and MOS2). We did not use the EPIC-MOS observations of 2002 because MOS1 was oper- ated in Timing mode, which is very poorly calibrated for this instrument, and MOS2 was operated in Small Window mode, with a field-of-view 10000 × 10000 (for the central CCD) too small to reliably subtract the background. We found that the two EPIC-pn spectra of J1856 are well consistent with each other in the 0.3–1 keV range (there is no spectral information available below 0.3 keV in the data collected in Timing mode). Since J1856 does not show a nonthermal component, we fit the spectra with a single- component BB model and plot the corresponding confidence contours in Figure 4.13 [nH,20 = 0.66 ± 0.3, 0.04 (−0.04, +0.12), and 0.03(−0.02, +0.41) for the pn, MOS1 and MOS2 detectors, respectively]. In the same figure we also plot the confidence contours obtained from fitting the 449.9 ks observation of 2001 October 8–15 with the Low Energy Transmission Grating Spectrometer (LETGS) on Chandra (see Burwitz et al. 2003); the corresponding hydrogen column density is nH,20 = 0.86 ± 0.15. We see that the obser- vations with different X-ray instruments yield quite different spectral parameters. This demonstrates once more the lack of proper cross-calibration of instrument responses to soft spectra and the fact that systematic uncertainties greatly exceed statistical ones for spectra with good statistics. Even with allowance for the uncertainties in instrument responses, we see from Figure 4.13 that the UV contours lie well above the X-ray contours, i.e., the extrapolation of the X-ray blackbody spectrum of J1856 into the UV-optical range strongly underpre- dicts the observed UV-optical fluxes, contrary to Geminga (cf. Fig. 4.9). The UV-optical excess in the thermal spectra of J1856 and other NSs (e.g., RX J0720.4−3125 and PSR B0656+14) could be explained assuming that X-rays are emitted from a small hotter area while the optical-UV radiation is emitted from the bulk of NS surface, including 138 colder areas invisible in X-rays (e.g., Pavlov, Zavlin, & Sanwal 2002). Obviously, the ap- parently smaller UV-emitting area of Geminga, as compared to the X-ray-emitting area, cannot be explained by a nonuniform temperature distribution. We might speculate that the temperature distribution over the bulk of Geminga’s surface is more uniform than in the case of J1856, e.g., because of a different geometry of the magnetic field that af- fects heat conductivity and, hence, the surface temperature distribution. It is surprising, however, that the more uniformly heated Geminga exhibits quite substantial pulsations of its thermal radiation (fp ≈ 30%) while no pulsations have been detected from J1856. Any realistic interpretation of thermal emission from NSs should take into account possible deviations of thermal spectra emitted from surface layers (e.g., atmospheres) of NSs from the idealized Planck spectra and the anisotropy of the surface emission associated with strong magnetic fields (e.g., Pavlov et al. 1995; Rajagopal, Romani, & Miller 1997; Zavlin & Pavlov 2002). For instance, since the X-ray spectrum emitted from a strongly ionized hydrogen atmosphere is harder than the Planck spectrum, blackbody fits of such a spectrum give a (blackbody) temperature exceeding the actual effective temperature by a factor of 1.5–2 and a radius a factor of a few smaller than the actual radius of the NS. Moreover, the optical part of the spectrum emitted from such an atmosphere strongly exceeds the extrapolation of the blackbody fit of its X-ray spectrum into the optical domain (Pavlov et al. 1996). In principle, such an effect might explain the large difference between the observed UV spectrum and the continuation of the blackbody fit of the X-ray thermal spectrum in J1856 and similar NSs. However, no realistic models adequately describing the observed broad-band spectrum of J1856 have been suggested so far, which is not surprising given the extremely complicated physics of the dense, strongly magnetized matter at the relatively low temperature of the surface layers. If we adopt such an interpretation of the strong deviation of the J1856 broad-band spectrum from a pure blackbody spectrum, then we have to explain why the broad-band spectrum of Geminga is so different from that of J1856. Possible hypotheses might involve different chemical compositions of the surface layers and/or substantially different magnetic fields (a crude estimate of the Geminga’s magnetic field is ∼ 2 × 1012 G, but we have no idea about the magnetic field of J1856). Moreover, the surface layers of Geminga and J1856 might be in different phase states. For instance, one could speculate that the cold surface of Geminga is in a solid state while the (possibly hotter) surface of J1856 is in a gaseous or liquid state, which might explain their different spectra. To distinguish between these possibilities, reliable models for NS thermal emission at relatively low temperatures, which account for contribution of molecules in gaseous atmospheres with strong magnetic fields (Turbiner & Lopez Vieyra 2004) and possible condensation of the surface layers into a liquid or solid state (van Adelsberg, Lai, & Potekhin 2004), are to be developed and compared with the observational data. Until reliable models are available, the temperatures and radii obtained from using simplified models (blackbody, fully ionized atmospheres, partially ionized atmospheres without molecules) should be considered as crude estimates only, and any conclusions based on such fits should be considered with caution. However, although we cannot trust absolute values of the parameters obtained with the aid of simplified models, some interesting qualitative results can be obtained from comparison of the same parameter measured with the same model for different NSs. For instance, fits of the soft X-ray spectra of 139

Geminga and an older PSR B1055–52 with any model available give a lower temperature for the younger Geminga, which may have very interesting implications for the NS cooling models, suggesting different masses of these NSs (Yakovlev & Pethick 2004). As we mentioned in §3.1, in addition to the thermal soft (TS) component, the X-ray spectrum of Geminga apparently has a thermal hard (TH) component, with a 29 much higher temperature, Th ≈ 2 MK, and an isotropic luminosity Lpc ∼ 4 × 10 ergs s−1. Although such a component has been seen in the spectra of other middle-aged pulsars, its effective radius, Rh ∼ 50 d200 m, is surprisingly small in comparison with 3 1/2 −1/2 the “canonical” polar cap radius, Rpc = (2πfR ) c ≈ 300 m, suggested by pulsar models for Geminga. This small value of Rh might be explained by a projection effect (if the magnetic axis remains almost perpendicular to the line of sight in the course of NS rotation), but it would be hard to reconcile with the high pulsed fraction at energies where the TH component contribution is maximal (see §4.5.2). On the other hand, we should remember that the TS component was obtained assuming a Planck spectrum for the TS component and a pure power law for the magnetspheric spectrum. Because both these assumptions are not necessarily applicable, we cannot rule out the possibility that the “TH component” is simply associated with a harder Wien tail of the surface radiation (compared to the Planck spectrum) or it is due to a steepening of the slope of the phase-integrated magnetospheric spectrum with decreasing energies (see §4.5.3).

4.5.2 Pulsations in thermal emission One of the most intriguing results of our STIS MAMA observations of Geminga is the strong, non-sinusoidal pulsations in the FUV range, where the spectrum is dominated by the thermal component, most likely emitted from the bulk of NS surface. The shape of the FUV pulsations is different from that of the soft X-ray pulsations, where the TS component dominates (see Fig. 12). Obviously, neither FUV nor soft X-ray pulsations can be produced by the locally isotropic blackbody emission. To explain the unusual pulse shape and the large pulsed fraction of the thermal FUV and soft X-ray radiation, we have to invoke effects of strong magnetic field on the angular dependence of NS surface emission or assume that there is a “screen” in the NS magnetosphere which may partially eclipse the surface emission at some rotation phases. In a strong magnetic field, B À 1011(E/1 keV) G, when the electron cyclotron energy Ec exceeds the photon energy, the local emission is essentially anisotropic (in particular, beamed along the direction of the magnetic field), which may lead to strong pulsations of the thermal radiation. The angular distribution and the shape of pulsations depend on the properties of the emitting region. For instance, the angular distribution of local emission from a fully ionized NS atmosphere shows a strong, narrow peak [∆θ ∼ 1/2 (E/Ec) ] along the magnetic field (pencil component) and a broad fan-like component across the magnetic field (Pavlov et al. 1994). When integrated over the visible surface of a NS with a dipole magnetic field, the angular distribution of NS radiation shows two prominent peaks, along the magnetic axis, even in the case of a uniformly heated NS surface (Shibanov et al. 1995; see also Zavlin & Pavlov 2002). Such peaks could explain soft X-ray pulsations (at E ∼> kTeff ), including the observed increase of pulsed fraction with energy. However, the peaks are too low at E ¿ kTeff (e.g., in the FUV 140 band) to be responsible for the observed FUV pulsations. On the other hand, as we mentioned above, the fully ionized atmosphere models are not directly applicable to the cold Geminga, while the partially ionized atmospheres have not been well investigated. If the NS surface matter is in a condensed state, we also should expect an anisotropic emission. Although the angular distribution of emission from a condensed surface has not been studied, the examples of spectral emissivity for several directions, calculated by van Adelsberg et al. (2004), suggest that at least local radiation is beamed along the magnetic field. To understand whether the radiation from the entire NS sur- face can show pulsations similar to those observed from Geminga, the local specific fluxes should be integrated over the visible NS surface, for various magnetic field geometries and orientations of the spin and magnetic axes. An alternative explanation for the narrow deep minima in the UV pulse profiles could be a partial eclipse by an object co-rotating with the NS. Since the shapes of the UV and soft X-ray light curves are different (in particular, the minima are broader in soft X-rays), the eclipsing object should have a wavelength-dependent effective size. A natural candidate for such a screen is magnetospheric electron-positron plasma which can efficiently absorb the NS surface radiation as a result of the cyclotron resonance scattering in a resonance layer, where the cyclotron energy is equal to the photon energy in the rest frame of the electron (e.g., Blandford & Scharlemann 1975). Two types of models have been discussed for the scattering region: a stationary nonrelativistic plasma in the closed magnetic field lines zone (Rajagopal & Romani 1997; Wang et al. 1998; Ruderman 2003) and streams of ultrarelativistic electron-positron pairs ejected along the open field lines (e.g., Lyubarskii & Petrova 1998,2000, and references therein). In the latter case, the effects of the resonant inverse Compton scattering on the properties of observed UV/X-ray radiation have not been investigated in detail; however, crude estimates show that a very large pair multiplicity is needed to reach an optical depth of ∼> 1. In the case of nonrelativitic plasma in the closed zone, which can be supported against the gravitational force by the thermal radiation pressure enhanced by the cyclotron resonance (Mitrofanov & Pavlov 1982; Rajagopal & Romani 1997), the effects of resonant cyclotron scattering become significant if the electron/positron number density is a factor 2 13 −3 of ∼ 10 larger than the corotation (Goldreich-Julian) density, nGJ ∼ 10 cm for Geminga. The electron-positron pairs could be supplied from acceleration zones, but rapid pair production (large multiplicity) is needed to provide so high densities. In addition, it remains unclear how the electrons/positrons would lose the longitudinal momentum to become nonrelativistic particles (the transverse momentum is essentially nonreltivistic due to the fast synchrotron/cyclotron losses). If, nevertheless, there is such a nonrelativistic plasma screen in the closed zone, the wavelength dependence of its optical thickness depends on spatial distribution of scattering particles. In particular, the assumption that the minima in the UV light curves of Geminga are caused by such a rotating screen implies a insignificant amount of electron-positron pairs at a distance 9 of ∼ 15 RNS, where the magnetic field is ∼ 10 G. If the broader minima in the soft X-ray light curve are caused by a partial eclipse by the screen, then the X-ray resonance layer (at a distance ∼ 5 RNS) subtends a larger solid angle (covers a larger part of the “NS sky”) than the UV resonance layer. Alternatively, if the soft X-ray pulsations are caused not by the screen but by the intrinsic anisotropy of the thermal radiation in the 141 strong magnetic field, then we can assume that the inner boundary of the plasma screen is beyond the radius (r ∼ 5 RNS) corresponding to the resonance layer for soft X-ray photons. For the dipole field the absorbing screen is likely to become “leaky” (less opaque) right above the magnetic pole since the electrons are injected along almost straight magnetic field lines orthogonal to the NS surface and the probability of absorbing a photon [∝ (1 − β cos θ); β = v/c] is small if the angle θ between the electron speed ~v and the photon wave-vector is small. Therefore, the radiation from central hottest part of the polar cap(s) could pierce through the screen and give rise to the “TH component” (§3.1). This could explain the high pulsed fraction (in 0.6-1.0 keV band) and small emitting area observed for the TH component. Alternatively, the “TH component” could be produced is the magnetosphere (§4.1.1). The non-thermal magnetospheric emission generated high enough above the NS surface will be unaffected by the scattering screen since the resonance condition is nowhere met.

4.5.3 Nonthermal emission of Geminga As shown in §3.1, the fits to the X-ray spectrum result in very different PL spectral indices depending on whether the TH thermal component is included in the fit. With the data available we cannot statistically prove or reject the presence of TH component or prove that the non-thermal spectrum curves at between 2 − 10 keV. However, we can extrapolate different best-fit PL models toward the lower frequencies and compare the extrapolations with the measured non-thermal fluxes in the optical (Figs. 7 and 10). The extrapolation is marginally consistent with optical data when the PL model is fit to the spectrum in the 2.5 − 10 keV band (see §3.1) and low interstellar extinction is assumed (see lower panel in Fig. 10). In the case when BB+PL fit carried out in the full X-ray band (0.2 − 10.0 keV) the extrapolation of the PL component exceeds the optical fluxes by more that two orders-of-magnitude. This would suggest the spectral flattening at UV–optical frequencies. Such a flattening cannot be ruled out since it has been observed in young pulsars with strong non-thermal emission – e.g., the Crab pulsar (Sollerman et al. 2000), PSR B0540−69 (Nasuti et al. 1997). For instance, the optical spectrum of the Crab pulsar is flatter then the X-ray spectrum by ∆Γ ≈ 0.8. For the older (11 kyrs) Vela pulsar the extrapolation of X-ray spectrum to the optical frequencies also suggests spectral flattening. So far, it is not clear whether such a flattening is typical only for young pulsars with relatively strong magnetospheric components or it is also present in the spectra of older pulsars. The non-thermal spectral component of the middle- aged PSR B0656+14 can be fitted with a single PL from optical to X-rays within the data uncertainties. There are no other middle-aged pulsars for which sufficiently good photometric measurements are available. One can also extrapolate the best-fit X-ray PL components toward higher energies to see how they relate to the γ-ray data (Fig. 14). The PL component from TH+TS+PL fit to the X-ray data is only marginally consistent with the gamma-ray data points. One can hardly hope to fit the non-thermal, optical through gamma-ray spectrum (span- ning 10 orders-of-magnitude in frequency) with a single PL. It is more likely that the high-energy non-thermal emission of Geminga is comprised of several components with 142 different spectral properties (cf. Vela pulsar spectrum in §2.3.3; Harding et al. 2002). Phase resolved spectroscopy at ∼> 10 keV energies could help to resolve this issue.

Figure 4.14 Multiwavelength spectrum of Geminga including gamma-ray data points from OSSE (Strickman et al. 1996), COMPTEL (Schonfelder et al. 2000), and EGRET (Kanbach et al. 1994).

The non-thermal pulsations observed in hard X-rays show two peaks per period with a slightly narrower separation in phase than the γ-ray peaks (see Fig. 10). Contrary to the γ-ray pulse profile, the first peak is stronger than the second one in the X-ray light curve (2−8 keV). Although the UV and soft X-ray light curves exhibit single broad peak, thus suggesting that only one of the two polar caps is visible, it still may be possible to see two non-thermal peaks since in the so-called “polar cap” models the non-thermal emission is expected to be peaked in a hollow cone inscribed in the surface formed by the last open field lines (see Harding & Muslimov 1998 and references therein). The optical pulse profile reported by Shearer et al. (1998) also has a double peaked structure and resembles the 2 − 8 keV pulse profile. This may suggest that optical, X-ray and γ-ray pulsations are produced in the same region of the pulsar magnetosphere.

4.6 Summary and conclusions

We obtained the spectrum of Geminga in the far-ultraviolet and performed pho- tometry in near-ultraviolet. The FUV spectrum is thermal with T ≈ 0.3 − 0.4 MK (assuming the distance of 200 pc and 13 km NS radius). The NUV emission is also 143 expected to be largely thermal, with noticeable contribution of the non-thermal com- ponent. The extrapolation of the Geminga’s thermal X-ray spectrum matches (or goes slightly below) UV fluxes. This makes Geminga different from other neutron stars with measured X-ray and optical spectra (e.g. J1856) – for them the extrapolations of their thermal X-ray spectra to the lower frequencies underestimate optical/UV fluxes by a factor of 2-6. We speculate about possible reasons for such distinct spectral behavior. We also obtained Geminga’s pulsed profiles at different frequencies. Surprisingly, ther- mal emission shows high (∼ 30%) pulsed fraction both in UV and soft X-rays; the pulse profile exhibits one broad peak. This can hardly be explained by the non-uniformity in the surface temperature alone. The other possible mechanisms are discussed. The X-ray data indicate the presence of highly pulsed (pulsed fraction ≈ 60% ) hot thermal emission (T ≈ 2 MK) originating from a very small area (∼ 50 m), possibly the central region of a polar cap. The spectrum of the non-thermal emission in X-rays can be fitted with a power-law whose spectral index strongly depends on the presence of the hot thermal component. If such a component is accounted for, then the extrapolation of the non-thermal spectrum to the lower fluxes is marginally consistent with the optical data points. Otherwise, the extrapolation overpredicts optical fluxes by more than two orders-of-magnitude and would require the flattening of the spectrum at optical wavelengths. The pulse profile of the non-thermal emission shows two peaks and a pulsed fraction of 34%. A better measurements of the hard X-ray spectrum are needed to distinguish between these two possibilities. 144

Chapter 5

HST observations of PSR B0656+14.

This Chapter is devoted to recent observations of the nearby (d = 288 ± 30 pc; Brisken, et al. 2003), middle-aged (≈ 100 kyrs) pulsar B0656+14 with the Space Tele- scope Imaging Spectrograph FUV-MAMA (Far-Ultraviolet Multi Anode Micro-channel Array). The main goal of the observation was to determine the nature of pulsar’s FUV spectrum (i.e. thermal or non-thermal) and better constrain the temperature of the NS surface and the spectral slope of the not-thermal optical emission.

5.1 Previous observations.

PSR B0656+14 (P = 385 ms; τ = 1.1 × 105 yrs) is the brightest of middle-aged pulsars, in both X-rays and optical. Its X-ray spectrum and pulse profile were studied by Finley et al. (1993), Anderson et al. (1993), Possenti et al. (1996), Greiveldinger et al. (1996), Marshall & Schulz (2002), Pavlov et al. (2002), and Zavlin & Pavlov (2003). The best-fit model for its X-ray spectrum (0.1–6 keV), obtained from XMM observations (Zavlin & Pavlov 2003), consists of three components: thermal soft (TS) component (Ts = 0.82 ± 0.04 MK, Rs = 7.3 ± 0.2 km, for a distance of 288 pc) emitted from a large part of the NS surface, thermal hard (TH) component (Th = 1.72 ± 0.12 MK, Rh = 0.5 ± 0.06 km), presumably emitted from smaller, hotter areas (perhaps hot polar caps), and nonthermal power-law (PL) component, with the photon index Γ = 1.5 ± 0.3, emitted from the pulsar magnetosphere. The X-ray radiation is pulsed, with a pulsed fraction of 15%–20% at lower energies, where the TS component dominates (upper panel of Fig. 5.1). The optical counterpart of the Geminga pulsar (V ≈ 25) was discovered by Car- aveo et al. (1994). Because a nearby galaxy (minimum distance ≈ 100–200) contaminates the ground-based images (Koptsevich et al. 2001), the best near-IR/optical/near-UV (λ = 2, 000–20,000 A)˚ data were obtained with the HST. The pulsar was imaged with FOC (Pavlov, Stringfellow & C´ordova 1996a; Pavlov, Welty & C´ordova 1997), WFPC2 (Mignani, Caraveo & Bignami 1997; Mignani, De Luca & Caraveo 2000), and NICMOS (Harlow, Pavlov & Halpern 1998; Koptsevich et al. 2001). The low-resolution NUV spec- trum of the pulsar was obtained with the STIS NUV-MAMA detector using PRISM1 as the spectral element. The observation was carried out in time-tagged mode and also provided the NUV lightcurve (bottom panel of Fig. 5.1). The lightcurve shows two peaks per period and a pulsed fraction of ∼ 50%–70%, much larger than that of the soft X-ray lightcurve, thus suggesting that the NUV emission is largely non-thermal. The

1See HST STIS instrument handbook at http://www.stsci.edu/hst/stis/documents/handbooks/currentIHB/c04 spectros5.html#310764 145

Figure 5.1 Pulse profiles in soft X-rays (upper panel) and the NUV range (lower panel). Adopted from Zavlin et al. (2004). Note that these light curves are not aligned in phase with the FUV light curve in Figure 6.4.

broad-band NIR/optical/NUV spectrum is shown in Figure 1.4 (Chapter 1). Fitting this spectrum with a power-law model leaves large residuals in the NUV range, which can be attributed to an appreciable contribution of a thermal (Rayleigh-Jeans) component at NUV wavelengths (see Fig. 5.4)

5.2 STIS/FUV-MAMA observation.

PSR B0656+14 was observed with the HST STIS FUV-MAMA on 2004 January 20 (start date is 53, 024.18876456 MJD UT). The low-resolution grating G140L (which covers the wavelength interval ≈ 1150–1700 A)˚ with the 5200 × 000. 5 slit was used. The data were taken during two consecutive orbits (including the target acquisition). The total scientific exposure time was 4950 s. FUV-MAMA was operated in TIME-TAG mode which allows the photon arrival times to be recorded with 125 µs resolution. The observation setup was same as in the observation of Geminga (§4.2) and the data were reduced in a similar way (described in details in §4.2).

5.2.1 FUV Spectrum.

The FUV spectrum of PSR B0656+14 is shown in FigureP 6.2. The totalP flux in the ˚ ˚ −1 1155–1702 A range (∆λ = 547 A), can be estimated as F ' ∆λ ( ihFλii∆λi)( i ∆λi) ' −15 −1 −2 2 (3.48 ± 0.23) × 10 erg s cm , corresponding to the luminosity LFUV = 4πd F = 28 2 −1 (3.44 ± 0.23) × 10 d288 erg s . αλ We first fit the spectrum with the absorbed power-law model, Fλ = F1500 (λ/1500 A)˚ × −0.4A(λ) E(B−V ) 10 . For plausible value of E(B − V ) = 0.02 (as inferred from nH = 1.4 × 146

Figure 5.2 The measured (absorbed) FUV spectrum of PSR B0656+14. The dashed line shows best fit absorbed BB model (T = 0.6 MK; R = 13 km; d = 288 pc; E(B-V)=0.02) 147

20 −2 10 cm measured in X-rays), we found the best-fit power-law index αλ = −3.00±0.66 −18 −2 −1 −1 and the normalization F1500 = 7.32 ± 0.57 × 10 erg cm s A˚ , respectively 2 (χν = 0.98 for 10 degrees of freedom). The inferred slope αλ is close to that of the Rayleigh-Jeans spectrum, Fλ ∝ λ−4, suggesting thermal radiation from the NS surface. To estimate the NS surface temperature, we fit the absorbed blackbody model to the observed spectrum. Since the FUV fluxes are in the Rayleigh-Jeans part of the spectrum, the temperature values are strongly correlated with the radius-to-distance ratio (approximately, T ∝ d2/R2; cf. Fig. 4.6 in §4.2.2). For a typical NS radius R = 13 km and the distance d = 288 pc, the 2 inferred surface temperature is 0.60 ± 0.03 MK, for E(B − V ) = 0.02 (χν = 1.08 for 11 degrees of freedom).

5.2.2 Timing analysis. For the timing analysis of the FUV-MAMA data, we used the so-called TIME- TAG data files that contain the photon arrival times, recorded at a 125 µs time resolution, and high-resolution detector coordinates (see §4.2.1) associated with each of the events. The arrival times are corrected for the Earth and spacecraft motions and transformed to barycentric dynamical times (TDB) at the solar system barycenter, using the STSDAS task “odelaytime”. For the two FUV-MAMA exposures (Tspan = 7, 390 s), we extracted 1098 events from the λ-bins shown in Fig. 6.2, with heights of extraction box varying from 14 to 22 high-resolution pixels, depending on the λ-bin (≈ 56% of these counts are expected to come from the source). The frequency of pulsations predicted from the radio ephemeris2 for the epoch of 2 this observation (53024.194180929 MJD) is f = 2.59803089335(6) Hz. We applied the Zn test (Buccheri et al. 1983) at this frequency, for 1 ≤ n ≤ 6 (n is the number of harmonics 2 included) and found the highest significance of 99.99992% (4.9σ) for n = 2 (Z2 = 33.8). 2 The Zn search for pulsations around this frequency resulted in the most significant peak, 2 Z4 = 34.41 (99.99994% [5.0σ] significance) located 5 µHz below the predicted frequency. Within the uncertainties associated with the FUV timing (∆f ≈ ±30 µHz) this frequency 2 coincides with the predicted frequency. The Zn peaks with even n are systematically more significant that those with odd n, which suggests an even number of peaks per period. Figure 5.3 shows the light curve folded at the radio frequency (see above) and comprised of the source plus background counts from both orbits. The background level is shown by the dash-dotted line in the same figure. The pulsed fraction in the obs observed (source + background) radiation is fp = 27%; the corresponding intrinsic pulsed fraction is 62%. Despite the apparently thermal nature of the spectrum, the FUV lightcurve re- sembles the NUV lightcurve, i.e. it shows surprisingly large (for the thermal emission from NS surface) pulsed fraction (≈ 62%; vs. 61% in NUV) and two peaks of similar height and width (cf. Figs. 5.1 and 5.3).

2Taken from the ATNF catalog available at http://www.atnf.csiro.au/research/pulsar/psrcat/. 148

Figure 5.3 FUV pulse profile of PSR B0656+14.

5.3 Broadband optical-UV spectrum. Summary.

We also fitted the de-reddened optical and UV data (see Fig. 5.4) with the R-J 2 6 + PL model. The best-fit R-J parameter T6(R13/d288) = 0.70 ± 0.04 (T6 = T/(10 K); nat the temperature of ≈ 0.6 − 0.7 MK R-J provides good approximation to the BB spectrum in UV-optical band). The best-fit (χν = 1.67 for 18 d.o.f.) spectral index, 15 αν = −0.39 ± 0.08, and normalization, Fν = 0.28 ± 0.02 µJy at ν = 10 Hz, are consistent with the extrapolation of the non-thermal X-ray component to the optical range (Koptsevich et al. 2000; Zavlin & Pavlov 2003). However, the extrapolation of the soft X-ray blackbody component (T = 0.82 MK and R = 7.3 km; Zavlin & Pavlov 2003) to the optical frequencies falls a factor of two below the measured FUV fluxes (Fig. 5.5). Similar UV-optical excess was also observed in other NSs (e.g., RX J1856.5−3754 and RX J0720.4−3125) with a notable exception of the Geminga pulsar which does not show such an excess (see Chapter 4). The excess could arise if X-rays are emitted from a small hotter area while the optical-UV radiation is emitted from the bulk of NS surface, including colder areas invisible in X-rays (e.g., Pavlov, Zavlin, & Sanwal 2002). Rigorously speaking, one has to simultaneously fit the multiwavelength data (from optical to X-rays) with the multi-component model (e.g., BB radiation produced by the non-uniformly heated NS surface plus PL component) to accurately determine the temperature of the NS surface and the slope and normalization of the PL component. However, the unknown functional form of the NS surface temperature distribution, the unknown (in most cases) orientation of the NS magnetic axis with respect to the observer, 149

Figure 5.4 De-reddened optical/UV spectrum of PSR B0656+14 with the best fit R-J + PL model shown by the dashed line (separate components of this model are also shown by the dashed lines). The extrapolation of the best-fit thermal soft-X-ray component (Zavlin & Pavlov 2003) is shown by the dotted line. The dash-dotted lines show the extrapolation of the X-ray PL component with associated 1σ uncertainties. 150

Figure 5.5 The near-infrared through X-ray spectrum of PSR B0656+14. The solid line shows the fit to X-ray data with PL+TH+TS model (see §5.1). The model components are also shown separately by the dotted and dash-dotted lines. For the PL component 1σ uncertainties of the fit are also shown by the dash-dotted lines. Notice that the observed UV fluxes are above the extrapolation of the X-ray model (see §5.3). and the different responses of detectors that were used to collect multiwavelength data make this a challenging task. The wide-band photometry of B0656+14 hints on spectral feature(s) between the J and U bands (Fig. 5.5). However, this could be the result of inaccurate photometry or underestimated uncertainties (cf. Geminga photometry in §4.3.3). The scheduled IR observations with Spitzer will better establish the level and slope of the non-thermal continuum in the optical. 151

Chapter 6

HST observations of the millisecond pulsar J0437−4715.

This Chapter describes the results of the HST observations of the millisecond pulsar J0437−4715. The goal of the observations was to measure the pulsar’s spectrum and pulsations in the far-ultraviolet (FUV). For the first time, UV emission from a millisecond pulsar was detected. The measured flux, (2.0 ± 0.2) × 10−15 erg s−1 cm−2 in 27 −1 the 1150–1700 A˚ range, corresponds to the luminosity LFUV = (4.7 ± 0.5) × 10 erg s , for the distance of 140 pc and negligible interstellar extinction. The shape of the observed spectrum suggests thermal emission from the neutron star surface with a surprisingly high temperature of about 1 × 105 K, above the upper limit on the surface temperature of the younger “ordinary” pulsar J0108−1431. For the few-Gyr-old J0437−4715, such a temperature requires a heating mechanism to operate. The spectrum of J0437−4715 shows marginal evidence of an emission line at 1372 A,˚ which might be a gravitationally redshifted Zeeman component of the Hydrogen Lyα line in a magnetic field ∼ 7 × 108 G. No pulsations are detected, with a 3σ upper limit of 50% on the pulsed fraction.

6.1 Optical observations of millisecond pulsars.

Millisecond (recycled) pulsars are very old neutron stars (NSs) spun up by accre- tion in binary systems. So far, X-ray observations have been the only source of infor- mation about emission from millisecond pulsars (MSPs) outside the radio band (Becker & Pavlov 2001; Becker & Aschenbach 2002). Based on their X-ray pulse profiles and spectra, the X-ray emitting MSPs can be divided into two distinct groups. The pulsars from the first group (e.g., PSR B1821−24, B1937+21, J0218+4232) show X-ray pulse profiles with narrow peaks, resembling those seen in radio, and large pulsed fractions, ∼> 50%. They have hard power-law spectra, with photon indices Γ = 1–2, and high spin-down luminosities, E˙ ∼ 1035–1036 erg s−1. The X-ray radiation from these MSPs is interpreted as nonthermal emission produced in the pulsar magnetosphere. The second group consists of MSPs with smoother X-ray pulsations, lower pulsed fractions, and smaller E˙ (∼ 1033–1034 erg s−1). In those few cases when the X-ray spectra are available (e.g., PSR J0437−4715 and J0030+0451), they cannot be fitted with a single power-law model. The fits with simple spectral models (power-law, blackbody) require at least two spectral components, one of which is very soft. Likely, this soft component can be interpreted as thermal emission from NS polar caps, with a temperature ∼ 1 MK. Such polar caps, heated by a backward flow of relativistic particles accelerated in the magnetosphere above the NS magnetic poles, are predicted by virtually all pair-cascade pulsar models (e.g., Ruderman & Sutherland 1975; Arons 1981; Harding & Muslimov 2002). The thermal component cannot be seen in the first group of MSPs because it 152 is buried under the stronger nonthermal component, similar to young ordinary pulsars (e.g., Pavlov, Zavlin, & Sanwal 2002). Detailed X-ray studies of PSR J0437−4715, the brightest MSP of the second group, suggest that the thermal component of its radiation is emitted from a region with a nonuniform temperature, decreasing from the magnetic poles towards the equator (Zavlin & Pavlov 1998; Zavlin et al. 2002). Such a nonuniformity could be interpreted as due to a heat flow away from the polar cap. In addition to the external (polar- cap) heating, a variety of internal heating mechanisms can operate in the NS interiors, such as dissipation of the NS rotational energy and magnetic field (Schaab et al. 1999, and references therein). Consequently, the temperature distribution and, particularly, the lower value of the surface temperature depend on the thermal conductivity of the NS matter and the relative contributions from the external and internal heating. X- ray observations mainly probe thermal emission from the hot polar regions, being less sensitive to the emission from the rest of the NS surface with a lower temperature. This low-temperature emission can only be observed in the optical-UV range. Measuring the temperature of the NS surface in MSPs is important because it can constrain the NS heating models and provide information about the physical processes operating in the NS interior. If the magnetospheric component dominates in the optical-UV, its detection would help elucidate the properties of relativistic particles in the MSP magnetospheres. Most MSPs reside in binary systems, usually with a low-mass white dwarf (WD) companion that, as a rule, is expected to be brighter in the optical than the MSP itself. Therefore, solitary MSPs look more suitable for studying the NS optical emission. How- ever, no firm detections of optical/UV emission from solitary MSPs have been reported. Even very deep VLT observations of the solitary MSPs J0030+0451 (Koptsevich et al. 2003) and J2124−3358 (Mignani & Becker 2004) gave negative results, putting some constraints on the nonthermal emission in the optical. On the other hand, if the com- panion of a binary MSP is sufficiently cold, it is very faint in the UV range, which can be used to observe NSs in nearby binary MSPs, particularly their thermal emission. The best target for such observations is PSR J0437–4715, the nearest and the brightest binary MSP (P = 5.76 ms, d = 139 ± 3 pc, τ ≡ P/(2P˙ ) = 4.9 Gyr, E˙ ≡ 2 ˙ −3 33 −1 4π IPP = 3.8 × 10 I45 erg s — van Straten et al. 2001). Its binary companion is a cold WD with the effective surface temperature of about 4000 K (Danziger et al. 1993) and orbital period of 5.5 days. Optical emission from the binary is dominated by the WD (R = 20.1, V = 20.8, B = 22.2), making optical detection of the pulsar impossible. This prompted us to carry out observations of the system in the far-ultraviolet (FUV) range with the Hubble Space Telescope (HST). For the first time UV emission from a non-accreting MSP was detected.

6.2 HST Observation

PSR J0437−4715 (J0437 hereafter) was observed on 2001 August 24 (start date 52 145.23638667 MJD) with the Space Telescope Imaging Spectrograph (STIS). The source was imaged on the Far-Ultraviolet Multi Anode Micro-channel Array (FUV- MAMA). The low-resolution grating G140L (which covers the wavelength interval ≈ 153

1150–1700 A)˚ with the 5200 × 000. 5 slit were used. The data were taken during five con- secutive orbits, including target acquisition. We used the WD companion of the pulsar as the acquisition target, centering it in the slit to a ±000. 01 nominal accuracy. The total scientific exposure time was 14,150 s (2,150 s for the first exposure and 3,000 s for each of the subsequent exposures). FUV-MAMA was operated in TIME-TAG mode which allows the photon arrival times to be recorded with 125 µs resolution.

6.3 Data reduction.

For each exposure, we processed the raw, “high-resolution” images (2048 × 2048 pixels; plate scale of 000. 0122 per pixel — see §11 of the STIS Instrument Handbook 4, IHB hereafter) using the calibration files available on January 23, 2003. As an output, we obtained flat-fielded “low-resolution” (1024 × 1024 pixels; plate scale 000. 0244 pixel−1; spectral resolution 0.58 A˚ pixel−1) images and used them for the spectral analysis. The processed images show a nonuniform detector background that consists of a flat (constant) component and the so-called “thermal glow” component (Landsman 1998) that dominates over most of the detector area. The thermal glow is the strongest in the upper-left quadrant of the detector (Fig. 6.1), where the dark count rate can exceed the nominal value, 6 × 10−6 counts s−1 pixel−1, by a factor of 20. The brightness of the thermal glow increases exponentially with increasing the FUV-MAMA power supply temperature above 38.9 C (Landsman 1998). In our observation, this temperature was rising from 40.89 C during the first orbit to 42.36 C during the last orbit, resulting in brightening thermal glow. In addition, the overall shape and small-scale structure of the thermal glow varied slightly between the exposures. Because of the high background, the dispersed source spectrum is hardly dis- cernible in the separate exposures. Nevertheless, we find the spectrum centered at Y = 351 ± 2 pixels in each of the flat-fielded images (the centroid slightly varies with X), where X and Y are the image coordinates along the dispersion and spatial axes, respectively. This is within 2 pixels (000. 05) of the nominal position where the target was expected to be acquired. At this location on the detector, the contribution of the thermal glow to the background is still quite large — the background averaged along the dispersion direction exceeds the nominal background by a factor of 10. To improve the signal-to-noise ratio (S/N), we combined the images from five exposures into a single image using the STSDAS5 task “mscombine”. The Y -positions of the centroids differ by less than 3 pixels for different exposures and different wavelengths (X-positions). The spectrum of the source is clearly seen in the summed image shown in Figure 6.1. Accurate subtraction of the enhanced, nonuniform background is crucial to mea- sure the spectrum of our faint target. The spectral extraction algorithm implemented in the standard STIS pipeline (task X1D) does not adequately correct for the nonuniform background while extracting the spectrum of such a faint source. Therefore, we devel- oped an IDL routine with additional capabilities of grouping and fitting the background to reduce the data.

4http://www.stsci.edu/hst/stis/documents/handbooks/currentIHB/c11 datataking2.html 5Space Telescope Data Analysis System available at http://stsdas.stsci.edu/STSDAS.html 154

Figure 6.1 Distribution of counts on the FUV-MAMA detector. The spatial (Y) and dis- persion (X) axes are in the vertical and horizontal directions, respectively. The spectrum of J0437 is shown by horizontal arrows. The background is clearly dominated by the nonuniformly distributed “thermal glow” which is the strongest at the upper left corner and the weakest at the bottom. The vertical arrow shows the location of the possible spectral feature (see §6.7 and Fig. 6.3 ). 155

Since the source spectrum occupies only a small region on the detector, we do not attempt to subtract the background globally. Instead, we scan the count distribution within two strips, 324 ≤ Y ≤ 343 and 362 ≤ Y ≤ 381, adjacent to the source region, 344 ≤ Y ≤ 361. To obtain the spectrum with a sufficiently high S/N, we have to bin the spectrum heavily; after some experimenting, we chose four spectral bins (λ-bins): 1155– 1187, 1248–1283, 1316–1376, and 1400–1702 A.˚ The first two λ-bins are chosen to avoid contamination by the geocoronal line emission (Lyα line at 1216 A˚ and the Oxygen line at 1304 A;˚ the other geocoronal Oxygen line, at 1356 A,˚ is not seen in this observation). Because of an enhanced background at 1376–1400 A,˚ we also exclude this region from the spectral analysis, which determines the choice of the third λ-bin (1316–1376 A).˚ The remaining counts are grouped into a single bin (1400–1702 A)˚ to have comparable S/N in the second through fourth λ-bins. For each of the λ-bins, we calculate the total number of counts, Nt, within the extraction boxes of different heights (one-dimensional apertures): As = 3, 5, 7, 9, 11, 13, 15, and 17 pixels, centered at Y = 351, 352, 353, and 352 for the 1st, 2nd, 3rd, and 4th λ-bins, respectively. To evaluate the background, we first clean the background strips (see above) from outstanding (> 10−3 cts s−1 pixel−1) values (“bad pixels”) by setting them to local average values (median filtering or standard sigma-clipping algorithms are not applicable in this case — see IHB §7.4.2). Then, for each of the λ-bins, we fit the Y - distribution of the background counts with a first-order polynomial (interpolating across the source region), estimate the number Nb of background counts within the source extraction aperture As, and evaluate the number of source counts, Ns = Nt − Nb (Table 6.1). The uncertainty δNs of the source counts can be evaluated as δNs = [Nt + 2 1/2 (δNb) ] , where δNb is the background uncertainty in the source aperture. For a uni- uni 1/2 form, Poissonian background, this quantity can be estimated as δNb = [Nb(As/Ab)] , where Ab (= 40 pixels) is the aperture where the background was measured. To account for the background nouniformity, we estimated δNb directly from the image. We binned the distribution of background counts along the Y -axis with the bin sizes equal to As (for As = 3, 5, and 7) and calculated δNb as root-mean-square of the differences between the actual numbers of background counts in the bins and those obtained from the fit to the background. The background uncertainties obtained in this way are systematically larger (see Table 6.1) than the uncertainties estimated assuming a uniform, Poissonian background. We find that the signal-to-noise ratio, S/N = Ns/δNs, calculated for each λ-bin and for different extraction box heights, is the largest for As = 3 or 5 pixels, depending on the λ-bin. Since the results at small heights are sensitive to the deviation of the spectrum from the straight line (along the dispersion direction) and possible small misalignments between the frames taken in the different orbits, we choose As = 5 pixels as the optimal value. We adopt this source extraction aperture for further analysis, which contains 53%, 61%, 64%, and 65% of source counts for the first through the fourth λ-bins, respectively). For each λ-bin, we calculate the average spectral flux defined as R Rλλ Fλ dλ C hF i ≡ ∆Rλi ≡ R i , (6.1) λ i R λ dλ R λ dλ ∆λi λ ∆λi λ 156

Table 6.1 Counts and fluxes in λ-bins.

a uni b λ-bin Nt Nb δNb δNb Ns δNs S/N Fλ (A)˚ 1155-1187 367 313 9.3 6.2 54.3 21.3 2.5 7.5 ± 2.6 1248-1283 615 465 15.0 7.6 149.3 28.0 5.1 5.4 ± 0.9 1316-1376 816 609 22.6 8.7 206.7 36.5 5.8 4.6 ± 0.6 1400-1702 1369 1078 25.1 11.6 290.6 44.7 6.5 2.9 ± 0.4 Summedc 3167 2466 38.2 17.5 700.8 68.0 10.3 3.7 ± 0.3

aNumber of background counts scaled to the 5 pixel extraction box. bObserved average spectral flux, in units of 10−18 erg s−1 cm−2 A˚−1, corrected for the finite aperture. cValues for summed λ-bins.

where Ci is the source count rate in the i-th λ-bin, and Rλ is the system response (which includes the Optical Telescope Assembly throughput and accounts for the grating and slit losses and the finite size of the source extraction aperture; see §3.4.12 of the HST Data Handbook for STIS6 for details). The resulting flux values are given in Table 6.1, while ˚ the spectrum is shown in Figure 6.2.P The total fluxP in the 1150–1700 A range (∆λ = 550 ˚ −1 −15 −1 A), can be estimated as F ' ∆λ ( ihFλii∆λi)( i ∆λi) ' (2.0 ± 0.2) × 10 erg s −2 2 27 2 −1 cm , corresponding to the luminosity LFUV = 4πd F = (4.7 ± 0.5) × 10 d140 erg s . In the original spectrum we see a brightening around 1372 A˚ (marked with a vertical arrow in Fig. 6.1), resembling an emission line. The count rate spectrum of the possible line and its vicinity, binned to 1.16 A˚ (4 high-resolution pixels) bins, is shown in Figure 6.3. The count excess, 30 ± 10 counts in the three bins, corresponds to the flux (4.0 ± 1.3) × 10−17 erg cm−2 s−1 in the 1370.1–1373.6 A˚ range. This spectral feature, detected at a 3 σ level, is clearly not of a geocoronal origin (the nearest geocoronal oxygen line, at 1356 A,˚ is not seen in this observation), but we cannot rule out the possibility that it may be associated with an anomaly in the FUV-MAMA background seen right above the feature (in the cross-dispersion direction). Therefore, we consider this as a marginal detection until the feature is confirmed in another observation. For the timing analysis, we used the so-called TIME-TAG data files that contain the photon arrival times, recorded at a 125 µs time resolution, and high-resolution detec- tor coordinates (see §6.3) associated with each of the events. We extracted 2964 events from the above-defined four λ-bins, with the height of extraction box equal to 9 high- resolution pixels (≈ 22.5% of these counts are expected to come from the source). Note that the background count rate in these data is about 3% higher than that in the data used for the spectral analysis where “outstanding pixels” were filtered out (see above). The arrival times of the events were corrected for the Earth and spacecraft motions and

6http://www.stsci.edu/hst/stis/documents/handbooks/currentDHB/STIS longdhbTOC.html 157

Figure 6.2 FUV spectrum of J0437. The error bars on the left represent the measured average fluxes in four λ-bins. The dash-dotted line is the fit with the absorbed power-law model for E(B − V ) = 0.03. The dotted line shows the same model but dereddened. The dashed line is a blackbody spectrum with the temperature of 4 000 K, fitting the dereddened B,V,R,I WD fluxes, taken from Danzinger et al. (1993). 158

Figure 6.3 Total (source + background) count rate distribution in the region around the possible emission feature at 1372 A.˚ 159 transformed to barycentric dynamical times (TDB) at the solar system barycenter, using the STSDAS task “odelaytime”. To correct the TDB arrival times for the effect of the binary orbital Doppler shift (Taylor & Weisberg 1989) and to extract the light curve, we used the pulsar and binary orbit ephemerides from van Straten et al. (2001). Since the frequency of radio pulsations, f = 173.687948857032 Hz at the epoch of the STIS observation, is known with high precision, much higher than one can achieve in the time span Tspan = 24 638 s of our observation, there is no need to search for the period in the FUV data. We folded the corrected arrival times with the pulsar’s period and obtained the light curves for different numbers of phase bins. An example of the light curve for 4 phase bins, with an arbitrarily fixed reference phase (histogram) and averaged over the reference phase (smooth line; see Gregory & Loredo 1992 for a description of this procedure) is shown in Figure 6.4. The observed pulsed fraction can be estimated +5 as fp = 4−4%, which means that the pulsations are not statistically significant.

Figure 6.4 Pulsar light curve for 4 phase bins. The smooth line shows the light curve averaged over the reference phase.

2 The upper limit on the pulsed fraction can also be estimated from the Zn test 2 (e.g., Buccheri et al. 1983) that gives Zn = 2.7, 2.8, 5.2, 8.1, and 8.7 for n = 1, 2, 3, 4, and 5, respectively, at the radio pulsation frequency (n is the number of harmonics 2 included). For randomly distributed arrival times, the probabilities of getting Zn larger 160 than these values are 0.26, 0.59, 0.52, 0.42, and 0.56, respectively, which confirms that no periodic signal is detected. An upper limit on the pulsed fraction can be estimated 2 from the Z1 value, assuming sine-like pulsations. At a 3σ confidence level, the limit is 11%–12%, depending on the method used for estimation (e.g., Protheroe 1987; Vaughan int et al. 1994; Brazier 1994). It translates into an upper limit fp < 48%–53% for the intrinsic pulsed fraction of J0437, corrected for the background contribution. The upper limit is close to the pulsed fraction at E ∼> 1 keV, and it exceeds the pulsed fraction, ∼ 30%, observed in soft X-rays (Zavlin & Pavlov 1998). If the FUV radiation is thermal, as suggested by the spectrum (see §6.4.1), we expect the pulsed fraction to be even lower than 30% (because the FUV radiation is presumably emitted from a large fraction of the NS surface), so the limit is not truly restrictive. The reason for that is the very high detector background. We attempted to improve the S/N repeating the analysis for the first four orbits, with the lower detector background, but obtained approximately the same upper limit.

6.4 Neutron star or white dwarf?

First of all, we should understand whether the observed FUV spectrum is emitted by the WD companion or by the NS. The results of the optical photometry (Danziger et al. 1993; Bailyn 1993) yield Teff ≈ 3750–4500 K for the WD. The dashed line in Figure 6.2 shows a blackbody spectrum (for T = 4000 K, R = 0.025RJ, d = 140 pc) that crudely fits the photometric data and clearly falls well below the FUV data points. More accurate comparison should use cool WD atmosphere spectra (e.g., Bergeron et al. 1995; Hansen 1999), which can be harder than the blackbody at UV frequencies. We have applied a number of such models (provided by P. Bergeron 2003, private communication) for various chemical compositions, effective temperatures and gravitational accelerations, scaling them to fit the optical data, and found that the observed FUV flux exceeds the WD atmosphere model predictions by several orders of magnitude in all the cases. Thus, we conclude that the observed FUV emission originates from the NS.

6.4.1 Thermal origin of the FUV spectrum. Broadband Spectrum.

αλ We fit the spectrum with the absorbed power-law model, Fλ = F1500 (λ/1500 A)˚ × 10−0.4A(λ) E(B−V ), where the ultraviolet extinction curve A(λ) is adopted from Seaton (1979). The (low) interstellar extinction in the direction of J0437 is poorly known; dif- ferent authors use the color excess E(B −V ) values from < 0.01 (Bell et al. 1993) to 0.07 (Danziger et al. 1993). We performed the fits for three values, E(B − V ) = 0, 0.03, and 0.07, and found the power-law indices αλ = −4.0 ± 1.2, −4.2 ± 1.2, and −4.4 ± 1.2, and −18 −2 −1 −1 the normalizations F1500 = 2.6 ± 0.4, 3.4 ± 0.5, and 4.4 ± 0.7 × 10 erg cm s A˚ , respectively (see Fig. 6.5). The inferred slope αλ (albeit rather uncertain because of the −4 strong detector background) is close to that of the Rayleigh-Jeans spectrum, Fλ ∝ λ . It indicates that, most likely, the observed radiation is thermal radiation from the NS sur- face rather than magnetospheric radiation. At d = 140 pc, the normalization parameter −2 of the Rayleigh-Jeans fit corresponds to the brightness temperature T5 = 0.215 F1500R13 5 K, where T5 = T/(10 K), R13 is the radius of the emitting sphere in units of 13 km. 161

(Here and below, the temperature and the radius are given as measured by a distant 2 observer.) Our fits (with fixed αλ = −4) give T5R13 = 0.62 ± 0.06, 0.79 ± 0.08, and 1.1 ± 0.1, for E(B − V ) = 0, 0.03, and 0.07, respectively.

Figure 6.5 Confidence levels (68% and 90%) for the absorbed power-law model fit, for E(B − V ) = 0, 0.03, 0.07.

5 At T ∼< 10 K the blackbody spectrum deviates appreciably from the Rayleigh- Jeans limit in the FUV range. To investigate the range of lower temperatures, we also fit the absorbed blackbody model to the observed spectrum. The confidence contours in the T -R plane (Fig. 6.6) show that the lower limit on the surface temperature is 4.2 × 104 K, corresponding to a radius of 37 km, at a 68% confidence level (3.1 × 104 K and 59 km at a 90% level). For a typical NS radius R = 13 km, the inferred surface temperature is 0.107 ± 0.010, 0.121 ± 0.012, and 0.156 ± 0.014 MK, for E(B − V ) = 0, 0.03, and 0.07, respectively. The corresponding bolometric luminosity can be estimated 29 4 2 −1 29 −1 as Lbol = 1.2 × 10 T5 R13 erg s ; for instance, Lbol = (2.6 ± 1.0) × 10 erg s for E(B − V ) = 0.03, R = 13 km. Because of the large uncertainties of the FUV data points, deviations of the source spectrum from the Rayleigh-Jeans limit cannot be established from the FUV data alone. Therefore, to infer the upper limit on T (lower limit on R), we have to use the X-ray data. For the single-temperature blackbody model, we find that T should be lower than 162

Figure 6.6 Confidence levels (68% and 90%) for the absorbed blackbody model fit, for E(B − V ) = 0.03. The contours are cut (the dashed line in the top left corner) because the X-ray model flux exceeds the observed one at higher temperatures and smaller radii (see Fig. 6.7). The horizontal dashed line shows the temperature corresponding to a plausible NS radius of 13 km. 163

0.23 MK (R > 8.0 km), for E(B − V ) = 0.03, in order not to exceed the observed soft X-ray spectral flux (see Fig. 6.7). It is clear from Figure 6.7 that the FUV and X-ray data cannot be described by a single-temperature model. Based on the X-ray observations, Zavlin et al. (2002) suggested a two-temperature model: Tcore = 2.1 MK, Rcore = 0.12 km; Trim = 0.54 MK, Rrim = 2.0 km, where the “core” and the “rim” correspond to central and peripheral parts of the pulsar’s polar caps. We see from Figure 6.7 that extension of this model to the FUV range underestimates the observed FUV spectral flux. Most probably, this means that the NS surface temperature is a function of the polar angle, such that it decreases from ∼ 2 MK at the magnetic poles to ∼ 0.1 MK at the bulk of the surface. Of course, the estimates for the brightness temperature above do not imply a uniform surface temperature away from the polar caps. To determine the dependence of the surface temperature on magnetic colatitude, phase-resolved spectroscopy is required.

6.5 Heating mechanisms.

The inferred surface temperature, T ∼ 105 K, is much higher than the tempera- 3 tures ∼< 10 K expected for a passively cooling few-Gyr-old neutron star (e.g., Tsuruta 1998; Schaab et al. 1999 [S99 hereafter]). Therefore, it requires a heating mechanism to operate in J0437.

6.5.1 Internal heating If the sources of heat are in the highly conductive (hence almost isothermal) NS interiors, the surface temperature of 0.1 MK implies the interior temperature of order 1 MK (Gudmundsson, Pethick, & Epstein 1983). Various mechanisms of internal NS heating were investigated in a number of works (e.g., S99, and reference therein). The mechanisms relevant to MSP heating can be divided into two groups. Firstly, heat can be produced by the dissipation of energy of differential rotation caused by frictional interaction between the faster rotating superfluid core and the slower rotating outer solid crust (Shibazaki & Lamb 1989; Larson & Link 1999, and references therein). The heating mechanisms from the second group are associated with readjustment of the NS structure to a new equilibrium state as star rotation slows down. If the NS crust is solid, it will undergo cracking when the tension force exceeds a critical value, and the crust strain energy will be released as heat (Cheng et al. 1992). In addition, as the star spins down, the centrifugal force decreases and central density increases causing the shift in chemical equilibrium, which modifies the rate of nuclear reactions and may lead to heat release (Reisenegger 1995). The high surface temperature of J0437 strongly constrains heating mechanisms. For instance, such a temperature rules out crust cracking and chemical heating of the crust as the main heat sources (cf. Fig. 7 of S99). Chemical heating of the core and frictional heating remain viable mechanisms. For the latter, one can constrain the excess angular momentum ∆Js, residing in the superfluid, and the angular velocity lagω ¯, between the superfluid and the crust, averaged over superfluid moment of inertia. Using ˙ 41 4 2 equation (9) of Larson & Link (1999), we obtain ∆Js = Lbol/|Ω| = 1.1 × 10 T5 R13 erg 164

Figure 6.7 Multiwavelength spectrum of J0437. The data points on the left represent the measured FUV fluxes; the unabsorbed (dereddened) fluxes are only slightly higher for plausible values of E(B − V ) (see Fig. 6.2). The data points on the upper right are the unabsorbed X-ray fluxes from Chandra ACIS and ROSAT PSPC observations (Zavlin et al. 2002). Three dashed lines marked with temperature and radius values show the range of formally acceptable blackbody models (see §6.4 for details). The dashed line marked “WD” corresponds to the blackbody with the temperature of 4 000 K (cf. Fig. 6.2). The dash-dotted line that goes through the X-ray data points is the two-temperature hydrogen atmosphere + power-law model (see §6.4.1, §6.8, and Zavlin et al. 2002). The power-law component with the photon index Γ = 1.6 is shown separately by the dotted line. 165

4 2 −1 ˙ −14 −2 s,ω ¯ = ∆Js/Is = 0.15 T5 R13 rad s , where Ω = −1.086 × 10 rad s is the time 43 2 derivative of the angular frequency of the pulsar, Is = 7.3 × 10 g cm is the moment of inertia of the differentially rotating portion of the superfluid, estimated for the Friedman & Pandharipande (1981) equation of state. Because other mechanisms can contribute to heating of J0437, these estimates of ∆Js andω ¯ should be considered as upper limits.

6.5.2 External heating In addition to the above-discussed internal sources, heat can be provided by rela- tivistic particles created in the pulsar’s acceleration zones and bombarding the NS surface (e.g., Harding & Muslimov 2002, and references therein). The energy of these particles 3 1/2 is released in polar caps at the NS magnetic poles, with a radius rpc ∼ (R Ω/c) ≈ 2 (R/10 km)3/2(P/6 ms)−1/2 km. Moreover, inward-directed radiation from this particle population or even precipitating secondary particles created in the closed field line zone can heat the surface outside of the traditional polar caps (Wang et al. 1998). The energy dissipated in the NS polar regions per unit time (heating luminosity) depends on the geometry of the acceleration region and the degree of electric field screening. The numer- ical calculations, carried out by Harding & Muslimov (2002) for the case of MSPs, give heating rates somewhat lower than (but close to) the bolometric luminosity inferred from pc 30 −1 the X-ray observations of J0437, Lbol ≈ 2 × 10 erg s (Zavlin et al. 2002). A major fraction of the thermal energy deposited by the relativistic particles propagates towards the surface and is radiated in soft X-rays from the polar cap(s). However, some energy flows inwards, heating deeper NS layers beneath a larger surface area. If a fraction of this energy reaches the inner crust, it spreads over the whole interior of the NS because of its very high thermal conductivity, so eventually it will be radiated from the entire NS surface, together with the heat supplied by possible internal heating mechanisms. The effect of the external heating on the temperature distribution in an NS requires the numerical solution of a complicated problem of heat transport, with allowance for radi- ation from the surface. This problem has not been solved, to the best of our knowledge, so it is hard to assess the contribution of the polar cap heating to the observed FUV radiation. We can only state that if the external heating dominates, then a fraction surf pc ∼ Lbol /Lbol ∼ 0.1–0.5 of the energy deposited at the polar cap goes to heating of the NS. Crude estimates show, however, that such a large fraction of heat flowing inwards would require thermal conductivities much higher than calculated for the NS crust (e.g., Jones 1978), suggesting that particle precipitation only on the open field line zone cannot account for general surface heating of old NSs. In principle, a very old NS could be heated by exotic particles (or products of their decay) captured in the NS matter. For instance, Hannestad, Ker¨anen,& Sannino (2002) consider NS heating by products of decay of Kaluza-Klein majorons and gravitions, that form a halo around the NS, and conclude that the thermal luminosity of an old NS should reach a constant level corresponding to the energy deposited by decay particles. (See Pavlov, Stringfellow, & C´ordova 1996 for references to earlier papers.) Although the Occam razor suggests that less exotic mechanisms should be explored first, the possibility to indirectly investigate exotic particles through thermal radiation from MSPs cannot be dismissed at the present stage. 166

6.6 Are millisecond pulsars hotter than ordinary old neutron stars?

It is interesting to compare the inferred surface temperature of J0437 with the temperatures (or upper limits) for other old pulsars, including MSPs. We compiled the results of the available UV-optical observations of old (∼> 1 Myr), nearby (∼< 300 pc) NSs in Table 6.2 and re-estimated the temperatures using the most recent results on the distances. In addition to the old pulsars, we included the famous “dim” isolated NS, RX J1856.5−3754, whose age is unknown, because it might be an MSP (Pavlov & Zavlin 2003). We see from Table 6.2 that the temperature of J0437 is the lowest measured temperature for a NS. The observations of the other two nearby MSPs, J2124−3358 and J0030+0451, were not nearly as deep as required to detect their thermal radiation at a similar temperature. All the upper limits on T in Table 6.2 are also above the temperature of J0437 with one exception — T5 < 0.88 for PSR J0108−1431, whose spin- down age is a factor of 30 smaller than that of J04371. Although the difference in the temperatures is not very large, it should be noted that the upper limit in Table 6.2 (see also Mignani et al. 2003b) is rather conservative, in the sense that it is obtained assuming d = 200 pc, the largest among the distances, 60–200 pc, estimated from various models of Galactic electron distribution (Tauris et al. 1994; Taylor & Cordes 1993; Cordes & Lazio 2002). For instance, the limit is T5 < 0.45 for d = 130 pc (Mignani et al. 2003a). Even if the true distance is somewhat larger than 200 pc, the upper limit remains surprisingly low, given the much younger spin-down age of J0108−1431. The higher temperature of the older J0437 cannot be attributed to accretion in the binary system because the accretion ceased about 3 Gyrs ago, while the time for 5 a NS to cool to 10 K, losing the accretion-generated heat, is ∼< 10 Myr. The high temperature can possibly be explained by stronger frictional heating, consistent with a factor of 15 larger |Ω˙ |. It is also possible that “rotochemical heating” of the NS core (Reisenegger 1995,1997) has been turned on in this MSP, or J0437 is simply sufficiently old to accumulate enough heat by capturing exotic particles (see §4.4). Finally, the higher temperature of J0437 might be associated with stronger magnetospheric heating, since its E˙ is about 700 times larger than that of J0108−1431. In this case one should expect MSPs with higher E˙ (up to 3 orders of magnitude in most powerful MSPs, such as PSR B1821−24) to be even hotter than J0437, but it would be difficult to discern their surface emission since these pulsars are also strong sources of magnetospheric radiation. Whatever is the reason of the higher temperature of J0437, it is tempting to assume that the surface temperatures of MSPs are generally higher than those of old “ordinary” pulsars of similar or even younger ages. Since ordinary isolated NSs cool down with age even in the presence of internal heating (Tsuruta 1998; S99), this as- sumption implies that the transition from ordinary pulsars to MSPs is accompanied by a considerable growth of NS temperature. Moreover, the temperature is maintained high in the course of the Gyr-long MSP thermal evolution by a heating process, probably

1Although the true age of a pulsar may differ substantially from its spin-down age, the low temperature of the WD companion implies (e.g., Hansen & Phinney 1998) that J0437 is older than 3 Gyr, that is a factor of 18 larger than the spin-down age of PSR J0108−1431. 167

Table 6.2 Blackbody temperatures of nearby old neutron stars.

a b c d e f g NS T Distance Age Fν λ E(B − V ) Ref. (105 K) (pc) (Myr) (10−31 cgs) (µm) B1929+10 < 4.9 331 ± 10 3.2 5.4 0.24 0.10 1 B0950+08 < 2.5 262 ± 5 16 5.1 0.31 0.01 2 J0108−1431 < 0.88 200 170 < 1.5 0.49 0.01 3 J1856−3754 5.6h 117 ± 12 ? 240 0.15 0.03 4 J0437−4715 1.2 139 ± 3 4900 20 0.15 0.03 5 J2124−3358 < 4.6 270 7200 < 3.3 0.49 0.05 6 J0030+0451 < 9.2 320 7700 < 4.8 0.49 0.05 7

aBlackbody (brightness) temperature from optical/UV observations, for an NS radius of 13 km and quoted distance and color index. bDistances estimated from parallaxes (with ± uncertainties; see Brisken et al. 2002; Walter & Lattimer 2002; van Straten et al. 2001) or from the dispersion measure (Cordes & Lazio 2002). cCharacteristic age of pulsars, τ = P/(2P˙ ). dObserved spectral flux (or upper limit), in units of 10−2 µJy, at the wavelength quoted in the next column. eReference wavelength. f Adopted color index. gReferences for the spectral flux measurements.–(1) Mignani et al. 2002; (2) Pavlov et al. 1996; (3) Mignani et al. 2003b; (4) Pons et al. 2002; (5) this work; (6) Mignani & Becker 2004; (7) Koptsevich et al. 2003. h Lower temperatures, T5 < 3.9, corresponding to R > 16 km, are required in a two-component blackbody model (Pavlov et al. 2002; Braje & Romani 2002). 168 associated with specific properties of MSPs, such as fast rotation or old age. To under- stand the apparently “nonmonotonic” thermal evolution of old NSs, thermal emission from a larger sample of these objects should be investigated.

6.7 Possible spectral line at 1372 A˚

Although the detection of the emission line at 1372 A(˚ hν = 9.04 eV) is marginal, it is interesting to speculate as to about its origin. Firstly, this could be an electron cyclotron line (e.g., formed in a corona above the polar cap) in the magnetic field B = 7.8 × 108(1 + z) G, where z is the gravitational redshift. Such a field is close to the 8 −3 1/2 −1 “conventional” magnetic field, Bp = 6.6 × 10 R6 I45 (sin α) G, at the magnetic poles 6 45 of an NS losing energy via magnetodipole radiation (R = 10 R6 cm and I = 10 I45 g cm2 are the NS radius and moment of inertia, α is the angle between the magnetic and rotational axes). The main difficulty with this interpretation is the small width of the observed line, ∼ 3 A.˚ First, it implies a very uniform field in (hence, a small size of) the emitting region, ∆B/B < ∆λ/λ. For instance, if the emitting region is a hot spot at the magnetic pole, its size should be smaller than ∼ 0.5 km. Second, the thermal (Doppler) 2 1/2 1/2 ˚ width of the cyclotron line is ∆λD = λ(2kT/mec ) | cos θ| ≈ 25 T6 | cos θ| A, where θ is the angle between the line of sight and the direction of the magnetic field. For the −1/2 thermal width to be smaller than ∆λ, a phase-averaged | cos θ| must be ∼< 0.12 T6 ◦ (θ ∼> 83 for T6 = 1), which is hard to reconcile with the constraints on the rotation and magnetic inclinations obtained from the radio polarimetry (e.g., Manchester & Johnston 1995). Alternatively, if the NS surface is covered with a hydrogen atmosphere with overheated outer layers (e.g., due to convection), the observed line may be one of the three gravitationally redshifted Zeeman components of the Lyα line in a magnetic field B ∼ 108–109 G. For instance, at B = 7 × 108 G, the wavelengths of the Zeeman compo- nents at the NS surface are 730, 1069, and 1334 A˚ (Ruder et al. 1994). If the observed line is the redshifted π-component, the redshift is z = 0.28, so the wavelengths of the redshifted σ-components, 937 and 1712 A,˚ are outside of the observed FUV range. The 1/2 ˚ thermal width of the Zeeman component, ∼ 0.6 T6 A, is much smaller than the ob- served width. The line broadening can be caused by a magnetic field nonuniformity: ∆λ = 3 A˚ corresponds to ∆B/B ∼ 0.3 (estimated from Fig. A.2.1 of Ruder et al. 1994), that is the putative corona may spread over a substantial fraction of the NS surface. 26 −1 The luminosity in the line, L1372 ≈ 0.9 × 10 erg s , is a small fraction, ≈ 2%, of the observed FUV luminosity. If the emitting region is in collisional (coronal) equilibrium, 2 49 50 −3 the corresponding emission measure is nH V ∼ 10 –10 cm for T ∼ 0.1–1 MK. If the 1372 A˚ line is confirmed in a future FUV observation, the most convincing confirmation of the Lyα interpretaion would be detection of another Zeeman component (e.g., the σ-component in the NUV range), which would allow one to measure both the magnetic field and the gravitational redshift. 169

6.8 Magnetospheric component in J0437 spectrum

Zavlin et al. (2002) found that, in addition to the two-temperature thermal com- +0.3 ponent, a power-law component with a photon index Γ = 2.2−0.6 is needed to fit the X-ray spectrum at energies above 2 keV (Fig. 6.7). However, extension of this compo- nent with the best-fit Γ to the FUV range is well above the observed FUV spectrum, and even for Γ = 1.6 the extension is only marginally consistent with the FUV data (Fig. 6.7). We can crudely estimate the upper limit on the magnetospheric luminosity pl 27 −1 is the FUV range as LFUV ∼< 4.2 × 10 erg s . The apparent discrepancy can be ex- plained assuming that the spectrum of the magnetospheric radiation breaks down when the frequency decreases from X-rays to the FUV range. The optical upper limits for MSPs J0030+0451 (Koptsevich et al. 2003) and J2124−3358 (Mignani & Becker 2003), well below the extensions of their X-ray power-law components, suggest that it might be a common property of MSPs, contrary to, e.g, ordinary middle-aged pulsars. Alter- natively, as Zavlin et al. (2002) noticed, it is possible that the excess counts at higher energies in MSP spectra might be interpreted as thermal radiation from a very hot, small area within the polar cap (e.g., T ∼ 12–15 MK, R ∼ 1–2 m for J0437). To understand which of the two interpretations is correct, deeper observations of J0437 in hard X-rays are required.

6.9 Summary and conclusions

The STIS/FUV-MAMA observation of J0437 provided first firm detection of an MSP in the optical-UV range. The FUV spectrum is best interpreted as thermal emission from the NS surface with a temperature of about 0.1 MK. This temperature exceeds the upper limit on the temperature of the younger, but less luminous, ordinary pulsar J0108–1431. This is likely associated with a difference in spindown-driven heating. If magnetospheric heating plays a role, it must be effectively communicated, perhaps by radiation or secondary particles, to the bulk of the NS surface. Evolutionary differences between ordinary pulsars and MSPs might plausibly affect the internal thermal history. To understand thermal evolution of old NSs, more MSPs and ordinary old pulsars should be observed in the optical-UV range. Comparison of the FUV and X-ray spectra shows that the temperature is not uniformly distributed over the NS surface. The X-ray observations, sensitive to higher temperatures, show a smaller size of the emitting region, naturally interpreted as a pulsar polar cap, perhaps also with a nonuniform temperature. To understand the temperature distribution over the NS surface, phase-resolved spectroscopy in both X-rays and FUV is needed. We failed to detect FUV pulsations because the source was placed at a region of high detector background. An FUV observation of J0437 with an optimal positioning on the detector could detect pulsations (or put a stringent limit on the pulsed fraction) and provide information on the temperature distribution. The FUV upper limit on the nonthermal (magnetospheric) component, observed in hard X-rays, suggests a spectral turnover of this component at EUV wavelengths, which can be a generic property of MSPs. However, the upper limit is not very strong 170 because of large errors associated with the high detector background. To tightly con- strain the nonthermal component, another FUV-MAMA observation with improved S/N (scheduled for 2005) as well as deep NUV and X-ray exposures are required. The marginally detected emission line at 1372 A˚ can be interpreted as an electron cyclotron line or, more likely, a Zeeman component of the Hydrogen Lyα line in a magnetic field of ∼ 109 G. Confirming this line would be of profound importance as it provides an opportunity to directly measure the MSP magnetic field and gravitational redshift (if another Zeeman component is also detected). 171

Chapter 7

Chandra observations of CCO J0852−4617.

The Chapter describes the results of Chandra ACIS observations of Compact Cen- tral Object (CCO) in Supernova Remnant G266.2–1.2 (RX J0852.0–4622). The spectrum of this object can be described by a blackbody model with the temperature kT = 404±5 eV and radius of the emitting region R = 0.28 ± 0.01 km, at a distance of 1 kpc. Power- law and thermal plasma models do not fit the source spectrum. The spectrum shows a marginally significant feature at 1.68 keV. Search for periodicity yields two candidate periods, about 301 ms and 33 ms; the corresponding pulsed fractions are 13% and 9%, respectively. (Both candidates are significant at a 2.1σ level.) We find no evidence for long-term variability of the source flux or extended emission around the central object. We suggest that CXOU J085201.4–461753 is similar to CXOU J232327.9+584842, the central source of the supernova remnant Cas A. It could be either a neutron star with a low magnetic field, slowly accreting from a fossil disk, or, more likely, an isolated neu- tron star with a superstrong magnetic field. In either case, a conservative upper limit on surface temperature of a 10 km radius neutron star is about 90 eV, which suggests accelerated cooling for a reasonable age of a few thousand years.

7.1 Previous observations.

The shell-like supernova remnant (SNR) G266.2–1.2 (also known as RX J0852.0– 4622, or “Vela Junior”) at the south-east corner of the Vela SNR was discovered by Aschenbach (1998) in the ROSAT All-Sky Survey data. Possible detection of the 1.156 MeV γ-ray line of the radioactive isotope 44Ti (half-life ∼ 90 yr) with the Compton Gamma-Ray Observatory (Iyudin et al. 1998) may imply a very young SNR age of ∼ 680 yr, at a distance of ∼ 200 pc. Aschenbach, Iyudin, & Sch¨onfelder(1999) estimated upper limits of 1100 yr for the age, and 500 pc for the distance. Observations with ASCA (Tsunemi et al. 2000; Slane et al. 2001) demonstrate that the X-ray spectra of the SNR shell are nonthermal. Fits of these spectra with a power-law (PL) model yield the hydrogen column density substantially higher than that for the Vela SNR, implying a plausible distance to the remnant of 1–2 kpc, and an age of a few thousand years. Aschenbach (1998) suggests that G266.2–1.2 was created by a core-collapse su- pernova that left a compact remnant — a neutron star (NS) or a black hole (BH). Three compact remnant candidates have been reported from the observations with ROSAT (Aschenbach 1998; Aschenbach et al. 1999), ASCA (Slane et al. 2001), and Beppo-SAX (Mereghetti 2001). Pavlov et al. (2001) observed G266.2–1.2 with the Chandra Ad- vanced CCD Imaging Spectrometer (ACIS) and found only one bright X-ray source, CXOU J085201.4–461753 (J0852 hereafter), close to the SNR center. They measured the source position with accuracy better than 200 and proved that J0852 is not an X-ray 172 counterpart of bright optical stars in the field. Follow-up optical observations (Pavlov et al. 2001; Mereghetti, Pelizzoni, & De Luca 2002a) revealed an object located only 200. 4 south-west of the J0852. The colors of the optical source are consistent with those of a main sequence star at a distance of 1.5–2.5 kpc; most likely, this is a field star. The lim- iting optical magnitudes at the position of the X-ray source (B > 22.5, R > 21 — Pavlov et al. 2001; B > 23, R > 22.5 — Mereghetti et al. 2002a) rule out the possibility of the X-ray source being an AGN. The lack of variability combined with the X-ray spectral properties makes a cataclysmic variable interpretation also implausible. The nature of the source remains elusive, although an isolated cooling NS or a NS with a “fallback” disk seem to be possible interpretations. The large frame time, 3.24 s, of the previous snapshot (3 ks) ACIS observation made it impossible to search for short periods and led to strong saturation (pile-up) of the source image, precluding an accurate spectral analysis. To search for pulsations from the compact source and obtain a more accurate spectrum, we observed J0852 with Chandra ACIS with a time resolution of 2.85 ms.

7.2 Chandra observations and data reduction.

J0852 was observed with ACIS-S3 in Continuous Clocking (CC) mode on 2001 August 30 (31.5 ks total exposure). CC mode allows one to achieve time resolution of 2.85 ms at the expense of spatial information in one dimension. There were no substantial “background flares” during the observation, so we do not exclude any time intervals from the analysis. For data reduction and analysis, we used CIAO 2.2.1 (CALDB 2.7) and XSPEC v.11.0. The FWHM of the one-dimensional (1-D) source image is 000. 7, consistent with the ACIS point spread function. The Chandra observations show no evidence for an extended emission around the point source. The 3σ upper limit on the pulsar wind nebula (PWN) brightness (in counts arcsec−2) from 3 ks Timed Exposure observation can be estimated as 3(b/A)1/2, where b = 0.03±0.01 counts arcsec−2 is the background surface brightness, 2 2 and A is the PWN area. We will scale the area as A = 1000A3 arcsec (1000 arcsec area corresponds to the PWN transverse size of about 5 × 1017 cm at a distance of 1 kpc). For a typical power-law PWN spectrum with a photon index γ = 1.5 − 2, this −16 −1 upper limit corresponds to the unabsorbed PWN intensity of (1.5 − 3) × 10 A3 erg −2 −1 −2 cm s arcsec , for the typical nH obtained below.

7.3 Spectrum.

For the spectral analysis, we extracted 11,450 source-plus-background counts from a 400 segment of the 1-D image. The background was taken from two adjacent 1000 segments. The background-subtracted source count rate is 0.313 ± 0.004 counts s−1. Figure 7.1 shows the pulse-height spectrum in the 0.6–8.0 keV band, grouped into 77 bins with ≥ 100 source counts per bin. We ignored all counts below 0.6 keV for spectral fitting because of the poorly known ACIS response at lower energies. Fitting the spectrum with a power-law (PL) model yields a large photon index γ = 4.32±0.06 (all uncertainties at a 1σ confidence level), and a hydrogen column density 173

21 −2 nH,21 ≡ nH/10 cm = 11.2 ± 0.2, close to the total Galactic HI column density in this direction, ≈ 1 × 1022 cm−2 (Dickey & Lockman 1990; estimated with the W3NH 1 2 tool ). The quality of the fit is so poor (χν = 3.94 for 74 degrees of freedom [d.o.f.]) that this model can be rejected. Thermal plasma emission models (thermal bremsstrahlung 2 and mekal with solar abundances) also do not fit the observed spectrum (χν = 1.63 and 14.26 for 74 d.o.f., respectively). On the contrary, a single blackbody (BB) model fits the spectrum reasonably 2 well (χν = 1.130 for 74 d.o.f.; see Fig. 7.1). It yields a temperature T = 4.68 ± 0.06 MK (kT = 404 ± 5 eV) and a radius of equivalent emitting sphere R = (0.28 ± 0.01) d1 32 2 km, where d1 ≡ d/1 kpc. The bolometric luminosity is Lbol = (2.5 ± 0.2) × 10 d1 ergs −1 s . The hydrogen column density, nH,21 = 3.45 ± 0.15, considerably exceeds the highest value, nH,21 = 0.6, found by Lu & Aschenbach (2000) for the Vela SNR. It indicates +76 that the source is substantially more distant than the Vela pulsar (dVela = 294−50 pc — Caraveo et al. 2001). Adding a PL component to the BB model only marginally 2 2 improves the fit (χν = 1.126 for 72 d.o.f.). The F-test shows that the reduction of χ caused by adding the PL component is significant only at a 66% confidence level. Fits with the magnetic hydrogen NS atmosphere models (Pavlov et al. 1995) give a lower effective temperature (kT ≈ 270 eV) and a larger emitting area (R ≈ 1.2 km). In both BB and H atmosphere fits, the inferred temperature is too high, and the radius too small, to interpret the detected X-rays as emitted from the whole surface of a uniformly heated NS. To constrain the temperature of the entire NS surface, we fit the spectrum with a two-component BB model. The fits to the ASCA spectra of the outer, brighter parts of the SNR give a range of hydrogen column densities from 1.4 to 5.3 × 1021 cm−2 (Slane et al. 2001). To find a conservative upper limit on the surface temperature Ts, we fix the column density at nH,21 = 5.3, add a soft BB component with Rs = 10 d1 km, and fit T and R at different values of Ts, increasing Ts until the fit probability falls to 0.1%. This gives an upper limit Ts ≤ 89 eV, at a 99.9% confidence level. If we fix the column density at nH,21 = 3.4 (as obtained for the single BB fit), the limit becomes as low as Ts ≤ 75 eV.

7.4 Timing. No pulsations?

For timing analysis, we extracted 10,957 photons from a 200. 5 segment centered on J0852 (≥ 89% of these counts are expected to come from the point source). The time span of the observation is Tspan = 31.5 ks. We corrected the event times for telescope dither and Science Instrument Module motion using the approach described by Zavlin et al. (2000). We transformed the corrected times to the solar system barycenter using the axBary tool of CIAO. 2 We used the Zm test (Buccheri et al. 1983) to search for periodic pulsations. We 2 8 calculated Zm for m = 1–5 (where m is the number of harmonics) at 10 equally spaced frequencies f in the 0.001–100 Hz range. This corresponds to oversampling by a factor

1http://heasarc.gsfc.nasa.gov 174

Figure 7.1 Fit of the ACIS-S3 spectrum of J0852 with a blackbody model. The contours correspond to 68%, 90% and 95% confidence levels. 175

−1 2 of about 30, compared to the expected width of Tspan ≈ 30 µHz of the Zm(f) peaks, and guarantees that we miss no peaks. The two most significant peaks we found are at f = 3.324231 Hz±3 µHz (P ≈ 301 ms) and f = 30.369484 Hz±2 µHz (P ≈ 33 ms)2. The most significant Zm,max values, Z4,max = 52.9 for the 301 ms period and Z1,max = 36.7 for the 33 ms period, correspond to 96.7% and 96.8% significance levels, respectively, for 6 the number of independent trials N = fmaxTspan ≈ 3 × 10 . The pulsed fractions obtained from the pulse profiles are 13%±3% and 9.1%±2.5% for the 301 ms and 33 ms period candidates, respectively. Because of the low significance, we consider 13% as an upper limit for the pulsed fraction. To search for variability on larger time scales, we binned the data into 200 s bins. Using the Kolmogorov-Smirnov test, the hypothesis that the observed numbers of counts in the bins come from a Poisson distribution (with the mean of 69.7564 counts per bin) can not be rejected at a 70% confidence level. We have also used the Fourier transform and found no periodic signal with the pulsed fraction larger than 12% in 1–10 mHz frequency range. Therefore, we find no evidence for long-term variability in the data.

7.5 The nature of CCO in G266.2–1.2

The X-ray data and optical limits indicate that J0852 is the compact remnant (NS or BH) of the supernova explosion. The spectral properties and the lack of a pulsar-wind nebula (PWN) and radio emission (Duncan & Green 2000) suggest that J0852 is not an active pulsar. Its observational properties strongly resemble those of the other radio- quiet central compact objects (CCOs) in SNRs (see Pavlov et al. 2002a for a review), particularly the CCO in the SNR Cas A (Murray et al. 2002, and references therein). At least one of these sources, 1E 1207.4–5209, has been proven to be a NS rotating with a period of 424 ms (Zavlin et al. 2000; Pavlov et 2002b). A number of possible interpretations of CCOs have been recently discussed by several authors (e.g. Pavlov et al. 2000, 2001, 2002a; Chakrabarty et al. 2001). The limits on X-ray-to-optical flux ratio for J0852 and the Cas A CCO virtually rule out models which involve accretion onto a NS or a BH from a binary companion. If these are accreting objects, a more plausible source of accreting matter might be a “fossil disk”, left over after the SN explosion (van Paradjis, Taam, & van den Heuvel 1995). Alternatively, thermal emission from an isolated, cooling NS could explain the observational results. We discuss these two options below.

7.5.1 Accretion-powered X-ray pulsar? 32 2 −1 If J0852 is an accreting NS, the observed luminosity, Lx ∼ 2 × 10 d1 erg s , 12 −1 2 −1 could be due to a rather low accretion rate,m ˙ ∼ 1.5 × 10 R6M1 d1 g s , where 6 R6 = RNS/(10 cm), M1 = M/M¯. The accreting matter could be supplied from a fossil (“fallback”) disk. The formation of such a disk from the ejecta produced by a SN ex- plosion was discussed by a number of authors (e.g. Marsden, Lingenfelter, & Rothschild

2The frequency uncertainties, at a 90% confidence level, are estimated using the method of Gregory & Loredo (1996); see also Zavlin et al. (2000). 176

2001, and references therein). Some models suggest that a fossil disk can be formed several days after the SN explosion (“prompt” disk) and range from 0.001M¯ to 0.1M¯, while others suggest that the disk can be formed later, years after the SN explosion (“de- layed” disk). The details of the formation mechanism and the disk properties are highly uncertain, and, consequently, the accretion ratem ˙ is also poorly constrained, but the required value of ∼ 1012 g s−1 is low enough not to exhaust the disk at any reasonable age of J0852. The accretion onto a NS can proceed in two different regimes (e.g., Frank, King, & Raine 1992), depending on the relation between the corotation radius, Rc = 1.5 × 8 2/3 1/3 9 4/7 −2/7 −1/7 12/7 10 P M1 cm, and the magnetospheric radius, RM = 3.5×10 B12 m˙ 12 M1 R6 12 cm, where P is the NS spin period, B = 10 B12 G is the magnetic field at the NS 12 −1 surface, andm ˙ 12 =m/ ˙ (10 g s ). If RM > Rc, the infalling material is stopped at the magnetospheric radius and expelled as a wind due to the centrifugal force. In this “propeller regime” (Illarionov & Sunyaev 1975), X-ray emission is mainly due to optically thin thermal bremsstrahlung produced in the flow (Wang & Robertson 1985). Since the thermal bremsstrahlung model does not fit the observed spectrum, we consider this case unlikely. 2 6/7 −3/7 −5/7 18/7 9 7/6 1/2 5/6 −3 If RM < Rc (i.e., P ∼> 10 B12 m˙ 12 M1 R6 s, or B ∼< 4×10 P m˙ 12 M1 R6 G), the accreting matter is able to reach the NS surface. At extremely low magnetic 5 1/2 1/4 −5/4 fields, B ∼< 6 × 10 m˙ M1 R6 G, when the magnetospheric radius is smaller than the NS radius, a hot layer is formed at the boundary between the accretion disk and the NS surface (e.g., Frank et al. 1992). Since this boundary layer is expected to be opti- cally thin atm ˙ ¿ 1016 g s−1 (Inogamov & Sunyaev 1999), its radiation cannot explain 6 1/2 1/4 −5/4 the observed BB spectrum. At reasonable magnetic fields, B À 10 m˙ M1 R6 G (RM À RNS), the accretion flow is channeled onto the NS poles, producing hot spots 3/2 1/2 −2/7 1/7 1/14 9/14 of radius a ∼ RNS /RM ∼ 0.17B12 m˙ 12 M1 R6 km. The observed size and tem- perature of the BB-like radiation are consistent with being emitted from such a cap at 11 B ∼ 10 G. Such an estimate requires a pulsar period P ∼> 10 s, much longer than our candidate periods. If we assume P = 301 ms, the condition RM < Rc requires 9 1/2 5/6 −3 1/7 1/14 9/14 B ∼< 10 m˙ 12 M1 R6 G and a ∼> 1.2m ˙ 12 M1 R6 km, considerably larger than the size of emitting region, R ≈ 0.3d1 km, inferred from the BB fit. However, given the crudeness of the polar cap size estimate, which can be much smaller than adopted above (see, e.g., Frank et al. 1992, and references therein), we cannot rule out the candidate period of 301 ms based on the apparent inconsistency between a and R. Thus, in the accretion hypothesis, J0852 could be a low-luminosity X-ray pulsar, presumably with a magnetic field much lower than those of binary X-ray pulsars, slowly accreting from a fossil disk. An argument against this interpretation is a lack of irregular variability in the radiation from J0852, which is commonly observed from accreting sources (at least, X-ray binaries). On the other hand, variability could be found in further observations of this source. A direct confirmation of the accreting hypothesis would be detection of an accretion disk, which would require deep IR-optical observations with high angular resolution. 177

7.5.2 Isolated cooling neutron star? One can also assume that J0852 is an isolated (non-accreting) NS emitting thermal radiation from its surface. The “standard” NS cooling models predict a luminosity of ∼ (0.5–2)×1034 erg s−1 for a NS of 0.1–10 kyr age (e.g., Tsuruta 1998). The lower observed luminosity of J0852 could be interpreted as due to an accelerated cooling mechanism, but applicability of the cooling models to J0852 is questionable because the models assume a uniformly heated NS surface while the size of the emitting region obtained from the BB fit is only ≈ 0.3 d1 km. Apparent sizes of the emitting region much smaller than the canonical NS radius have been observed from other isolated NSs (Pavlov et al. 2002a,c). In particular, the Cas A CCO shows a (blackbody) size of 0.3 km with a temperature of 0.6 keV (Pavlov et al. 2000), which hints that it is an object similar to J0852, with a higher temperature possibly due to its younger age. Pavlov et al. (2000) suggested a two-component thermal model for the Cas A CCO, in which the observed X-rays are emitted from hydrogen polar caps of about 1 km radius and 0.24 keV effective temperature, while the rest of the NS surface is iron at a temperature of 0.15 keV, too cold to be observable because of strong interstellar absorption. In this model, the polar caps are hotter because of the higher thermal conductivity of hydrogen. Weaker ISM absorption for J0852 allowed us to find a lower temperature limit for the cold component, < 90 eV, too low to explain the temperature difference by different chemical compositions. It should be mentioned that this limit is well below the temperatures predicted by the standard cooling models for NSs younger than 10 kyr, which means that if J0852 is a 10-km radius NS, it undergoes fast cooling, perhaps associated with direct Urca processes in the NS core (e.g., Yakovlev et al. 2002). Hot spots on the NS surface could also be associated with a very strong magnetic field, B À 1013 G. Due to anisotropic heat conductivity of the NS crust, the surface temperature is higher at the magnetic poles (Greenstein & Hartke 1983; Shibanov & Yakovlev 1996). To produce small hot spots, the surface magnetic field should be strongly nonuniform (e.g., an offset dipole or a quadrupole — Page & Sarmiento 1996). Fast 14 decay of a superstrong magnetic field (B ∼> 10 G) could provide an additional source of polar cap heating (Thompson & Duncan 1996; Colpi, Geppert & Page 2000). In such strong magnetic fields, electron-positron pair creation should be suppressed due to photon splitting (Baring & Harding 2001), which is consistent with the apparent lack of pulsar activity in J0852. One can crudely estimate the magnetic field assuming that one of the two candi- date periods, 33 ms or 301 ms, is the true period. If the initial period of the pulsar was much shorter than the current period, then the period derivative, rotation en- ergy loss rate, and “canonical” magnetic field [B ≡ 3.2 × 1019(P P˙ )1/2 G], can be es- ˙ −11 −1 ˙ 36 −2 −1 −1 timated as P = 3.2 × 10 P [(n − 1)t3] , E = 1.25 × 10 P [(n − 1)t3] erg s , 14 −1/2 3 and B = 1.8 × 10 P [(n − 1)t3] G, where t = 10 t3 yr is the NS age, and n is the braking index. Assuming n = 2.5, (close to that observed in young pulsars), we obtain, ˙ −13 −1 ˙ 38 −1 −1 12 −1/2 for P = 33 ms, P = 7.0 × 10 t3 , E = 8.6 × 10 t3 erg s , and B = 4.9 × 10 t3 G — parameters typical for a young, active pulsar, in apparent contradiction with ob- ˙ −12 −1 servations. On the other hand, for the 301 ms period, we obtain P = 6.4 × 10 t3 , 178

˙ 36 −1 −1 13 −1/2 E = 9.2 × 10 t3 erg s , and B = 4.4 × 10 t3 G. Since the local magnetic field can be much higher than the canonical value (e.g., for an offset dipole), one can speculate that, for P = 301 ms, it is high enough to explain the hot spot(s) and the lack of radio- pulsar activity. If this hypothesis is correct, the J0852 could be a very young Anomalous X-ray Pulsar (AXP) whose period will become of order 6–12 s (as observed in AXPs) when it grows older by a factor of 20–40. However, there are considerable differences between the properties of AXPs and J0852. Contrary to AXPs, whose spectra contain both the BB and PL components of comparable luminosities (Mereghetti et al. 2002b), the spectrum of J0852 fits well with a single BB model. The size of the emitting region in J0852 is substantially smaller (0.3 km vs. 0.7–5 km), and the temperature somewhat lower (0.4 keV vs. 0.4–0.6 keV), than those of AXPs. These differences (particularly, the lack of a PL component in J0852) hint at different NS parameters. For instance, one can speculate that none of the candidate periods is correct, and the true period is even longer than the AXP periods. In this case, the magnetic field could be even higher than those adopted in the magnetar interpretation 15 −1 of AXPs — e.g., B = 2.4×10 (P/20 s)t3 G. Such a strong field can inhibit not only the pair cascade, but also the emission of primary particles from the NS surface, which might explain the lack of particles in the NS magnetosphere (hence, the lack of nonthermal 4/15 −12/15 radiation) in J0852. If the NS rotates sufficiently slow, P ∼> 0.5B15 (Z/26) s, the critical parallel electric field required to pull out electrons from the NS surface, 12 6/5 3/5 −1 Ek,crit ≈ 2.7 × 10 (Z/26) B15 V cm (Usov & Melrose 1995), is higher than the 10 −3/2 −1 maximum parallel electric field at the surface, Ek,max ≈ 1×10 B15(P/20 s) V cm . 4/5 2/5 On the other hand, the surface temperature, kTe ≈ 0.5(Z/26) B15 keV, above which the thermoionic emission of electrons becomes efficient (Usov & Melrose 1995), grows with increasing magnetic field. (These estimates assume that the NS has no light-element [e.g., hydrogen] atmosphere.) Therefore, a long period and a superstrong magnetic field might explain the lack of the PL tail in the spectrum of J0852 and other enigmatic CCOs (e.g., in the Cas A and Pup A SNRs; Pavlov et al. 2002a).

7.6 Conclusion.

Thus, the observations of J0852 can be explained assuming it is a NS. We consider the interpretation in terms of an isolated NS with a very strong magnetic field somewhat more plausible than the others, but further observations are required to confirm or reject this hypothesis. Particularly important would be the long X-ray timing observations to measure the period unequivocally, high-resolution X-ray spectral observations to look for spectral features, and IR-optical observations to search for a NS counterpart (e.g., a fossil disk). 179

Chapter 8

Overview and summary.

Throughout the thesis I considered a number of objects with quite different ob- servational properties. They include young pulsars enveloped by synchrotron nebulae (the Vela pulsar/PWN and pulsars/PWNe from Chapter 3), two middle-aged pulsars (Geminga and PSR 0656+14) whose spectra show both the thermal component origi- nating from the NS surface and the non-thermal magnetospheric component (which dom- inates in young pulsars), the ancient 5-Gyr-old millisecond pulsar J0437−4715 whose UV to X-ray spectrum is predominantly thermal, and, finally, the enigmatic Central Com- pact Object (CCO) in the SNR G266.1−1.2 whose X-ray spectrum can be described by a blackbody model with a much higher temperature and a smaller radius than in the previous cases. All these objects are believed to be neutron stars (although the CCO could be a “quark star”), while PWNe are direct products of NS/pulsar activity. Thus, in this thesis I have demonstrated that neutron stars are extremely diverse in their observational manifestations. This diversity is likely associated with more profound dif- ferences in the internal structure of neutron stars (e.g., density and composition of NS interiors). The latter can result from different ages of neutron stars, different magnetic fields and/or masses acquired by the neutron star after the SN explosion. According to theoretical models, changing any of these parameters should leave distinct imprints on the observable properties of neutron stars (e.g., the spectra and pulse profiles). However, the differences in these fundamental NS properties are often masked by other factors such as the composition and physical state of NS surface layers, often unknown (or poorly constrained) orientation of the NS spin and magnetic axes, and poorly constrained in- terstellar absorption toward many NSs. Evaluating the impacts of these factors on the observed properties represents a challenging but rewarding task. At the end, one can hope to differentiate between the competing models of magnetospheric radiation and constrain the NS surface temperature and radii, composition, and eventually equation- of-state for the superdense matter in the NS interior. For pulsars with PWNe one has to also disentangle the PSR and PWN emission components to study their spectra separately. The high-resolution X-ray and optical studies and spectroscopy of PWNe can be used to investigate the structure and dynamics of the relativistic pulsar winds, elucidate the mechanisms of PWN formation, evolution and interaction with the ambient medium, and establish the properties of the relativistic magnetized outflows. Many of the above objectives have become achievable only recently with the launch of the Chandra and XMM observatories which provided excellent sensitivity, angular and spectral resolution, and timing capabilities. This thesis is mainly based on the data obtained with Chandra, XMM and Hubble Space Telescope. Below, I briefly summarize most important results which follow from this work. 180

1. Optical through X-ray spectra of the Vela, Geminga and B0656+14 pulsars show both thermal and non-thermal emission. The non-thermal emission is most promi- nent in the spectrum of the youngest of these pulsars – the Vela pulsar. Its optical–FUV emission is almost purely nonthermal and highly pulsed (at least 4 peaks can be seen in the pulse profile). The slope of the nonthermal spectrum becomes flatter at the optical frequencies similar to the younger Crab pulsar. For the Vela pulsar, the temperature of −2 2 the bulk of the NS surface is ∼< 0.7R13 d300 MK as measured from the fits to UV spectrum (this limit is consistent with the temperatures obtained from the X-ray fits). For the −2 2 other two pulsars, Geminga and B0656+14, these temperatures are about 0.4R13 d200 −2 2 MK and 0.7R13 d288 MK, respectively. These neutron stars also have hot polar caps around the magnetic poles. Despite the predominantly thermal nature of the FUV spec- tra, the latter two pulsars exhibit surprisingly large pulsed fractions of about 60%-70% in FUV and NUV. To explain such high pulsed factions, one has to invoke effects of strong magnetic field on the angular dependence of NS surface emission or assume that there is a “screen” in the NS magnetosphere which may partially eclipse the surface emission at some rotation phases. In the case of Geminga, the extrapolation of the best-fit X-ray blackbody matches (or even falls below) the observed FUV fluxes. For PSR B0656+14 and the other two isolated neutron stars with measured FUV fluxes (RX J1856.5−3754 and RX J0720.4−3125) the opposite behavior is observed – the extrapolation of their X- ray blackbody spectra into the UV-optical range underpredicts the observed UV-optical fluxes. One could speculate that the cold surface of Geminga is in a solid state while the hotter surfaces of the other three neutron stars are in a gaseous or liquid state, which might explain the differences in their spectra. Finally, optical photometry of Geminga with HST/ACS shows that the previously reported spectral feature around 5500 A˚ was likely a result of inaccurate photometry. This eliminates the need to invoke proton cy- clotron lines (which have been widely discussed in this context until now) to explain the shape of Geminga’s optical spectrum. 2. We observed the millisecond pulsar J0437−4715 with HST/STIS in the FUV range. For the first time, UV emission from a millisecond pulsar was detected. The shape of the observed spectrum suggests thermal emission from the neutron star surface with a surprisingly high temperature of about 1 × 105 K, above the upper limit on the surface temperature of the younger “ordinary” pulsar J0108−1431. For the few-Gyr-old J0437−4715, such a temperature requires a heating mechanism to operate. The spectrum of J0437−4715 shows marginal evidence of an emission line at 1372 A,˚ which might be a gravitationally redshifted Zeeman component of the Hydrogen Lyα line in a magnetic field ∼ 7 × 108 G. 3. The spectrum of RX J0852.0–4622 (the Central Compact Object in Supernova Remnant G266.2–1.2) can be described by a blackbody model with the temperature kT = 404 ± 5 eV and radius of the emitting region R = 0.28 ± 0.01 km, at a distance of 1 kpc. No extended emission or long-term variability of the source flux has been detected. This, together with the spectral properties, makes RX J0852.0–4622 similar to the central source of the supernova remnant Cas A. We speculate that RX J0852.0–4622 could be either a neutron star with a low magnetic field, slowly accreting from a fossil disk, or, more likely, an isolated neutron star with a superstrong magnetic field. In either case, a conservative upper limit on surface temperature of a 10 km radius neutron star is 181 about 90 eV, which suggests accelerated cooling for a reasonable age of a few thousand years. 4. The Vela pulsar emits a wind of ultra-relativistic particles which powers a spectacular PWN. Thirteen observations of the Vela PWN with Chandra spanning a period of 3 years reveal its complex and variable structure which consists of arcs, jets, knots and diffuse emission. Especially interesting is the long external jet which changes its shape on a timescale of weeks and contains blobs moving at speeds of (0.5-0.6)c. We also observe a significant variability of the inner PWN elements on timescale of a month. In addition to the fine structure of the inner PWN, a much larger and fainter asymmetric X-ray nebula emerges in the deep summed images. The shape of this outer PWN is similar to that of the radio PWN. This suggests that the X-ray and radio emitting electrons are carried with the same outflow which is mostly confined to a low- latitude (equatorial) region. In terms of relative brightness, the radio emission is brighter further away from the pulsar while the X-ray emission is the brightest close to the pulsar. We also obtained a high-resolution spectral map of the Vela PWN in X-rays. These results make possible the detailed modeling of the pulsar-wind structure which would account for particle energy losses and anisotropy of the pulsar wind and allow us to evaluate such important physical parameters as the wind magnetization and the flow speed, the pulsar particle injection rate and pair multiplicity, the electron/positron number density and magnetic filed structure in the wind. 5. A growing number of pulsars and PWNe observed with Chandra finally opens an opportunity for a population study. Preliminary analysis of X-ray properties of pulsars with PWNe suggests strong correlation between the pulsar and PWN luminosities and significant correlation between the pulsar and PWN spectral indices. This could establish a link between the spectra of particles in the pulsar magnetosphere and downstream the termination shock and put strong constraints on the poorly understood mechanism(s) of particle acceleration in the relativistic magnetized wind. We also refine the previously reported correlation between the pulsar spin-down energy loss and X-ray luminosity. This will help to distinguish between competing magnetospheric emission models, such as the polar cap models and outer gap models. 182 Bibliography

[1] Akhiezer, A. I., Akhiezer, I. A., Polovin, R. V., Sitenko, A. G., & Stepanov, K. N. 1975, Plasma Electrodynamics, (Oxford: Pergamon), p.112

[2] Arons, J. 1981, ApJ, 248, 1099

[3] Achterberg, A. 1991, in “Galactic High-Energy Astrophysics”, eds J. van Paradijs & H. Maitzen, p. 14

[4] Aschenbach, B., & Brinkmann, W. 1975, A&A, 41, 147

[5] Aschenbach, B. 1998, Nature, 396, 141

[6] Aschenbach, B., Iyudin, A. F., & Sch¨onfelder,V. 1999, A&A, 350, 997

[7] Bailes, M., Reynolds, J. E., Manchester, R. N., Kesteven, M. J., & Norris, R. P. 1989, ApJ, 343, L53

[8] Baring, M. G., & Harding, A. K. 2001, 547, 929

[9] Becker, W., & Tr¨umper, J. 1997, A&A, 326, 682

[10] Becker, W., Pavlov, G. G. 2002, in The Century of Space Science, eds. J. A. M. Bleeker, J. Geiss, & M. C. E. Huber (Dordrecht: Kluwer), 721, (astro-ph/0208356)

[11] Becker, W., & Aschenbach, B. 2002, Proc. 270 WE-Heraeus Seminar on Neutron Stars, Pulsars and Supernova Remnants, eds. W. Becker, H. Lesch, & J. Tr¨umper, MPE-Report 278, 64 (astro-ph/0208466)

[12] Begelman, M. C., Blandford, R. D., Rees, M. J. 1984, Rev. Mod. Phys., 56, 255

[13] Begelman, M. C. 1998, ApJ, 493, 291

[14] Begelman, M. C. 1999, ApJ, 512, 755

[15] Bell, J. F., Bailes, M., & Bessell, M. S. 1993, Nature, 364, 603

[16] Benford, G. 1984, ApJ, 282, 154

[17] Bergeron, P., Saumon, D., & Wesemael, F. 1995, ApJ, 443, 76

[18] Bertch, D. L., et al. 1992, Nature, 357, 306

[19] Bignami,G. F., Caraveo, P. A., & Lamb, R. C. 1983, ApJ, 272, L9

[20] Bignami,G. F., et al. 1987, ApJ, 319, 358

[21] Bignami,G. F., Caraveo, P. A., & Paul, J. A. 1988, A&A, 202, L1

[22] Bignami,G. F., et al. 1996, ApJ, 456, L111 183

[23] Bignami, G. F., Caraveo, P. A., De Luca, A., et al. 2003, Nature, 423, 725

[24] Bitenholz, M. F., Frail, D. A., & Hankins, T. H. 1991, ApJ, 376, L41

[25] Bitenholz, M. F., & Kronberg, P. P. 1992, ApJ, 393, 206

[26] Blandford, R.D., & Scharlemann, E.T. 1976, MNRAS 174, 59

[27] Bohlin, R. 1999, Instrument Science Report STIS 1999-07 (Baltimore: STScI)

[28] Bowyer, C.S., Byram, E.T., Chubb, T.A., Friedman, H., 1964, Nature, 201, 1307

[29] Bradt, H.V., Rappaport, S., Mayer, W., Nather, R.E., Warner, B., Macfarlane, M., Kristian, J., 1969, Nature, 222, 728

[30] Braje, T. M., & Romani, R. W. 2002, ApJ, 580, 1043

[31] Brazier, K. T. S. 1994, MNRAS, 268, 709

[32] Brisken, W. F., Benson, J. M., Goss, W. M., & Thorsett, S. E. 2002, ApJ, 571, 906

[33] Buccheri, R., et al. 1983, A&A, 128, 245

[34] Burwitz, V., Haberl, F., Neuh¨auser,R., et al. 2003, A&A, 399, 1109

[35] Butler, R. F., Golden, A. & Shearer, A. 2002, A&A, 395, 845

[36] Caraveo, P.A., Bignami, G.F., Mignani, R., & Taff L.G., 1996, ApJ 461,L91

[37] Caraveo, P. A., Mignani, R. P., De Luca, A., et al. 2000, in A decade of HST science, eds. Mario Livio et al. (Baltimore) 105, (astro-ph/0009035)

[38] Caraveo, P. A., De Luca, A., Mignani, R. P., & Bignami, G. F. 2001, ApJ, 561, 930

[39] Caraveo, P. A., et al. 2003, Science, 301, 1345

[40] Caraveo P. A., et al. 2004, Science, 305, 376

[41] Cha, A., Sembach, K. M. & Danks, A. C. 1999, ApJ, 515, L25

[42] Chakrabarty, D., Pivovaroff, M. J., Hernquist, L. E., Heyl, J. S., & Narayan, R. 2001, ApJ, 548, 800

[43] Cheng, K. S., Ho, C., & Ruderman, M. A. 1986, ApJ, 300, 500

[44] Cheng, K. S., Chau, W. Y., Zhang, J. L., & Chau, H. F. 1992, ApJ, 396, 135

[45] Cocke, W.J., Disney, M.J. Taylor, D.J. 1969 Nature, 221, 525

[46] Colpi M., Geppert U., & Page D. 2000, 529, L29

[47] Cordes, J. M., & Lazio, T. J. W. 2002, astro-ph/0207156

[48] Danziger, I. J., Baade, D., & della Valle, M. 1993, A&A, 276, 382 184

[49] Davis, J. E. 2001, ApJ, 548, 1010

[50] Daugherty, J. K., & Harding, A. K. 1982, ApJ, 252, 337

[51] Daugherty, J. K., & Harding, A. K. 1994, ApJ, 429, 325

[52] de Jager O. C., Harding, A. K., & Strickman, M. S. 1996, ApJ, 460, 729

[53] Dickey, J. M., & Lockman, F. J. 1990, ARA&A, 28, 215

[54] Dodson, R. G., McCulloch, P. M., & Costa, M. E. 2000, IAU Circ. 7347

[55] Dodson, R., Legge, D., Reynolds, J. E., & McCulloch, P. M. 2003a, ApJ, 596, 1137

[56] Dodson, R., Lewis, D., McConnel, D., & Deshpande, A. A. 2003b, MNRAS, 343, 116

[57] Duncan, A. R., & Green, D. A. 2000, A&A, 364, 732

[58] Fichtel, C. E., et al. 1975, ApJ, 198, 163

[59] Frank, J., King, A., & Raine, D. 1992, Accretion Power in Astrophysics (Cambridge: Cambridge Univ. Press)

[60] Friedman, B., & Pandharipande, V. R. 1981, Nucl. Phys. A., 361, 502

[61] Fritz, G., Henry, R.C., Meekins, J.F., Chubb, T.A., Friedman, H., 1969, Science, 164, 709

[62] Gaensler, B. M. 2001, in Young Supernova Remnants, eds. S.S. Holt & U. Hwang, AIP, New York, AIP Conf. Proc., Vol. 565, p.295, (astro-ph/0012362)

[63] Gaensler, B. M., Arons, J., Caspi, V. M., Pivovaroff, M. J., Kawai, N., & Tamura, K. 2002, ApJ, 569, 878

[64] Gallant, Y. A., & Arons, J. 1994, ApJ, 435, 230

[65] Gedalin, M. 1993, Phys. Rev. E, 47, 4354

[66] Coroniti, F. V. 1990, ApJ, 349, 538

[67] Green D. A. 2004, A Catalogue of Galactic SNRs, http://www.mrao.cam.ac.uk/surveys/snrs/

[68] Ginzburg, V. L., & Syrovatskii, S. I. 1965, ARA&A, 3, 297 [GS65]

[69] Gold, T., 1968, Nature, 218, 731

[70] Gold, T., 1969, Nature, 221, 25

[71] Gotthelf, V. E. 2003, ApJ, 591, 361

[72] Gouiffes, C. 1998, in Neutron Stars and Pulsars, eds. N. Shibazaki, N. Kawai, S. Shibata, & T. Kifune (Tokyo: Univ. Acad. Press), 363 185

[73] Greenstein, G., & Hartke, G. J. 1983, ApJ, 271, 283

[74] Gregory, P. C., & Loredo, T. J. 1996, ApJ, 473, 1059

[75] Greiveldinger, C., & Aschenbach, B. 1999, ApJ, 510, 305

[76] Gudmundsson, E. H., Pethick, C. J., & Epstein, R. I. 1983, ApJ, 272, 286

[77] Halpern, J. P., & Holt, S. S. 1992, Nature, 357, 222

[78] Halpern, J. P., & Tytler, D. 1988, ApJ, 330, 201

[79] Hannestad, S., Ker¨anen,P., & Sannino, F. 2002, Phys. Rev. D 66, 045002

[80] Hansen, B. M. S., & Phinney, E. S. 1998, MNRAS, 294, 557

[81] Hansen, B. M. S. 1999, ApJ, 520, 680

[82] Haberl, F., Schwope, A. D., Hambaryan, V., Hasinger, G., & Motch, C. 2003a, A&A, 403, L19

[83] Halpern, J. P., & Ruderman, M. 1993, ApJ, 415, 286

[84] Halpern, J. P., Martin, C., Marshall, H. L. 1996, ApJ, 473, 37L

[85] Halpern, J. P., & Wang, F. Y.-H. 1997, ApJ, 477, 905

[86] Harding, A. K., & Muslimov, A. G. 1998, ApJ, 500, 862

[87] Harding, A. K., & Muslimov, A. G. 2002, ApJ, 568, 862

[88] Harding, A. K., Muslimov, A. G., & Zhang, B. 2002, ApJ, 576, 366

[89] Harding, A. K. 2002, in Proc. of 34th COSPAR Scientific Assembly, Houston, TX, USA, p.1990

[90] Harlow, J. J., Pavlov, G. G. & Halpern, J.P. 1999, BAAS, 193, 41.07

[91] Harnden, F. R., Grant, P. D., Seward, F. D., & Kahn, S. M. 1985, ApJ, 299, 828

[92] Helfand, D. J., Gotthelf, E. V., & Halpern, J. P. 2001, ApJ, 556, 380

[93] Hester, J. J., et al. 1995, ApJ, 448, 240

[94] Hester, J. J. 1998, in Neutron Stars and Pulsars: Thirty Years after Discovery, eds. N. Shibazaki, N. Kawai, S. Shibata and T. Kifune, Univ. Acad. Press (Tokio), p.431

[95] Hester, J. J., Mori, K., Burrows, D., et al. 2002, ApJ, 577, L49

[96] Hibschman, J., & Arons, J. 2001, ApJ, 560, 871

[97] Illarionov, A. F., & Sunyaev, R. A. 1975, A&A, 39, 185

[98] Inogamov, N. A., & Sunyaev, R. A. 1999, Astron. Lett., 25, 269 186

[99] Iyudin, A. F., et al. 1998, Nature, 396, 142

[100] Jackson, M. S., Halpern, J. P., Gotthelf, E. V., & Mattox, J. R. 2002, ApJ, 578, 935

[101] Jerius, D., et al. 2001, Proc. SPIE, 4012, 17 (http://asc.harvard.edu/cal/Hrma/hrma/psf/index.html)

[102] Jones, B. B. & Finlay, E. A., 1974, Aust. J. Phys., 27, 687

[103] Jones, P. B. 1978, MNRAS, 184, 807

[104] Kanbach, G., et al. 1994, A&A, 289, 855

[105] Kargaltsev, O., Pavlov, G. G., Sanwal, D., & Garmire, G. P. 2002, in Neutron Stars in Supernova Remnants, eds. P.O.˙ Slane & B. M. Gaensler, ASP Conf. Ser., v.271 (San Francisco: ASP), 181

[106] Kargaltsev, O., Pavlov, G. G., Sanwal, D., et al. 2002, ApJ, 580, 1060

[107] Kargaltsev, O., Pavlov, G. G., & Romani, R. W. 2003, ApJ, 602, 327

[108] Kargaltsev, O. & Pavlov G. G. 2004, in Young Neutron Stars and Their Environ- ments (IAU Symposium 218, ASP Conference Proceedings), eds. F. Camilo and B. M. Gaensler, p.195

[109] Kaspi, V. M., Gavriil, F. P., Woods, P. M., Jensen, J. B., Roberts, M. S. E., & Chakrabarty, D. 2003, ApJ, 588, L93

[110] Kaspi, V. M. 2004, in Young Neutron Stars and Their Environments (IAU Sympo- sium 218, ASP Conference Proceedings), eds. F. Camilo and B. M. Gaensler, (astro- ph/0402175)

[111] Kaspi, V. M., & Gavriil F. P. 2004, in Proc. of the BeppoSAX Symposium: “The Restless High-Energy Universe”, Eds. E.P.J. van den Heuvel, J.J.M. in’t Zand, & R.A.M.J. Wijers, (astro-ph/0402176)

[112] Kaspi, V., Roberts, M. & Harding, A. K. 2004, in Compact Stellar X-ray Sources, eds. W.H.G. Lewin and M. van der Klis, (astro-ph/0402136)

[113] Kennel, C. F. & Coroniti, F. V. 1984, ApJ, 283, 710

[114] Kirk, J. G., Skjæraasen, O., & Gallant, Y. A. 2002, A&A, L29

[115] Kennel, C. F. & Coroniti, F. V. 1984, ApJ, 283, 710

[116] Koptsevich, A. B., Pavlov, G. G., Zharikov, S. V. et al. 2001, ApJ, 370, 1004

[117] Koptsevich, A. B., Lundqvist, P., Serafimovich, N. I., Shibanov, Yu. A., & Soller- man, J. 2003, A&A, 400, 265

[118] Kouveliotou, C. et al. 1998, Nature, 393, 235 187

[119] Kouveliotou, C. et al. 1999, ApJ, 510, L115

[120] Kuzmin, A. D., & Losovskii, B. Ya. 1997, Astron. Lett., 23, 323

[121] Lai, D., Chernoff, D. F., & Cordes, J. M. 2001, ApJ, 549, 1111

[122] Landau, L., 1932, Phys.Z. Sowjetunion, 1, 285

[123] Landsman, W. 1998, Characteristics of the FUV-MAMA Dark Rate, STIS IDT report

[124] Lang K. R. 1978, Astrophysical Formulae, New York: Springer-Verlag, p. 41

[125] Larson, M. B., & Link, B. 1999, ApJ, 521, 271

[126] Leahy, J. P. 1991, in Beams and Jets in Astrophysics, ed. P. A. Hughes (Cambridge: Cambridge Univ. Press), 147

[127] Lewis, D., Dodson, R., McConnel, D., & Deshpande, A. 2002, in Neutron Stars in Supernova Remnants, eds. P.O.˙ Slane & B. M. Gaensler, ASP Conf. Ser., v.271 (San Francisco: ASP), 191

[128] Lou, Y. 1998, MNRAS, 294, 443

[129] Lundmark, K. 1921, PASP, 33, 195

[130] Lyubarskii Y. E., & Petrova S. A. 1998, A&A 333, 181

[131] Lyubarsky, Y. & Kirk, J. G. 2001, ApJ, 547, 437L

[132] McLaughlin,M. A., Cordes, J. M., Hankins, T. H., & Moffett, D. A. 1999, ApJ, 512, 929

[133] Malofeev, V.M., & Malov, O. I. 1997, Nature, 389, 697

[134] Manchester, R. N., & Johnston, S. 1995, ApJ, 441, L65

[135] Manchester, R. N. et al. 2003, ATNF Pulsar Catalog, http://www.atnf.csiro.au/research/pulsar/psrcat/

[136] Markwardt, C. B., & Ogelman,¨ H. 1997, ApJ, 480, 13

[137] Markwardt, C. B., & Ogelman,¨ H. 1998, Mem. Soc. Astron. Italiana, 69, 927

[138] Martin, C., Halpern, J. P., & Schiminovich,D. 1998, ApJ, 494, L211

[139] Melrose D. 2004, in Young Neutron Stars and Their Environments (IAU Sympo- sium 218, ASP Conference Proceedings), eds. F. Camilo and B. M. Gaensler, (astro- ph/0308471)

[140] Michel, F. C. 1991, Theory of Neutron Star Magnetospheres. Univ. Chicago Press, Chicago 188

[141] Michel, F. C. & Li, H. 1999, Physics Reports, 318, 227

[142] Michel, F. C. 2004, AdSpR, 33, 542

[143] Mignani, R. P., Caraveo, P. A., & Bignami,G. F. 1998, A&A, 332, L37

[144] Mignani, R. P., De Luca, A., Caraveo, P. A., & Becker, W. 2002, ApJ, 580, 147

[145] Mignani, R. P., Manchester, R. N., & Pavlov, G. G. 2003a, ApJ, 582, 978

[146] Mignani, R. P., Pavlov, G. G., De Luca, A., & Caraveo, P. A. 2003b, ASpR, submitted (astro-ph/0301253)

[147] Mignani, R. P., De Luca, A., Kargaltsev, O., Pavlov, G. G., Zaggia, S., Caraveo, P. A., & Becker, W. 2003, ApJ, 594, 419

[148] Mignani, R. 2004, in Young Neutron Stars and Their Environments (IAU Sympo- sium 218, ASP Conference Proceedings), eds. F. Camilo and B. M. Gaensler, (astro- ph/0311468)

[149] Mignani, R. P., & Becker, W. 2004, AdSpR, 33, 616, (astro-ph/0301114)

[150] Mignani, R. P., et al. 2004, submitted to A&A

[151] Mitrofanov, I.G., & Pavlov, G.G. 1982, MNRAS, 200, 1033

[152] Mori, K., Hester, J. J., Burrows, D. N., Pavlov, G. G., & Tsunemi, H. 2002, in Neutron Stars in Supernova Remnants, ASP Conf. Ser., v. 271, eds. P. O. Slane & B. M. Gaensler (San Francisco: ASP), 157

[153] Mori, K., et al. 2004, ApJ, 609, 186

[154] Muslimov, A. G. & Harding, A. K. 2003, ApJ, 588, 430

[155] Nasuti, F. P., Mignani, R., Caraveo, P. A., & Bignami, G. F. 1997, A&A, 323, 839

[156] Ogelman¨ H. & Koch-Miramond, L. 1989, ApJ, 342, L83

[157] Ogelman,¨ H., & Zimmerman, H.-U. 1989, A&A, 214, 179

[158] Ogelman,¨ H., Finley, J. P., & Zimmerman, H.-U. 1993, Nature, 361, 136

[159] Page, D., & Sarmiento, A. 1996, ApJ, 473, 1067

[160] Pacholczyk, A. G. 1970, Radio Astrophysics (San Francisco: Freeman)

[161] Pacini, F., 1967, Nature, 216, 567

[162] Pacini, F., 1968, Nature, 219, 145

[163] Pavlov, G. G., Shibanov, Yu. A., Zavlin, V. E., & Meyer, R. D. 1995, in The Lives of the Neutron Stars, eds. M. A. Alpar, U.¨ Kiziloglu, & J. van Paradijs (Dordrecht: Kluwer), 71 189

[164] Pavlov, G. G., Stringfellow, G. S., & C´ordova, F. A. 1996, ApJ, 467, 370

[165] Pavlov, G. G., Sanwal, D., Garmire, G. P., Zavlin, V. E., Burwitz, V., & Dodson, R. G. 2000, AAS Meeting 196, #37.04

[166] Pavlov, G. G. 2000, AAS HEAD Meeting 32, #07.05

[167] Pavlov, G. G., Zavlin, V. E., Aschenbach, B., Tru ¨mper, J., & Sanwal, D. 2000, ApJ, 531, L53

[168] Pavlov, G. G., Sanwal, D., Kiziltan, B., & Garmire G. P. 2001 ApJ, 559, L131

[169] Pavlov, G. G., Kargaltsev, O. Y., Sanwal, D., & Garmire, G. P. 2001a, ApJ, 554, L189

[170] Pavlov, G. G., Zavlin, V. E., Sanwal, D., Burwitz, V,. & Garmire, G. P. 2001b, ApJ, 552, L129

[171] Pavlov, G. G., Sanwal, D., Garmire, G. P. & Zavlin, V. E. 2002a, in Neutron Stars in Supernova Remnants, eds. P. O. Slane, B. M. Gaensler, ASP Conf. Ser., p. 247

[172] Pavlov, G. G., Zavlin, V. E., Sanwal, D., & Tr¨umper, J. 2002b, ApJ, 569, L95

[173] Pavlov, G. G., Zavlin, V. E., & Sanwal, D. 2002c, Proc. 270 WE-Heraeus Seminar on Neutron Stars, Pulsars and Supernova Remnants, eds. W. Becker, H. Lesch, & J. Tr¨umper, MPE-Reports, 278, 273, (astro-ph/0206024)

[174] Pavlov, G. G., & Zavlin, V. E. 2003, Proc. XXI Texas Symposium on Relativistic Astrophysics, eds. R. Bandiera (World Scientific), p. 319, (astro-ph/0305435)

[175] Pavlov, G. G., Teter, M. A., Kargaltsev, O., & Sanwal, D. 2003, ApJ, 591, 1157

[176] Pavlov, G. G., Sanwal, D., & Teter, M. A. 2004, in Young Neutron Stars and Their Environments (IAU Symposium 218, ASP Conference Proceedings), eds. F. Camilo and B. M. Gaensler, (astro-ph/0311526)

[177] Pons, J. A., Walter, F. M., Lattimer, J. M., Prakash, M., Neuh¨auser,R., & An, P. 2002, ApJ, 564, 981

[178] Plucinsky, P. P., et al. 2002, in Astronomical Telescopes and Instrumentation 2002, eds. J. E. Tr¨emper & H. D. Tananbaum, SPIE Conf. Proc., in press (astro-ph/0209161)

[179] Possenti, A., et al. 2002, A&A, 387, 993

[180] Proffitt, C. 2003, STIS Cycle 9 Calibration Close-out Report, STIS ISR

[181] Protheroe, R. J. 1987, in Proc. Astron. Soc. Australia, vol. 7, no. 2, 167

[182] Radhakrishnan, V., & Deshpande, A. 2000, A&A, 379, 551

[183] Rajagopal, M., & Romani, R. W. 1997, 491, 296 190

[184] Rajagopal, M., Romani, R. W., & Miller, M. C. 1997, ApJ, 479, 347

[185] Rees, M. J., Gunn, J. E. 1974, MNRAS, 167, 1

[186] Reisenegger, A. 1995, ApJ, 442, 749

[187] Reisenegger, A. 1997, ApJ, 485, 313

[188] Romani, R. W. 1987, ApJ, 313, 718

[189] Romani, R. W. & Yadigaroglu, I.-A. 1995, ApJ, 438, 314

[190] Ruder, H., Wunner, G., Herold, H., & Geyer, F. 1994, Atoms in Strong Magnetic Fields (Berlin: Springer)

[191] Ruderman, M. A., & Sutherland, P. G. 1975, ApJ, 196, 51

[192] Ruderman, M. A. 2003, in 4th AGILE Science Workshop, X-ray and Gamma-ray Astrophysics of Galactic Sources, 2003 June 11-13, Rome, Italy, (astro-ph/0310777)

[193] Rybicki, G. & Lightman, A. P. 1979, Radiative Processes in Astrophysics, New York: Wiley-Interscience

[194] Sanwal, D., Pavlov, G. G., Kargaltsev, O., Garmire, G. P., Zavlin, V. E., Burwitz, V., Manchester, R. N. & Dodson, R. 2002, in Neutron Stars in Supernova Remnants, eds. P.O. Slane & B. M. Gaensler, ASP ser., v. 271, p. 353

[195] Sanwal, D., Pavlov, G. G., Zavlin, V. E., & Teter, M. A. 2002, ApJ, 574, L61

[196] Scargle, J. D. 1969, ApJ, 156, 401

[197] Seaton, M. J. 1979, MNRAS, 187, 73

[198] Serafimovich, N. I., Shibanov, Yu. A., Lundqvist P., & Sollerman J., 2004, accepted to A&A, (astro-ph/0407226)

[199] Seward, F. D. & Wang, Z. 1988, ApJ, 332, 199

[200] Schaab, Ch., Sedrakian, A., Weber, F., & Weigel, M. K. 1999, A&A, 346, 465

[201] Schonfelder, V., et al. 2000, A&AS, 143, 145

[202] Shearer, A., et al. 1998, A&A, 335, L21

[203] Shibanov, Y. A. & Yakovlev, D. G. 1996, A&A, 309, 171

[204] Shibanov, Yu. A., Koptsevich, A. B., Sollerman, J., & Lundqvist, P. 2003, A&A, 406, 645

[205] Shibazaki, N., & Lamb, F. K. 1989, ApJ, 346, 808

[206] Shitov, Yu. P., & Pugachev, V. D. 1997, NewA, 3, 101 191

[207] Slane, P., Hughes, J. P., Edgar, R. J., Plucinsky, P. P., Miyata, E., Tsunemi, H., & Aschenbach, B. 2001, ApJ, 548, 814

[208] Spitkovsky, A., & Arons, J. 2000, in Pulsar Astronomy - 2000 and Beyond, eds. M. Kramer, N. Wex, and R. Wielebinski, ASP Conference Series, v.202, p.507

[209] Sollerman, J., et al. 2000, ApJ, 537, 861

[210] Sollerman, J. 2003, A&A, 406, 639

[211] Strickman, M. S., et al. 1996, ApJ, 460, 735

[212] Tauris, T. M., et al. 1994, ApJ, 428, L53

[213] Taylor, J. H., & Weisberg, J. M. 1989, ApJ, 345, 434

[214] Taylor, J. H. & Cordes, J. M. 1993, ApJ, 411, 674

[215] Thompson, C., & Duncan, R. C. 1992, ApJ, 392, L9

[216] Thompson, C., & Duncan, R. C. 1996, ApJ, 473, 322

[217] Townsley, L. K., Broos, P. S., Garmire, G. P., & Nousek, J. A. 2000, ApJ, 534, L139

[218] Tsuruta, S. 1998, Phys. Rep., 292, 1

[219] Truemper, J. E., Burwitz V., Haberl F., & Zavlin, V. E. 2004, in Proc. of The Restless High-Energy Universe symposium, Amsterdam, 2003, (astro-ph/0312600)

[220] Tsunemi, H. et al. 2000, PASJ, 52, 887

[221] Turbiner, A.V., & Lopez Vieyra, J.C. 2004, Mod.Phys.Lett. A19 1919, (astro- ph/0404290)

[222] Usov, V. V., & Melrose, D. B. 1995, Australian Journ. Phys., 48, 571

[223] van Adelsberg, M., Lai, D., & Potekhin, A. Y. 2004, submitted to ApJ, (astro- ph/0406001)

[224] van Kerkwijk, M. H. & Kulkarni, S. R. 2001, A&A, 380, 221

[225] van Kerkwijk, M. H. 2004, in Young Neutron Stars and Their Environments (IAU Symposium 218, ASP Conference Proceedings), eds. F. Camilo and B. M. Gaensler, (astro-ph/0310389)

[226] van Paradijs, J., Taam, R. E., & van den Heuvel, F. P. G. 1995, A&A, 299, L41

[227] van Straten, W., Bailes, M., Britton, M., Kulkarni, S. R., Anderson, S. B., Manchester, R. N., & Sarkissian, J. 2001, Nature, 421, 158

[228] Vaughan, B. A., et al. 1994, ApJ, 435, 362 192

[229] Walter, F. M., & Lattimer, J. M. 2002, ApJ, 576, L145

[230] Wallace, P. T. et al. 1977, Nature, 266, 692

[231] Wang, F. Y.-H., Ruderman, M., Halpern, J. P., & Zhu, T. 1998, ApJ, 498, 373

[232] Wang, Y.-M., & Robertson, J. A. 1985, A&A, 151, 361

[233] Weisskopf, M. C., et al. 2000, ApJ, 536, L81

[234] Weiler, K. W., & Panagia, N. 1978, A&A, 70, 419

[235] Willmore, A. P., et al. 1992, MNRAS, 254, 139

[236] Yakovlev, D. G., Kaminker, A. D., Haensel, P., & Gnedin, O. Y. 2002, A&A, 389, 24

[237] Yakovlev D. G. & Pethick C. J. 2004, Ann. Rev. Astron. Astrophys., 42, 169

[238] Zavlin, V. E., & Pavlov, G. G. 1998, A&A, 329, 583

[239] Zavlin, V. E., Pavlov, G. G., Sanwal, D., & Tru ¨mper, J. 2000, ApJ, 540, L25

[240] Zavlin, V. E. & Pavlov, G. G. 2002, in Proc. 270 Heraeus Seminar on Neutron Stars, Pulsars and Supernova Remnants, eds. W. Becker, H. Lesch, & J. Tr¨umper, MPE Reports, 278, 283, (astro-ph/0206025)

[241] Zavlin, V. E., Pavlov G. G., Sanwal, D., Manchester, R. N., Tr¨umper, J., Halpern, J. P., & Becker, W. 2002, ApJ, 569, 894

[242] Zhang, B. & Harding, A. K. 2000, ApJ, 532, 1150

[243] Zhang, L., & Cheng, K. S. 1997, ApJ, 487, 370 Vita Oleg Kargaltsev Education The Pennsylvania State University State College, Pennsylvania 1999–Present Ph.D. in Astronomy & Astrophysics, expected in December 2004 Area of Specialization: High-energy astrophysics Moscow Institute of Physics and Technology Moscow, Russia 1992–1998 M.S. in Physics

Awards and Honors Graduate Alumni Association Dissertation Award 2003 Zaccheus Daniel Foundation for Astronomical Science,Travel Grants 2002,2003 Braddock Fellowship (for excellence in undegraduate studies) 1998-2001 I. E. Tamm fellowship at the Lebedev Physical Institute, Moscow 1996,1998

Research Experience Doctoral Research The Pennsylvania State University 2000–Present Thesis Advisor: Prof. George Pavlov X-ray and optical observations of neutron stars and pulsar-wind nebulae. Graduate Research The Pennsylvania State University 1999–2000 Research Advisor: Prof. Peter M´esz´aros Modeling light curves from Gamma-ray burst afterglows. Undergraduate Research Moscow Institute of Physics and Technology 1992–1998 Research Advisor: Prof. Yakov Istomin On possible origin of gamma-ray bursts from NS atmospheres. Teaching Experience Teaching Assistant for the courses Nebulae, Galaxies and Cosmology (ASTRO 011) – The Pennsylvania State University 1999-2000 Astronomy of the Distant Universe (ASTRO 292) – The Pennsylvania State University 1999-2000 Elementary Astronomy Laboratory (ASTRO 480)– The Pennsylvania State University 1999-2000