An X-Ray Study of Gravitational Lenses

The Pennsylvania State University

The Graduate School

Department of Astronomy and Astrophysics

AN X-RAY STUDY OF GRAVITATIONAL LENSES

A Thesis in

Astronomy and Astrophysics

Xinyu Dai

c 2004 Xinyu Dai

Submitted in Partial Fulﬁllment of the Requirements for the Degree of

Doctor of Philosophy

December 2004 The thesis of Xinyu Dai was reviewed and approved* by the following:

Gordon P. Garmire Evan Pugh Professor of Astronomy and Astrophysics Thesis Co-Adviser Co-Chair of Committee

George Chartas Sr. Research Associate of Astronomy and Astrophysics Thesis Co-Adviser Co-Chair of Committee

Michael Eracleous Associate Professor of Astronomy and Astrophysics

Robin Ciardullo Professor of Astronomy and Astrophysics

L. Samuel Finn Professor of Physics

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

*Signatures are on ﬁle in the Graduate School. iii Abstract

Gravitational lensing of distant quasars by intervening galaxies is a spectacular phenomenon in the universe. With the advent of Chandra, it is possible to resolve for the first time in the X-ray band lensed quasar images with separations greater than about 0.35 arcsec. We use lensing as a tool to study AGN and Cosmology with Chandra and XMM-Newton. First, we present results from a mini-survey of relatively high redshift (1.7 < z < 4) gravitationally lensed radio-quiet quasars observed with the Chandra X-ray Observa- tory and with XMM-Newton. The lensing magnification effect allows us to search for changes in quasar spectroscopic and flux variability properties with redshift over three orders of magnitude in intrinsic X-ray luminosity. It extends the study of quasar properties to unlensed X-ray flux levels as low as a few times 10−15erg cm−2 s−1 in the observed 0.4–8 keV band. For the first time, these observations of lensed quasars have provided medium to high signal-to-noise ratio X-ray spectra of a sample of relatively high-redshift and low X-ray luminosity quasars. We find a possible correlation between the X-ray powerlaw photon index and X-ray luminosity of the gravitationally lensed radio-quiet quasar sample. The X-ray spectral slope steepens as the X-ray luminosity increases. This correlation is still significant when we combine our data with other samples of radio-quiet quasars with z > 1.5, especially in the low luminosity range between 1043–1045.5 erg s−1. This result is surprising considering that such a correlation is not found for quasars with redshifts below 1.5. We suggest that this correlation can be understood in the context of the hot-corona model for X-ray emission from quasar accretion disks, under the hypothesis that the quasars in our sample accrete very close to their Eddington limits and the observed luminosity range is set by the range of black hole masses (this hypothesis is consistent with recent predictions of semi-analytic models for quasar evolution). The upper limits of X-ray variability of our relatively high redshift sample of lensed quasars are consistent with the known correlation between variability and luminosity observed in Seyfert 1s when this correlation is extrapolated to the larger luminosities of our sample. Second, we present the observations of the gravitationally lensed system Q 2237+0305 (Einstein Cross) performed with the Advanced CCD Imaging Spectrometer (ACIS) onboard the Chandra X-ray Observatory on 2000 September 6, and on 2001 December 8 for 30.3 ks and 9.5 ks, respectively. Imaging analysis resolves the four X-ray images of the Einstein Cross. A possible fifth image is detected; however, the poor signal-to-noise ratio of this image combined with contamination produced by a nearby brighter image make this detection less certain. We investigate possible origins of the additional image. Fits to the combined spectrum of all images of the Einstein Cross assuming a simple power law with Galactic and intervening absorption at the lensing galaxy yields a photon index, +0.05 Γ, of 1.90−0.05 consistent with the range of Γ measured for large samples of radio-quiet quasars. For the first Chandra observation of the Einstein Cross this spectral model yields a 0.4–8.0 keV X-ray flux of 4.6 × 10−13erg cm−2 s−1 and a 0.4–8.0 keV lensed luminosity of 1.0 × 1046erg s−1. The source exhibits variability both over long and short time scales. The X-ray flux has dropped by 20% between the two observations, and the iv

Kolmogorov-Smirnov test showed that image A is variable at the 97% confidence level within the first observation. The X-ray flux ratios of the images are consistent with the optical flux ratios which are affected by microlensing suggesting that the X-ray emission is also microlensed. A comparison between our measured column densities and those inferred from extinction measurements suggests a higher dust-to-gas ratio in the lensing galaxy than the average value of our Galaxy. We report the detection at the 99.99% confidence level of a broad emission feature near the redshifted energy of the Fe Kα line in only the spectrum of image A. The rest frame energy, width, and equivalent width +0.2 +0.30 +300 of this feature are Eline = 5.7−0.3 keV, σline = 0.87−0.15 keV, and EW = 1200−200 eV, respectively. The enhancement of the emission line in image A is possibly caused by microlensing since the combined spectrum of the other three images does not show such a significant feature. The redshift and broadening of the line may be the result of the Doppler effect and special and general relativistic effects. It is likely that the broad iron line region that is affected by the GR and SR effects is smaller than the X-ray continuum region. Finally, we present results from time-delay searches in our sample of gravitational lenses observed with Chandra and XMM-Newton. We applied cross correlation and auto correlation techniques to the X-ray light-curves of the gravitational lenses. The time-delays between some of the short separation systems are predicted to be of the order of several hours. We have measured two time-delays and one lower limit on a time-delay. In RX J0911.4+0551, we have detected a flare only in image A2 and not in image A1 constraining the time-delay between the two images to be greater than 23 ks. Although, we did not measure the time-delay in this system it was realized for the first time that short time-delays can be measured in single X-ray observations. In a Chandra +0.5 observation of Q 2237+0305, we detected a tentative time-delay of 2.7−0.9 hours between images A and B with image A leading. This time-delay is important in constraining the mass profile of the lensing galaxy and the amount of dark matter substructure in the lensing galaxy. In a Chandra observation of PG 1115+080, we detected a time-delay +0.02 of ∆τA1A2 = 0.162−0.01 days with image A1 leading. Furthermore, the analysis of an XMM-Newton observation of PG 1115+080 also yields a time-delay of 0.149 0.006 days, which is consistent with the time-delay between images A1 and A2 measured from the Chandra observation. Combining this time delay with other constraints in the +13 −1 −1 system, a Hubble constant of H0 = 67−8 3 km s Mpc is obtained. v Table of Contents

List of Tables ...... vii

List of Figures ...... viii

Acknowledgments ...... xi

Chapter 1. Introduction ...... 1 1.1 Gravitational Lenses ...... 1 1.1.1 Lens Equations ...... 2 1.1.2 Strategy for Solving the Lens Equation ...... 3 1.1.3 Lens Potentials ...... 3 1.1.4 Applications of Gravitational Lensing ...... 4 1.1.4.1 Placing Constraints on the Hubble Constant . . . . 4 1.1.4.2 Constraining the Cosmological Constant ΩΛ . . . . 5 1.1.4.3 Determining the Mass Profiles of the Lensing Galaxies 5 1.1.4.4 Studying the Properties of the Sources with the Aid of Lensing Magnification ...... 5 1.1.4.5 Micro-lensing and Milli-lensing Events ...... 6 1.2 X-ray Properties of Active Galactic Nuclei ...... 6 1.2.1 X-ray Continuum ...... 7 1.2.2 X-ray Reflection Component and the Fe Kα line ...... 7 1.3 Motivation of the Thesis ...... 7 1.4 Outline of the Thesis ...... 8 1.4.1 Chapter 1: A Study of Quasar Evolution with the Aid of Lensing 8 1.4.2 Chapter 2: An X-ray Microlensing Event in Q 2237+0305 . . 9 1.4.3 Chapter 3: X-ray Time-delay Measurements of Gravitational Lensing Systems ...... 9 1.4.4 Chapter 4: Conclusions ...... 10

Chapter 2. A Study of Quasar Evolution in the X-ray Band with the Aid of Grav- itational Lensing ...... 11 2.1 Introduction ...... 11 2.2 Observations and Data Reduction ...... 12 2.3 Spectral Analysis ...... 13 2.3.1 Power-law Continuum ...... 13 2.3.2 αox ...... 15 2.4 Magniﬁcation and Intrinsic X-ray Luminosities ...... 15 2.5 Variability Analysis ...... 16 2.6 Results and Discussion ...... 17 2.6.1 Luminosity and Spectral Index ...... 17 vi

2.6.2 Possible Interpretations of the Correlation Between the X-Ray Luminosity and Spectral Index ...... 19 2.6.3 The Optical-to-X-Ray Index, αox ...... 21 2.6.4 Short Time Scale Variability ...... 21 2.7 Conclusions ...... 22

Chapter 3. Chandra Observations of Q 2237+0305 ...... 37 3.1 Introduction ...... 37 3.2 Observations and Data Reduction ...... 38 3.3 Photometry and Astrometry ...... 39 3.4 Spectral Analysis ...... 40 3.4.1 Simple Absorbed Power-law Models ...... 40 3.4.2 Features in the Spectrum of Image A ...... 41 3.5 Discussion ...... 42 3.5.1 An Additional Image? ...... 42 3.5.2 Absorption at the Lensing Galaxy ...... 43 3.5.3 Image Flux Ratios ...... 44 3.5.4 Broad Fe Kα Line ...... 44 3.5.5 Variability ...... 47 3.6 Conclusions ...... 47

Chapter 4. Detecting Time-delays in Gravitational Lensing Systems in X-Rays . 59 4.1 Introduction ...... 59 4.2 Chandra Observation of RX J0911.4+0551 ...... 60 4.2.1 Timing Analysis of RX J0911.4+0551 ...... 61 4.2.2 Lens Modeling of RX J0911.4+0551 ...... 61 4.3 Q 2237+0305 ...... 67 4.3.1 Discussion ...... 67 4.4 PG 1115+080 ...... 74 4.4.1 Timing Analysis of Chandra Observations of PG 1115+080 . 74 4.4.1.1 Variability ...... 74 4.4.1.2 Time-Delay Between Images A1 and A2 in PG 1115+080 75 4.4.1.3 Discussion ...... 76 4.4.2 XMM-Newton observation of PG 1115+080 ...... 84 4.4.2.1 Discussion ...... 84 4.5 Conclusions ...... 85

Chapter 5. Conclusions ...... 90 5.0.1 Constraints on AGNs ...... 90 5.0.2 Constraints on Cosmology ...... 91

Bibliography ...... 93 vii List of Tables

2.1 The Sample of Gravitational Lensed Radio-Quiet Quasars ...... 24 2.2 Fits to the spectra of Gravitational Lensed Radio-quiet Quasars . . . . . 25 2.3 αox Values of Gravitationally Lensed Quasars in the Sample ...... 26 2.4 Magniﬁcation of Gravitationally Lensed Quasars in the Sample . . . . . 27 2.5 Excess Variance of Gravitational Lensed Radio-quiet Quasars ...... 28 2.6 Excess Variance of Quasars Observed with XMM ...... 29

3.1 Chandra Observations of Q 2237+0305a...... 49 3.2 Relative Optical and X-ray Positions of Q 2237+0305 Imagesa ...... 50 3.3 Results of Fits to the Chandra Spectra of Q 2237+0305a ...... 51 3.4 Fits to the Spectrum of Image A and the Combined Spectrum of Images B, C, and D of Q 2237+0305 with and without an Fe line Model . . . . 52 3.5 Hydrogen Column Densities in Q 2237+0305 Images ...... 53 3.6 X-ray and Optical Flux Ratio in Q 2237+0305 ...... 54

4.1 Time-Delays Measured Through Optical and Radio Observations . . . . 60 4.2 Tests of Variability of RX J0911.4+0551 ...... 62 4.3 Model Parameters, Time-delays and Magniﬁcations for Lens Models of RX J0911.4+0551 ...... 64 4.4 Kolmogorov-Smirnov Test of Variability for Q 2237+0305 ...... 69 4.5 K-S Test Results of Chandra PG 1115+080 Light-Curves ...... 77 4.6 Predicted Time-Delays Between Images A1 and A2 of PG 1115+080 and Resulting Values of the Hubble constant...... 87 viii List of Figures

1.1 The optical image of the gravitational lens Q 0957+561...... 1 1.2 Schematic plot of gravitational lensing...... 2

2.1 Spectra of gravitationally lensed radio-quiet quasars observed with Chan- dra, except for the spectra of APM 08279+5255 and PG 1115+080 that were observed with XMM-Newton. (Part I) ...... 30 2.2 Light-curves of gravitationally lensed radio-quiet quasars observed with Chandra. The light-curves are binned with a bin size of 1000 s in the observed-frame...... 32 2.3 Plots of (a) X-ray Luminosity vs. redshift. The squares represent 0.2– 2 keV luminosities and crosses represent 2–10 keV luminosities. (b)X- ray photon index vs. redshift. (c) X-ray photon index vs. 0.2–2 keV luminosity. (d) X-ray photon index vs. 2–10 keV luminosity...... 33 2.4 Γ–LX (2–10 keV rest-frame) diagram for high redshift quasars (z > 1.5). The data shown as filled triangles are from Page et al. (2003). The data shown as filled circles are from Reeves & Turner (2000). The data shown as crosses are from George et al. (2000). The data shown as open circles are from Vignali et al. (1999). The data shown as open squares are from our own sample of lensed quasars...... 34 2.5 Plots of αox vs. redshift and UV luminosity. The crosses represent BAL QSOs and squares represent non-BAL quasars for all of the plots in this figure. (a) αox vs. redshift. (b) αox vs. rest-frame 2500A˚ luminosity. The solid line represents the best fit αox–L relation obtained from 2500A˚ Vignali, Brandt, & Schneider (2003), and the shaded region represents a dispersion of 0.25 from the best fit line...... 35 2.6 Excess variance in the 0.2–10 keV band vs. 2–10 keV luminosity. The data points representing the Seyfert 1s shown as filled triangles were obtained from Nandra et al. (1997) and are fitted with a power law (solid line). The ASCA SIS light-curves of the Seyfert 1s were binned in 128 s bins. The data points for the NLS1s shown as open circles were obtained from Leighly (1999). The ASCA SIS light-curves of the NLS1s were binned in 128 s bins. The data points for the LINERS and LLAGNs shown as squares were obtained from Ptak et al. (1998). The data points shown as filled stars were obtained from z > 2 quasars of Manners, Almaini, & Lawrence (2002). The downward arrows represent upper limits for the excess variance of the gravitationally lensed quasars from the present sample...... 36 ix

3.1 (a) The raw image of the combined observations of Q 2237+0305 binned with a binsize of 000.05 and smoothed with a Gaussian of 000.05 (top). (b) The deconvolved image binned with a binsize of 000.1 (bottom left). (c) The deconvolved image binned with a binsize of 000.05 (bottom right). The green circles in each image are the corresponding HST image positions provided by CASTLES (http://cfa-www.harvard.edu/glensdata/Individual/Q2237.html). 55 3.2 68% confidence contours of photon index and neutral absorption at the lens (z = 0.0395) for images A, B, C, and D of the combined spectra from both observations. The shaded region represents the overlapping region of the four confidence contours...... 56 3.3 (a) Spectrum of image A combined from both observations (top). (b) Combined spectrum of images B, C, and D from both observations (bottom)...... 57 3.4 To evaluate the significance of the emission feature in image A, we determined the distribution of the F-statistic (shown as histogram) using a Monte-Carlo simulation. We also overplotted for comparison the analytical curve for the F-distribution (shown as dashed curve). The vertical line indicates the F value obtained from the real spectrum of image A. The simulation shows that the detection of the broad emission line is significant at the > 99.99% confidence level...... 58

4.1 This figure is a composite of the deconvolved X-ray image of the gravitational lens RX J0911.4+0551 (top panel) and the light-curves of the lensed images A2 (left panel) and A1 (right panel). Chandra clearly resolves the four lensed images of the distant quasar. A rapid flare that lasted for about 2000s was recorded in image A2 whereas image A1 does not show any variability...... 65 4.2 Cumulative probability distribution versus exposure number for image A2 (left panel) and image A1 (right panel) compared to the cumulative probability distribution of a constant source...... 66 4.3 The full band (0.2–10 keV) light-curves of the sum of all images and images A, B, C, and D, separately, for the first and second Chandra observations of Q 2237+0305. The data were taken continuously within each observation...... 70 4.4 Cumulative probability distribution vs. exposure number for image A of the first observation of Q 2237+0305 compared to the cumulative probability distribution of a constant source...... 71 4.5 Time-delay constraints of the slope of the mass profile of the lensing galaxy of gravitational lens Q 2237+0305. The shaded region indicates the error range of the tentative time-delay between images A and B in Q 2237+0305 measured with Chandra...... 72 4.6 Simulated 100 ks Chandra light-curve for image A of Q 2237+0305. . . 73 x

4.7 Light-curve and cumulative distribution of image A (A1 and A2 combined) of the 26.8 ks observation of PG1115+080 in the 2.1–3.1 keV energy band...... 78 4.8 Light-curve and cumulative distribution of image A1 of the 26.8 ks observation of PG 1115+080 in the 2.1–3.1 keV energy band...... 79 4.9 Light-curve and cumulative distribution of image A1 of the 10 ks observation of PG 1115+080 in the full energy band ( 0.3-8 keV)...... 80 4.10 Light-curves of images A1 and A2 of the 26.8 ks PG1115+080 observation in the 2.1-3.1 keV energy band...... 81 4.11 (a) Cross correlation between the light-curves of images A1 and A2 of the 26.8 ks PG1115+080 observation in the 2.1–3.1 keV energy band. (b) Auto correlation of the light-curve A12 of the 26.8 ks PG1115+080 observation in the 2.1–3.1 keV energy band...... 82 4.12 (a) Error estimation of cross correlation results based on Monte-Carlo simulation. (b) Error estimation of DCF results based on Monte-Carlo simulation...... 83 4.13 Left panel: XMM-Newton image (taken with the PN instrument) of the PG 1115+080 field, Right panel: Light Curve of PG 1115+080 in the 0.6 - 1.7 keV band taken with the PN instrument onboard XMM-Newton . 88 4.14 The histogram of the auto correlation (AC) lag times of the XMM- Newton light-curves of different X-ray bands of the combined images of PG 1115+080 corresponding to the maxima of the AC coefficients with K-S chance probabilities of variability in each light-curve of less than 0.1 and Monte-Carlo chance probabilities of obtaining each AC coefficient of less than 0.1...... 89 xi Acknowledgments

I would like to thank my thesis advisors Gordon Garmire and George Chartas. I thank them for introducing me to the fascinating field of gravitational lenses. The completion of this thesis would never have been possible without the patient guidance and continuous encouragement by them. Their foresight to the whole project benefited me greatly during the course of my studies. I thank them for their help and advice towards my career. In particularly, I thank Gordon for spending part of his Chandra GTO time to observe gravitational lenses and providing financial support through NASA NSF funds. I am grateful to him for giving me the opportunity to participate in many different projects. I thank George for teaching me the details of various techniques that I applied to the reduction of science data and to the physics of gravitational lenses. It was enjoyable collaborating with him. I also thank him for spending tedious hours correcting my grammatical errors in many of our manuscripts. I also like to thank the rest of the thesis committee members. I thank Mike Eracleous for several interesting scientific discussions and his many suggestions, especially for his contribution on interpreting the Γ−LX relation that we found in the high redshift quasars. I thank Robin Ciardullo and Sam Finn for their suggestions to the thesis. I would like to give a special thank you to Bing Zhang, who has been a friend of mine since I was an undergraduate back in China. We share many interests together besides Astronomy. I thank him for his encouragement, help, and advice towards my career. Particularly, I thank him for leading me in a project to explore the jet structure of Gamma-ray bursts. I would like to thank every one who helped me during my stay in the astronomy department at Penn State. Finally, I would like to thank my family especially my wife, Xuguang Wang, for their love and support. 1

Chapter 1

Introduction

1.1 Gravitational Lenses

Since the discovery of the ﬁrst gravitational lens Q 0957+561 (Walsh, Carswell, & Weymann 1979) more than eighty additional strong gravitational lenses have been detected with multiple images (Kochanek et al. 2004). Most of the sources of these gravitational lensing systems are quasars lensed by a galaxy. Occasionally a nearby galaxy and/or a cluster of galaxies is found to contribute to the lensing of the source. In Fig- ure 1.1, we show as an example an optical image of the gravitational lens Q 0957+561. The image was obtained from the CfA-Arizona Space Telescope LEns Survey (CAS- TLES) 1 of gravitational lenses website. The source is at a redshift of z = 1.41 and the lensing galaxy is at a redshift of z = 0.36. Two images are formed in this lens system. The ﬁeld of gravitational lensing has expanded rapidly since the discovery of Q 0957+561. A summary of the properties of gravitational lenses can be found in Schneider et al. (1992).

Fig. 1.1 The optical image of the gravitational lens Q 0957+561.

1The CASTLES website is located at http://cfa-www.harvard.edu/glensdata/. 2

1.1.1 Lens Equations

Lens Plane Source Plane

Image(x, y)

Projected Source Position Source(u', v') (u, v)

Observer

DOL D LS

DOS

Fig. 1.2 Schematic plot of gravitational lensing.

Traditionally, the lens equation is solved by the ray tracing method. An alternative method to compute the lens properties is through Fermat’s principle (e.g., Blandford & Narayan 1986) which states that the lens images are formed at the extrema of the time-delay surface between the source and the observer. Figure 1.2 shows a schematic plot of gravitational lensing, where the relation between the source, image and the observer is illustrated. We assume c = G = 1 in the following equations in this chapter. Given a surface mass density function Σ(x, y) at the lens plane, a time-delay potential φ(x, y) at the lens plane is deﬁned as

4D D 0 0 0 0 0 0 φ(x, y) = LS OL Σ(x , y )ln (x − x )2 + (y − y )2dx dy (1.1) D OS Z q where x and y are the two angular displacements in the lens plane and DLS, DOL, DOS are angular diameter distances between the lens and source, the observer and lens, and the observer and source, respectively. The virtual time-delay is

(1 + z )D D 1 2 1 2 ∆t = L OL OS ( (x − u) + (y − v) − φ(x, y)) (1.2) DLS 2 2 where u and v are the source positions projected on the lens plane. The images are formed at the extrema of the virtual time-delay surface based on Fermat’s principle. Therefore, the image positions are found through equations ∂∆t ∂∆t = 0, = 0 (1.3) ∂x ∂y which give ∂φ ∂φ u = x − , v = y − . (1.4) ∂x ∂y 3

The time-delay between two images is

tAB = ∆tA − ∆tB. (1.5)

The magniﬁcation of an image is calculated by

2 2 2 −1 ∂ φ ∂ φ ∂ φ 2 M = (1 − )(1 − ) − (1 − ) . (1.6) ∂x2 ∂y2 ∂x∂y An important scale of gravitational lensing is the Einstein radius deﬁned in the source plane as

4MDLS DOS rE = . (1.7) s DOL If the size of the source is much larger than the Einstein radius, the magniﬁcation of the source due to lensing will not be signiﬁcant.

1.1.2 Strategy for Solving the Lens Equation One of the advantages of using Fermat’s principle to solve the lens equation is that the lens potential is expressed as a scalar rather than a vector or a complex form. There- fore, it is relatively easier to solve the lens equation numerically. Usually, this approach first chooses some lens potentials with several free parameters representing the lensing galaxy. Then the lens equation can be solved numerically based on Equations (1.4) and (1.6) to obtain the predicted image positions and magnifications. These values can be compared with observations. By varying the free parameters in the lens potential and the positions of the source, a best match between the model predications and observables can be found through minimizing the χ2 values of the fitting. χ2 statistics is used to evaluate the goodness of the fit. This technique has been used by many researchers in the field (e.g., Kayser et al. 1990; Kochanek 1991). Recently, several software packages have been developed that model gravitational lenses following these steps. One of these packages, gravlens, has been developed by C. R. Keeton (Keeton 2001a,b). This software includes a vast variety of lens potentials and is currently widely used in the lensing community.

1.1.3 Lens Potentials In the early days, modeling of gravitational lenses was focused on the luminous part of the lensing galaxy. Later, it was realized that the dark matter contribution to the lensing effect must be significant for some of the large separation images. In these systems the luminous part of the galaxy alone cannot account for the large image separations. A singular isothermal sphere (SIS) mass profile is commonly used as a first order approximation for the dark matter component in the lensing galaxies. As most of the lensing galaxies are elliptical galaxies, it is more realistic to use the lens potentials which can represent the elliptical nature of the galaxies. In particular, such potentials are usually expressed in analytical equations to significantly improve the speed of the fitting process since no numerical integration is needed. Elliptical potentials (EP) (Kovner 4

1987a,b; Blandford & Kochanek 1987; Kochanek et al. 1989) were first introduced to model gravitational lenses. Analytical expressions for elliptical potentials are usually simple and they can approximate elliptical mass profiles quite well when the ellipticity is small. However, in principle, these potentials are unphysical especially when the ellipticity is large. The analytical expressions for lens potential obtained from elliptical mass distributions were derived by Kassiola & Kovner (1993); Kormann, Schneider, & Bartel- mann (1994). Among the family of lens potentials with elliptical mass distribution, the lens potential obtained from the singular isothermal elliptical (SIE) mass distribution is most commonly used at present to model gravitational lenses. With the increasing speed of computers, more complex lens potentials representing the dark matter component can be calculated numerically (e.g., NFW or cuspy mass profiles). The luminous part of the lensing galaxy is usually approximated with lens potentials derived from de Vaucouleurs or Hubble mass profiles. All of these lens potentials are included in Keeton’s gravlens software package, which is used in this thesis to model several gravitational lens systems.

1.1.4 Applications of Gravitational Lensing Applications of gravitational lensing can be very useful in many astrophysical areas. We will brieﬂy discuss some of the applications in the following sections.

1.1.4.1 Placing Constraints on the Hubble Constant Time-delays in gravitational lens systems can be used to measure the Hubble constant. Based on Equation (1.2), the time-delay is dependent on the angular diameter distances DLS, DOL, and DOS. These distances can be expressed in the form of 1 D(z1, z2) = H0 f(Ωm, ΩΛ, z1, z2) in general. Equation (1.2) indicates that the time-delay is inversely proportional to the Hubble constant. We note that the time-delay also depends on other parameters such as Ωm and ΩΛ. However, the dependence is weak. In addition, the values for Ωm and ΩΛ determined from independent studies can be used in this equation. The lensing method was first introduced by Refsdal (1964a,b) even before the detection of the first gravitational lens and provides a means of determining a global value for the Hubble constant. Thus, the Hubble constant determined from this method should truly reflect the cosmological expansion of the universe. In addition, compared with other H0 determination methods, this method is relatively straightforward since no distance ladder is needed. However, this method suffers from the difficulty that the underlying dark matter mass profile is generally unknown. Moreover, the limited observables of most gravitational lenses cannot constrain the mass distribution accurately from the lens Equations (1.4) and (1.6). The time-delays of only a small fraction of the lenses are currently measured. The Hubble constant is estimated by incorporating these time-delays, image positions and image fluxes into lens models of the system and solving the lens equation. Please refer to Chapter 4 for more details regarding estimates of the Hubble constant with the lensing method. 5

1.1.4.2 Constraining the Cosmological Constant ΩΛ Strong gravitational lensing can also be used as a tool to constrain the cosmological constant ΩΛ. First, the cosmological constant is sensitive to the statistics of several lensing properties such as the frequency of quasar-galaxy lensing, and the mean image separation of lenses (Turner, Ostriker, & Gott 1984; Kochanek 1996; Im, Griﬃths, & Ratnatunga 1997; Turner 1990). All of these studies point towards a large cosmological constant. In addition, as mentioned previously, the lens equation involves several angular diameter distances between the observer, the lens, and the source. Although these distances are weakly dependent on ΩΛ, the dependence is more important when the redshift increases. Of the several distances, ? showed that the distance between the observer and the lensing galaxy is more dependent on ΩΛ. Therefore, when the lensing galaxies are at high redshifts, it is possible to constrain the cosmological parameter through the lens equation. This method was applied to the gravitational lens HST 14176+5226 (Ohyama et al. 2002), where the cosmological constant was constrained to be larger than 0.7 (1σ) assuming a ﬂat universe.

1.1.4.3 Determining the Mass Profiles of the Lensing Galaxies A recent application of gravitational lensing aims at determining the mass profiles of lensing galaxies by solving the lens equation given the observed image positions and relative flux magnifications. This method can constrain the underlying dark matter mass distribution, which is not directly observable, in the lensing galaxies. The lensing effect depends on the total mass distribution of the lensing galaxy. The lensing method is particularly important for studying the dark matter distributions of high redshift galaxies where other methods, such as those measuring rotational curves, are difficult to apply. Preliminary efforts have been made to constrain the mass profiles of galaxies employing this approach (e.g. Kochanek 1991). However, the limited observables in presently known lensing systems do not provide significant constrains of the mass distribution of the lensing galaxies. One way to circumvent this problem is to constrain the dark matter properties through studying an ensemble of gravitational lenses. In addition, since the Hubble constant has been recently accurately measured with the HST Key Project (HSTKP) (Freedman et al. 2001) and with W MAP (Spergel et al. 2003), one can use the Hubble constant as a constraint and use the time-delay equation to break the degeneracy between lens models. Such analyses are performed in Kochanek (2002, 2003).

1.1.4.4 Studying the Properties of the Sources with the Aid of Lensing Magnification The flux magnification provided by gravitational lensing ranging from a few to ∼ 100 enables us to obtain high signal-to-noise (S/N) ratio spectra of the sources (mostly quasars) with less observing time. This allows us to detect quasars in bands where the output of the quasar luminosity is small, such as the CO and sub-millimeter bands. For example, the CO and sub-millimeter surveys (Barvainis & Ivison 2002; Barvainis, 6

Alloin, & Bremer 2002) have successfully detected most of the lensed quasars in their sample. It is extremely useful to obtain multi-wavelength information on quasars to study their properties. Broad absorption line (BAL) quasars are another class of objects that are typically X-ray weak and can be better studied when magnified by the lensing effect. Studies of gravitationally lensed BALs through X-rays have revealed important information on the X-ray properties of these quasars (e.g. Chartas et al. 2002b). In this thesis, we use the flux magnification provided by gravitational lensing to study high redshift radio-quiet quasars which would otherwise be too faint to obtain their spectral properties through X-rays. This is explained in detail in Chapter 2.

1.1.4.5 Micro-lensing and Milli-lensing Events In addition to macro-lensing produced by the lensing galaxy of a gravitational lens system, micro-lensing induced by stars moving in the line of sight of one of the lensed images can also contribute to the lensing effect. Micro-lensing will only affect one lensed image at a time. Micro-lensing events in lensed quasar images have been detected in several lenses, such as Q 2237+0305 (Irwin et al. 1989; Wo´zniak et al. 2000a,b), Q 0957+561 (Schild & Smith 1991; Schild 1996; Refsdal et al. 2000), HE 1104-1805 (Schechter et al. 2003), and some other systems and they can be useful tools for studying the source size of quasars in different energy bands and the mass and velocity of the 6 9 microlens. Milli-lensing is induced by masses of 10 –10 M in the lensing galaxy. It is similar to micro-lensing in that it can only affect one lensed image at a time. However, they are different in that the mass of a milli-lens is much larger than that of a micro-lens. Such large mass density anomalies are theoretically present in dark sub-structures which are predicted both from analytical and numerical simulations (e.g. Moore et al. 1999) of the cold dark matter (CDM). Recently, Metcalf et al. (2004) reported the detection of milli-lensing in Q 2237+0305. Milli-lensing can serve as an important test for dark matter models if it is confirmed by future studies.

1.2 X-ray Properties of Active Galactic Nuclei

Almost all of the sources of the strong lenses are quasars which belong to the high luminosity end of Active Galactic Nuclei (AGN). Moreover, a major part of the thesis involves a study of quasar properties in X-rays with the aid of gravitational lensing. Thus, a brief introduction to the subject is provided here. Please refer to Perterson (1997); Krolik (1999) for more details. AGNs are objects that emit bolometric luminosities ranging from 1042–1049 erg s−1 from the central nuclei of the galaxies. These objects are thought to be powered by the accretion of material onto a central supermassive black holes through an accretion disc. The AGNs are separated into Seyferts and quasars based on their luminosities. Quasars belong to the high luminosity end which have B magnitudes MB < −21.5 + 5 log h0 (Schmidt & Green 1983). Traditionally, another distinction between Seyferts and quasars is that the host galaxies of Seyferts can be resolved. However, the quasar host galaxies can also be resolved with recent HST observations. Quasars are divided into two sub-classes, radio-loud and radio-quiet, and about 90% of quasars are radio-quiet. 7

The radiation processes of quasars are extremely complicated. The energy output of quasars spans a extremely broad band from radio to hard X-ray to γ-rays. In addition, approximately equal amounts of energy is radiated per decade in frequency. However, recent studies have indicated that this broad band continuum is not associated with a single emission process but rather consists of several different processes associated with different components of the quasar. In addition, the sizes of these different emission regions are quite different. One important area of quasar studies involves constraining the sizes of these different emitting regions and understanding the underlying physics associated with them.

1.2.1 X-ray Continuum X-rays are thought to originate from the inner most regions of a quasar’s accretion disc. A popular model which explains the X-ray properties of quasars is the disc-corona model (e.g., Haardt & Maraschi 1993). In this model, the accretion disc is sandwiched by the hot corona. The accretion power is distributed to both the accretion disc and corona components. The disc and corona are coupled; however, the details of the coupling are not well understood. The soft photons from the disc are inverse-Compton scattered by the energetic electrons in the corona resulting in a powerlaw X-ray continuum.

1.2.2 X-ray Reflection Component and the Fe Kα line In addition to the X-ray powerlaw continuum component, observations also indicate the presence of an X-ray reflection component in AGN. This reflection component is thought to be the reflection of X-ray continuum from cold material, possibly the accretion disc itself, the accretion disc torus, or some other components. The detection of the reflection component in the X-ray spectra of AGN partially confirms the disc-corona assumption. A fluorescent Fe Kα line is associated with the reprocessed emission. This line is at an energy of about 6.4–6.7 keV (rest frame) depending on the ionization state of the reflecting material. It is particularly interesting if this process occurs extremely close to the supermassive black hole where the general and special relativistic effect are strong, resulting in a broad redshifted Fe Kα. Such broad Fe Kα lines are observed in several Seyferts and the first and most famous one is MCG-6-30-15 (Tanaka et al. 1995). Such lines can serve as evidence of the presence of super-massive black holes. Recently, many studies have focused on the broad Fe Kα line of MCG-6-30-15 (e.g. Wilms et al. 2001; Fabian & Vaughan 2003) to constrain the environment around the black hole and its spin rate.

1.3 Motivation of the Thesis

Studies of gravitational lenses are mainly focused in the optical and radio bands. The optical and radio bands can resolve the individual images of lensed quasars, which is essential for studying these lenses. Before the Chandra era, the study of gravitational lenses in X-rays was scarce (Chartas 2000). With the advent of Chandra, it is possible to resolve for the first time in the X-ray band lensed quasar images with separations greater than about 0.35 arcsec. In addition, the new generation X-ray telescopes (Chandra 8 and XMM-Newton) have significantly larger throughputs than their predecessors, which facilitate easy detection of gravitational lenses in X-rays. A mini-survey of gravitational lenses with Chandra has been performed, led by G. Garmire and G. Chartas at Penn State to study the properties of gravitational lenses in X-rays. In addition, we also have obtained several XMM-Newton observations of lensed quasars. Applications of gravitational lensing and the use of lensing to study the properties of quasars were briefly introduced in previous sections. The study of quasars in the X-ray band is essential in that X-rays probe the inner-most regions of the quasar’s accretion disc. For the field of gravitational lenses, this exploratory X-ray survey is new and complementary to the study from other bands. For example, some lens images have time-delays of order of hours, which practically can only be detected in X-rays. We provide an outline of the Thesis in the following section.

1.4 Outline of the Thesis

The Thesis consists of X-ray studies of gravitational lenses. The lensing flux magnification, ranging from a few to ∼ 100, enables us to obtain high signal-to-noise spectra and light-curves of high redshift quasars with less observing time and allows us to search for changes in quasar spectroscopic properties and X-ray flux variability over three orders of magnitude in intrinsic X-ray luminosity. We also use the microlensing effects induced by stars in the lensing galaxies to study the structure of the accretion discs of AGN, which cannot be resolved by current instruments. This is applied particularly in the case of Q 2237+0305. Finally we use gravitational lensing as a tool to study cosmology. By measuring the time-delays between different lensed images it is possible to constrain the Hubble constant independently from other techniques or to use the time- delays together with the Hubble constant obtained from other independent methods such as HSTKP and WMAP projects to constrain the mass profile of the lensing galaxies.

1.4.1 Chapter 1: A Study of Quasar Evolution with the Aid of Lensing In Chapter 1, we present results from a mini-survey of relatively high redshift (1.7 < z < 4) gravitationally lensed radio-quiet quasars observed with the Chandra X- ray Observatory and with XMM-Newton. The lensing magnification effect allows us to search for changes in quasar spectroscopic and flux variability properties with redshift over three orders of magnitude in intrinsic X-ray luminosity. It extends the study of quasar properties to unlensed X-ray flux levels as low as a few times 10−15erg cm−2 s−1 in the observed 0.4–8 keV band. For the first time, these observations of lensed quasars have provided medium to high signal-to-noise ratio X-ray spectra of a sample of relatively high-redshift and low X-ray luminosity quasars. We find a possible correlation between the X-ray powerlaw photon index and X-ray luminosity of the gravitationally lensed radio-quiet quasar sample. The X-ray spectral slope steepens as the X-ray luminosity increases. This correlation is still significant when we combine our data with other samples of radio-quiet quasars with z > 1.5, especially in the low luminosity range between 1043–1045.5 erg s−1. This result is surprising considering that such a correlation is not found for quasars with redshifts below 1.5. We suggest that this correlation can 9 be understood in the context of the hot-corona model for X-ray emission from quasar accretion disks, under the hypothesis that the quasars in our sample accrete very close to their Eddington limits and the observed luminosity range is set by the range of black hole masses (this hypothesis is consistent with recent predictions of semi-analytic models for quasar evolution). The upper limits of X-ray variability of our relatively high redshift sample of lensed quasars are consistent with the known correlation between variability and luminosity observed in Seyfert 1s when this correlation is extrapolated to the larger luminosities of our sample.

1.4.2 Chapter 2: An X-ray Microlensing Event in Q 2237+0305 In Chapter 2, we present the observations of the gravitationally lensed system Q 2237+0305 (Einstein Cross) performed with the Advanced CCD Imaging Spectrometer (ACIS) onboard the Chandra X-ray Observatory on 2000 September 6, and on 2001 December 8 for 30.3 ks and 9.5 ks, respectively. Imaging analysis resolves the four X- ray images of the Einstein Cross. A possible fifth image is detected; however, the poor signal-to-noise ratio of this image combined with contamination produced by a nearby brighter image make this detection less certain. We investigate possible origins of the additional image. Fits to the combined spectrum of all images of the Einstein Cross assuming a simple power law with Galactic and intervening absorption at the lensing +0.05 galaxy yields a photon index of 1.90−0.05 consistent with the range of Γ measured for large samples of radio-quiet quasars. For the first Chandra observation of the Einstein Cross this spectral model yields a 0.4–8.0 keV X-ray flux of 4.6 × 10−13erg cm−2 s−1 and a 0.4–8.0 keV lensed luminosity of 1.0×1046erg s−1. The source exhibits variability both over long and short time scales. The X-ray flux has dropped by 20% between the two observations, and the Kolmogorov-Smirnov test showed that image A is variable at the 97% confidence level within the first observation. The X-ray flux ratios of the images are consistent with the optical flux ratios which are affected by microlensing, suggesting that the X-ray emission is also microlensed. A comparison between our measured column densities and those inferred from extinction measurements suggests a higher dust-to-gas ratio in the lensing galaxy than the average value of our Galaxy. Finally, we report the detection at the 99.99% confidence level of a broad emission feature near the redshifted energy of the Fe Kα line in only the spectrum of image A. The rest frame energy, width, +0.2 +0.30 and equivalent width of this feature are Eline = 5.7−0.3 keV, σline = 0.87−0.15 keV, and +300 EW = 1200−200 eV, respectively.

1.4.3 Chapter 3: X-ray Time-delay Measurements of Gravitational Lensing Systems In Chapter 3, we present estimates of the time-delays in a sample of gravitational lenses observed with Chandra and XMM-Newton. We applied cross correlation and auto correlation techniques to the X-ray light-curves of the gravitational lenses. The time- delays between some of the short separation systems are predicted to be short, of the order of several hours. We have measured two time-delays and one lower limit on a time-delay. In RX J0911.4+0551, we have detected a ﬂare only in image A2 and not in image A1 constraining the time-delay between the two images to be greater than 23 ks. 10

Although, we did not measure the time-delay in this system, it was realized for the ﬁrst time that short time-delays can be measured in single X-ray observations. In a Chandra +0.5 observation of Q 2237+0305, we detected a tentative time-delay of 2.7−0.9 hours between images A and B with image A leading. This time-delay is important in constraining the mass proﬁle of the lensing galaxy and the amount of dark matter substructure in the lensing galaxy. In a Chandra observation of PG 1115+080, we detected a time-delay +0.02 of ∆τA1A2 = 0.162−0.01 days with image A1 leading. Furthermore, the analysis of an XMM-Newton observation of PG 1115+080 also yields a time-delay of 0.149 0.006 days, which is consistent with the time-delay between images A1 and A2 measured from the Chandra observation. Combining this time delay with other constraints in the +13 −1 −1 system, a Hubble constant of H0 = 67−8 3 km s Mpc is obtained.

1.4.4 Chapter 4: Conclusions In Chapter 4, we summarize the main results of the Thesis. 11

Chapter 2

A Study of Quasar Evolution in the X-ray Band with the Aid of Gravitational Lensing

2.1 Introduction

It1 is important to extend the study of quasars to high redshifts in order to understand the evolution of quasars and their environments. One of the main results of recent studies of quasar evolution is that the quasar luminosity function evolves strongly with redshift (e.g., Boyle et al. 1987). Many studies of quasar evolution are aimed at explaining this luminosity evolution. The X-ray band probes the innermost regions of the central engines of the active galactic nuclei (AGNs). The study of AGNs in the X-ray band may possibly answer the question of whether there is an evolution in their central engines and how it is related to the evolution of the quasar luminosity function. The observed X-ray continuum emission of AGNs is generally modeled by a power law of −Γ the form N(E) = N0(E/E0) , where N(E) is the number of photons per unit energy interval. Extensive studies of AGNs during the past decade indicate that this power-law component is produced by Compton scattering of soft photons by hot electrons in the corona (e.g., Haardt & Maraschi 1993; Haardt, Maraschi, & Ghisellini 1994). The study of this power-law component, its correlations with other AGN parameters, and its evolution reveals important information on the accretion process of the central object. The X-ray photon indices of low-redshift radio-quiet quasars are measured to have mean values of ∼2.6–2.7 in the ROSAT soft X-ray band (Laor et al. 1997; Yuan et al. 1998) and ∼1.9–2.0 in the ASCA hard X-ray band (George et al. 2000; Reeves & Turner 2000) and are correlated with the Hβ FWHM (Reeves & Turner 2000). There is no strong evidence to date that the X-ray power-law index evolves with redshift or correlates with X-ray luminosity (George et al. 2000; Reeves & Turner 2000). Another important parameter that describes the broad band spectral shape of quasars is the optical to X-ray spectral index, quantiﬁed as αox = log(f2keV/f )/ log(ν2keV/ν ), where f2keV and f 2500A˚ 2500 A˚ 2500 A˚ are the ﬂux densities at 2 keV and 2500 A˚ in the quasar rest-frame, respectively. Recently, several studies have provided estimates of αox for very high redshift (z > 4) quasars (Vignali, Brandt, & Schneider 2003; Vignali et al. 2003a,b; Bechtold et al. 2003). Vignali, Brandt, & Schneider (2003); Vignali et al. (2003a,b) found that αox is mainly dependent on the ultra-violet luminosity while Bechtold et al. (2003) found that αox primarily evolves with redshift. In addition to spectral studies, variability studies of Seyfert galaxies show that the variability amplitude (excess variance) is anti-correlated

1The work in this chapter has been previously published as Dai, X., Chartas, G., Eracleous, M., & Garmire, G. P. (2004) A Study of Quasar Evolution in the X-Ray Band with the Aid of Gravitational Lensing. Astrophysical Journal 605:45 12 with X-ray luminosity (Nandra et al. 1997; Leighly 1999). Variability studies have been extended to quasars by several groups (George et al. 2000; Almaini et al. 2000; Manners, Almaini, & Lawrence 2002). Low-redshift quasars (z < 2) are found to have an excess variance consistent with the luminosity relation found in Seyfert 1 galaxies, and there is a possible upturn of X-ray variability for high-redshift quasars with z > 2 (Almaini et al. 2000; Manners, Almaini, & Lawrence 2002). It is also important to compare the properties of quasars near the peak of their comoving number density, thought to have occurred at z ∼ 2 with low-redshift quasars. This comparison may provide clues as to what caused the dramatic decay of the quasar number density as the universe expanded. Most of the observational and analysis techniques employed to date to study the evolution and emission mechanism of faint, high-redshift quasars are based on either summing the individual spectra of many faint X-ray sources taken from a large and complete sample or obtaining deep X-ray observations of a few quasars. Although these techniques may yield important constraints on the average properties of high-redshift quasars, they each have significant limitations. Gravitational lensing provides an additional method for studying high-redshift quasars. The extra flux magnification, from a few to ∼100 times, provided by the lensing effect enables us to obtain high signal-to-noise ratio (S/N) spectra and light-curves of distant quasars with less observing time and allows us to search for changes in quasar spectroscopic properties and X-ray flux variability over three orders of magnitude in intrinsic X-ray luminosity. With the aid of lensing, we can probe lower flux levels than other flux limited samples with similar instruments and exposures. This could be an important factor because the X-ray properties of high-redshift, low-luminosity quasars could be different from those of other quasars and by studying them we could possibly obtain information about the evolution of quasars. Similar lensing studies have also been performed in the sub-millimeter and CO bands (Barvainis & Ivison 2002; Barvainis, Alloin, & Bremer 2002), which suggested that gravitational lensing could be an efficient method for studying various properties of high-redshift quasars. Here we present the results of an X-ray mini-survey of relatively high redshift gravitationally lensed radio-quiet quasars. We chose only the radio-quiet quasars in our sample because the powerful relativistic jets in the radio-loud quasars will introduce additional complication when modeling the continuum X-ray emission from the accretion disc. −1 −1 We use a H0 = 50 km s Mpc and q0 = 0.5 cosmology throughout the paper.

2.2 Observations and Data Reduction

Our mini-survey contains eleven gravitationally-lensed, radio-quiet quasars with redshifts ranging between 1.695 and 3.911. Five of them contain Broad Absorption Lines (BALs) or mini-BALs in their rest-frame ultraviolet spectra. Most of the lensed quasars of our sample were observed with the Advanced CCD Imaging Spectrometer (ACIS; Garmire et al. 2003) onboard Chandra as part of a Guaranteed Time Observing program (Principal Investigator: G. Garmire). The data for two of the them were obtained through the public Chandra archive. Several of them were observed twice. 13

Three of the lensed quasars were also observed with XMM-Newton. Table 2.1 presents a log of observations, including redshifts, Galactic column densities, and exposure times. Each observation was performed continuously with no interruptions. All of the sources observed with Chandra were placed near the aim point of the ACIS-S array, which is on the back-illuminated S3 chip. All of the data were taken in FAINT or VERY FAINT mode. The Chandra data were reduced with the CIAO 2.3 software tools provided by the Chandra X-Ray Center (CXC) following the standard threads on the CXC website. Only photons with standard ASCA grades of 0, 2, 3, 4, 6 were used in the analysis. We used events in the 0.4–8 keV energy range in the spectral analysis and events in the 0.2–10 keV range for the variability studies. The source events were extracted from circles with radii ranging from 300 to 500 depending on the separations of the lensed images of each quasar. The circles included all of the lensed images. Background events were extracted from annuli with inner and outer radii of 1000 and 3000, respectively, centered on the sources. We adjusted the inner and outer radii of the background subtraction annuli in some cases to avoid other sources in the field. The background contributes an insignificant amount to the count rate in a source region, even during a background flare. The average exposure time for the Chandra observations was about 25 ks. The detected source count rates ranged between 0.003–0.08 s−1. Three targets were observed with the European Photon Imaging Camera PN and MOS detectors (Struder¨ et al. 2001; Turner et al. 2001) onboard XMM-Newton. The XMM-Newton data were analyzed with the standard analysis software, SAS 5.3. The tasks epchain and emchain from SAS were used to reduce the PN and MOS data and photons of patterns ≤ 4 and ≤ 12 were selected from the PN and MOS data, respectively. The XMM-Newton data are affected more than the Chandra data by background flares because the Point Spread Function of XMM-Newton is significantly larger than that of Chandra-ACIS. Several strong background flares occurred during the XMM-Newton observations. These flares are filtered out in the spetral analysis.

2.3 Spectral Analysis

2.3.1 Power-law Continuum We performed spectral fitting in order to obtain the power-law indices of the X-ray continuum of the quasars in our sample. The photon indices that we measured were in the observed 0.4–8 keV energy range. We used the Chandra data for all of the lensed quasars in the spectral analysis except PG 1115+080, where we used the XMM- Newton data. RX J0911.4+0551 and APM 08279+5255 were also observed with XMM- Newton. We did not use these data, however, because there were large amplitude and long duration background flares in the XMM-Newton observations. The background flare in the XMM-Newton observation of RX J0911.4+0551 almost spans the entire observation. The background flare in the XMM-Newton observation of APM 08279+5255 occurs during the last ∼ 20 ks of the observation. We filtered the background flare time from this observation and performed a spectral analysis to compare with our Chandra results. For our later correlation analysis, we used the Chandra data of APM 08279+5255 to 14 avoid the possible complication from the cross calibration between Chandra and XMM- Newton instruments. For those sources observed twice with Chandra, we performed simultaneous fits to the spectra extracted from the two observations except in the case of APM 08279+5255, where we used only the second observation because it was much longer than the first one. We extracted spectra for each quasar using the CIAO tool psextract. We extracted events from all of the lensed images for each source except for the case of H 1413+117. A possible microlensing event in H 1413+117 appears to amplify and distort the spectrum of image A only and thus affects the spectral slope greatly (Char- tas et al. 2003). In this case, we extracted the spectrum of the microlensed image A and the spectrum of the other three images separately. A microlensing event is also detected in Q 2237+0305. However, the spectral shape of the microlensed image A of Q 2237+0305 is not significantly affected by the microlensing event (Dai et al. 2003). Spectral fitting was performed with XSPEC V11.2 (Arnaud 1996). There are typically several hundreds (180–6000) detected source events in the spectra of the target quasars, except for the spectrum of HE 2149−2745 which has only 23 detected events. The moderate S/N of our spectra allows us to fit each of them individually using relatively complex models. Thus we can constrain the underlying power-law slopes more accurately than in previous studies of unlensed quasars of similar redshift. The models we used are listed in Column 3 of Table 3.3. All spectral models included an underlying power-law model modified by Galactic absorption. The Galactic absorbing columns were obtained from Dickey & Lockman (1990). To account for the recently observed quantum efficiency decay of ACIS, possibly caused by molecular contamination of the ACIS filters, we have applied a time-dependent correction to the ACIS quantum efficiency implemented in the XSPEC model ACISABS1.1. 2 If the source was a BALQSO with a medium S/N spectrum, we added a neutral absorption component at the redshift of the source. For high S/N BALQSO spectra such as PG 1115+080 and APM 08279+5255 we used the absori model in XSPEC to model the intrinsic absorption component as an ionized absorber (Chartas et al. 2002b; Chartas, Brandt, & Gallagher 2003). We added a neutral absorption component at the redshift of the lens for Q 2237+0305 (Dai et al. 2003). For some of the spectra containing emission or absorption line features, we added Gaussian line components to model them accordingly. The spectra of the quasars are displayed in Figures 2.1. The spectral fitting results are given in Table 3.3. In Table 3.3, we also list the observed 0.4–8 keV fluxes and rest-frame 0.2–2 keV and 2-10 keV luminosities for the lensed quasars in the sample not corrected for the lensing magnification. The unlensed luminosities are calculated in §2.4. We have corrected for the various absorption components when calculating X-ray luminosities. These absorption components include Galactic absorption, absorption in the lensing galaxy, intrinsic absorption, and the ACIS contamination. The mean photon index of the radio-quiet quasars in our sample is 1.78 0.06 with a dispersion of 0.27 0.08 and the median photon index of the radio-quiet quasars in our sample is 1.86.

2ACISABS is an XSPEC model contributed to the Chandra users software exchange web-site http://asc.harvard.edu/cgi-gen/cont-soft/soft-list.cgi. 15

2.3.2 αox

We calculated the optical-to-X-ray power-law slope, αox, for the quasars in our sample. The differential magnification between the optical and X-ray band is insignificant because both of the source regions are estimated to be much smaller than the Einstein radius. The rest-frame 2 keV flux densities were calculated from the best-fit models to the spectra of the quasars. The redshifts of our sample range from 1.7 to 4, thus the rest-frame 2 keV energy falls in the 0.4–0.74 keV observed-frame energy range. We removed all of the absorption components including the intrinsic ones for the BALQSOs when calculating the rest-frame 2 keV flux densities in order to study the properties of the intrinsic continuum. The rest-frame 2500 A˚ fluxes were obtained from the published optical data in the literature and from current ongoing programs such as the CfA-Arizona Space Telescope LEns Survey (CASTLES) 3 and the Optical Gravitational Lensing Experiment (OGLE). 4 We first converted the optical magnitudes to flux densities at the effective wavelengths of the filters, then extrapolated them to the rest-frame 2500 A˚ flux densities. We used the standard relations between magnitudes and flux densities for the V and R bands. For the F814W magnitudes obtained with the HST WFPC2, we used the relation from Holtzman et al. (1995) to convert between −0.7 magnitudes and flux densities. We used fν ∝ ν in the extrapolation. Typical quasar optical spectral indices are in the -0.5 to -0.9 range (Schneider et al. 2001). We chose the optical magnitudes from the bands closest to the redshifted 2500 A˚ wavelength to reduce the error in the extrapolation. We corrected the Galactic extinction based on Schlegel, Finkbeiner, & Davis (1998). The extinction induced by the dust from the lensing galaxies is not significant except for Q 2237+0305, which is lensed by the central bulge of the galaxy. We corrected it according to the appendix of Agol, Jones, & Blaes (2000). The αox values are listed in Table 2.3. The listed error-bars of αox are at the 1σ level and account for the uncertainties in the X-ray spectral slope and normalization, the conversion from optical magnitude to flux density and the extrapolation of the optical/UV spectrum. We note that a source may have varied between the optical and X-ray observations thus leading to systematic errors in our estimates of αox. For the range of αox in our sample, a change of optical flux by a factor of two will lead to a change of ∆αox∼ 0.1. The rest-frame 2 keV and 2500A˚ flux densities and rest-frame 2500A˚ luminosity densities are also listed in Table 2.3. These values are corrected for lensing magnification as we discuss further in §2.4. In conclusion we find that the mean αox value for all the quasars in our sample is −1.70 0.02 (−1.66 0.02 without HE 2149−2745 which has only 23 X-ray events) with a dispersion of 0.20 0.03.

2.4 Magniﬁcation and Intrinsic X-ray Luminosities

We estimated the magnification for each of the lensed systems in order to obtain the unlensed X-ray luminosities of the quasars. We first searched in the literature for magnifications of well-modeled systems. However, not all of the systems in our sample

3The CASTLES website is located at http://cfa-www.harvard.edu/glensdata/. 4The OGLE website is located at http://bulge.princeton.edu/õgle. 16 have been previously modeled in detail and for some cases the magnification values are not included in the published analysis. We modeled these systems with the gravlens 1.04 software tool developed by C. Keeton (Keeton 2001a,b). We used a singular isothermal elliptical (SIE) mass profile with external shear in most cases, and took into account optical image positions and flux ratios obtained from the CASTLES survey. We assumed a 20% error-bar for the flux ratios to account for uncertainties from microlensing or differences between optical and X-ray flux ratios. Our modeling results are listed in Table 2.4. We compared the magnification values that we obtained with those published in Barvainis & Ivison (2002) and found them to be in good agreement. We note that the magnification values obtained may have large systematic errors because the SIE model adopted in this analysis may not be suitable for all the systems. For example, in PG 1115+080, a set of different mass potentials are used in the modeling of the magnification in Impey et al. (1998). A magnification range of 20–46 was obtained for this system. Based on this example, we adopt a factor of two as a typical systematic uncertainty in the magnification. In §2.6.1 we investigate how this systematic uncertainty could affect for our conclusions via Monte Carlo simulations.

2.5 Variability Analysis

The light-curves for the Chandra observations of the lensed quasars of our sample are displayed in Figure 2.2 binned with a bin size of 1000 s (observed-frame). We show the light-curves of the longer Chandra exposure if two Chandra observations of the same target are available. We excluded HE 2149−2745 in our timing analysis because of its low S/N (only 23 events). To estimate the relative variability of the light-curves, we used the normalized excess variance (Nandra et al. 1997; Turner et al. 1999; Edelson et al. 2002) deﬁned as

N 2 1 2 2 σrms = 2 [(Xi − µ) − σi ] (2.1) Nµ =1 Xi where N is the number of bins in the light-curve, Xi are the count rates per bin with 2 2 1/2 error σi, and µ is the mean count rate. The error on σrms is given by SD/[µ (N) ], where N 2 1 2 2 2 2 2 SD = {[(Xi − µ) − σi ] − σrmsµ } (2.2) N − 1 =1 Xi This method normalizes the variability amplitude to the flux, thus is less biased towards the low flux light-curves. It is better to apply this method to a sample of light-curves of similar lengths to avoid possible bias. For example, it would be easier to detect long time-scale variability from a light-curve with a long duration. In addition, the bin sizes should be similar in order to compare variability on similar time-scales. High S/N light- curves are needed for this analysis as the variability could be easily dominated by noise in the low S/N light-curves. This excess variance method also has some limitations. One of them is that it is not very sensitive to short flares of moderate amplitude. The excess variance values for Chandra light-curves with three different bin sizes are listed 17 in Table 2.5. We also calculated the excess variance for the three sources observed with XMM-Newton and the results are listed in Table 2.6. The background was subtracted in the calculation. Overall, the error-bars on the excess variance are quite large and in some cases, the values are negative. Therefore, for most quasars we can really only obtain an upper limit on the value of the excess variance.

2.6 Results and Discussion

2.6.1 Luminosity and Spectral Index The unlensed 0.2–2 keV and 2–10 keV X-ray luminosities of the lensed quasars in our mini-survey range from 1043 to 1046 erg s−1. The mean spectral index of our sample, 1.78, is consistent with the value of 1.84 from the recent study of very high redshift quasars (Vignali et al. 2003b) and the value of 1.89 from the radio-quiet ASCA sample (Reeves & Turner 2000), especially when one considers the large dispersion of spectral indices in these studies and our small sample size. We plot the rest-frame 0.2–2 keV and 2–10 keV X-ray luminosity against redshift in Figure 2.3(a), and the photon indices vs. redshift, 0.2–2 keV luminosity, and 2–10 keV luminosity in Figures 2.3(b), (c), and (d), respectively. Figures 2.3(c) and (d) show a correlation between the spectral indices of our sample of lensed quasars and their X-ray luminosities. We tested the significance of this correlation using the Spearman’s rank correlation method. We obtained a rank correlation coefficient of 0.94 significant at the greater than 99.997% confidence level for the correlation between photon index and 0.2–2 keV luminosity and a coefficient of 0.71 significant at the 98.6% confidence level for the correlation between photon index and 2–10 keV luminosity. We note that the measured rest-frame 0.2–2 keV luminosity for high redshift quasars obtained from Chandra and XMM-Newton data is less accurate than the rest-frame 2–10 keV luminosity because it depends on extrapolation and suffers from the uncertainty in the absorbing columns towards the quasars. We adopt a significance at the 98.6% confidence level for this correlation, evaluated with the 2-10 keV luminosities. We also tested for a possible correlation between X-ray luminosity and redshift and between photon index and redshift and found none. The correlation between the photon index and X-ray luminosity was a surprising result. Therefore, we tested if this correlation is driven by certain data points. Excluding one of our data points at a time and performing the Spearman’s rank correlation between Γ and the 0.2–2 keV luminosity to the rest of the data set, we find a strong correlation with a significance level greater than 99.98% each time. We performed a similar analysis with the 2–10 keV luminosity, and the correlation is significant at the greater than 95% confidence level each time. This indicates that the correlation is not driven by any particular data point. We further performed correlation tests by excluding data points with errors in Γ larger than 0.20. Two data points are excluded and the rest of the data points still show a correlation significant at the greater than 99.98% confidence level. The significance is at the 92% confidence level when 2–10 keV luminosities are used. We also tested if there is a bias from different flux levels in our sample such that quasars with low fluxes have a systematically flatter slope because of measurement errors. In principle, 18 this should not be a problem for the sample in this paper because some low luminosity quasars have high S/N spectra as a result of the gravitational lensing effect. To test this, we simulated spectra with the same photon index (Γ = 2) but with a wide range of S/N and then fitted them with the same models within XSPEC. We found that for low S/N spectra, when the total number of photons is less than ∼200, the measured Γ could possibly be flatter by ∼ 0.1. This would affect three of our data points: HE 2149−2745, LBQS 1009−0252, and Q 1208+101 with (one low-luminosity and two high-luminosity quasars). We tested this effect by increasing the photon index by 0.1 for these three quasars and performed the correlation test again and found the correlations between Γ and 0.2–2 keV (2–10 keV) luminosities are significant at the 99.99% (98.7%) confidence levels, respectively. A Γ–LX correlation has been previously searched for in other samples of radio- quiet quasars. Reeves et al. (1997) reported first a possible correlation between Γ and luminosity with nine radio-quiet quasars observed with ASCA. However, this correlation was later not found in the study of a larger sample of 27 radio-quiet quasars observed with ASCA (including the original nine) by Reeves & Turner (2000). George et al. (2000) also searched for a correlation between Γ and luminosity in another sample of radio-quiet quasars observed with ASCA and did not find one. However, the quasars in our sample all have relatively high redshifts 1.7 < z < 4 compared to the redshifts of quasars incorporated in previous studies of the Γ–LX correlation. There is only one out of 26 quasars with z > 1.5 in the sample of George et al. (2000), and there are six out of 27 quasars with z > 1.5 in the sample of Reeves & Turner (2000) and most of them have large errors on Γ. In addition, the high redshift quasars in the sample of George et al. (2000) and Reeves & Turner (2000) have high luminosities and span a small luminosity range of 1045–1046 erg s−1. The sample of lensed quasars in this paper have lower luminosities and span a larger luminosity range of 1043–1045 erg s−1. Recently, Page et al. (2003) presented another sample of quasars observed with XMM-Newton which contains several high redshift, low-LX quasars. We plotted the Γ–LX diagram for quasars of z > 1.5 from the sample of Page et al. (2003), Reeves & Turner (2000), George et al. (2000), and Vignali et al. (1999) in Figure 2.4. We excluded one data point from Page et al. (2003) with a large measurement error on Γ. We also excluded PHL 5200 from Reeves & Turner (2000) in our analysis because new XMM-Newton observations of the object showed that most of the X-rays originate from a nearby radio source (Brinkmann, Ferrero, & Gliozzi 2002). We corrected the X-ray luminosity of HE 1104−1805 reported in Reeves & Turner (2000) to account for the gravitational lensing magnification of about 12 based on our analysis presented in §2.4. We used rest- frame 2-10 keV luminosities in order to be consistent with the previous analysis. Most of the data from Page et al. (2003) are consistent with the Γ–LX correlation found in our 43.5 45.5 −1 sample of lensed quasars, especially in the low LX range between 10 –10 erg s . 45 −1 On the high luminosity end (LX > 3 × 10 erg s ) of high redshift quasars (z > 1.5), the Γ dependence on LX seems to flatten out or even has an anti-correlation pattern. We performed the Spearman’s rank correlation test to all of the (z > 1.5) quasars and did not find a correlation between Γ and 2–10 keV luminosity. We separated the quasars in two groups with luminosities below and above 3 × 1045 erg s−1 and performed the rank correlation again to each group. The low luminosity quasars show a strong 19 correlation between Γ and 2–10 keV luminosity at the 99.97% confidence level and the high luminosity quasars show an anti-correlation between Γ and 2–10 keV luminosity at the 98.9% confidence level. We performed a Monte-Carlo simulation to test how much the Γ–LX correlation is affected by the uncertainty of the magnification factors of our lensed quasars. We used the combined data sets from the lensed sample and from the quasars of Page et al. (2003) with z > 1.5, which show a strong Γ–LX correlation. We assumed a systematic uncertainty on the magnification of a factor of two (see discussion in §2.4) and simulated 10,000 data sets with LX perturbed from its measured value randomly, within the range of this error-bar. We fixed the data points from Page et al. (2003) at their original values. We performed the Spearman’s correlation test between Γ and 2–10 keV luminosity on the simulated data sets and found that the Γ–LX correlation in each simulated data set is at least significant at the 98.6% confidence level for 10,000 simulations and 9,888 of them have Γ–LX correlations significant at the greater than 99.5% confidence level. Therefore, it is unlikely that this correlation is driven by the uncertainties in the magnification factors. Possible errors in magnification factors, the small number of quasars in the present sample combined with the medium S/N of several of the observations may have led to an unaccounted systematic effect. Additional observations of z ∼ 2 lensed quasars with better S/N and a more detailed modeling of all the lenses in our sample will help confirm this result. Although the Γ–LX correlation found in this paper could be a result of selection effect, we discuss possible interpretations of this correlation below. Previous studies did not find any correlation between Γ and LX in low-redshift quasars and Seyfert 1s. Recently, several X-ray monitoring programs of Seyfert galaxies have indicated a correlation between X-ray spectral index and 2–10 keV X-ray flux (Chiang et al. 2000; Petrucci et al. 2000; Vaughan & Edelson 2001). The spectra of these Seyfert galaxies steepen as the X-ray flux increases. Vaughan & Edelson (2001) suggested that variations of several properties of the X-ray emitting corona (e.g., electron temperature, optical depth, size) with the X-ray flux may explain this Γ vs. X-ray- flux relation. Similarly, a Γ vs. X-ray-flux relation also exists in some Seyfert 2 and radio-loud objects (Georgantopoulos & Papadakis 2001; Zdziarski & Grandi 2001; Gliozzi, Sambruna, & Eracleous 2003). These observations indicate that although the Γ–LX relation does not apply to a sample of low-redshift quasars and Seyferts, this relation applies to individual objects. In contrast to the low-redshift quasars, the Γ– LX dependence found at high redshift, especially in high-redshift and low-LX quasars indicates that these quasars may represent a distinct sub-population of quasars. It is possible that the properties of the X-ray emitting coronae of the high-redshift quasars are more homogeneous than those in the low-redshift quasars.

2.6.2 Possible Interpretations of the Correlation Between the X-Ray Lumi- nosity and Spectral Index We explore two possible interpretations of the correlation between the spectral index and the X-ray luminosity in the context of the model of Haardt & Maraschi (1993) and Haardt, Maraschi, & Ghisellini (1994). Our first hypothesis is that there is a narrow 20 range (of order a few) of accreting black hole masses at high redshift while the observed range of observed X-ray luminosities (spanning aproximately two orders of magnitude) is caused by a large range in the accretion rate, i.e., a wide range of Eddington ratios (the ratio of the accretion rate to the Eddington rate). Our second hypothesis is that the opposite is true, namely that the range of accreting black hole masses at high redshift is large (spanning approximately two orders of magnitude), while the Eddington rate is fairly constant and close to unity (i.e., the accretion rate is always fairly close to the Eddington limit, regardless of the mass). In the model of Haardt & Maraschi (1993) and Haardt, Maraschi, & Ghisellini (1994) the inner accretion disk is sandwiched by a hot, tenuous, possibly patchy corona which emits the hard X-ray photons. The corona cools by inverse Compton scattering of soft photons (E ∼< 100 eV) from the underlying disk, which results in the hard X- ray photons that we observe. Haardt, Maraschi, & Ghisellini (1997) explored how the model predictions change for a wide range of the system parameters, namely the optical depth and temperature of the corona and the temperature of the (assumed) black-body spectrum of seed photons. In particular, Haardt, Maraschi, & Ghisellini (1997) found that the 2–10 keV spectral index is nearly proportional to the optical depth in the hot corona and also decreases as the temperature of seed soft-photon spectrum increases. Moreover, in the case of a “compact” corona, i.e., one in which pair production is high enough that the Compton scattering optical depth is dominated by electron-positron pairs, the 2–10 keV spectral index is nearly proportional to the log of the 2–10 keV luminosity, just as we have found observationally. In our first hypothesis the observed range of luminosities is set by the range of accretion rates, with the black hole mass being nearly constant. In this context the observed correlation might be explained if the optical depth in the hot corona is somehow related to the accretion rate; for example, the density of the corona could increase with accretion rate and so would the optical depth. There is a competing effect, however: as the accretion rate decreases so does the temperature of the underlying thin disk, which provides the seed photons, with the result that the spectral index of the emerging X-ray spectrum increases. In our second hypothesis, the accretion rate for all objects is very close to the Eddington limit, while the observed range in luminosity is set by a range in black hole masses. In the context of this hypothesis, and under the assumption that the optical depth of the corona is dominated by electron-positron pairs, Haardt, Maraschi, & Ghis- ellini (1997) predict a correlation between the 2–10 keV spectral index and luminosity just like the one we observe. The optical depth in this case depends only on the “com- 4 2 pactness” of the corona, which can be expressed as `c ∼ 10 (h/r )(LX /LEdd) (Haardt & Maraschi 1993), where LX /LEdd is the ratio of the X-ray luminosity to the Eddington luminosity (roughly proportional to the Eddington ratio) and h and r are the vertical and radial extent of the corona in units of the Schwartzschild radius. Thus, in this sce- nario, the spectral index could increase if the compactness of the corona increases with black hole mass (See equation 16 of Haardt & Maraschi (1993)), with the consequence that the emerging 2-10 keV luminosity increases as well. Moreover, as the optical depth reaches unity, the spectral index reaches its maximum value and begins to decline for larger optical depths. This feature may explain the turnover that we observe in the 21 spectral index vs luminosity plot of Figure 2.4. We therefore favor this interpretation over the previous one. This interpretation is also appealing because it is consistent with the predictions of semi-analytic models of Kauffmann & Haehnelt (2000) for the cosmological evolution of supermassive black holes and their fueling rates. In particular, these authors predict that at redshifts between 1.5 and 3, the fueling rate of supermassive black holes in quasars are within a factor of a few of the Eddington limit, while their 7 9 masses span the range between 10 and 10 M .

2.6.3 The Optical-to-X-Ray Index, αox Vignali, Brandt, & Schneider (2003); Vignali et al. (2003a,b) found that the optical-to-X-ray index, αox, of radio-quiet quasars is mainly dependent on the rest- frame ultra-violet luminosity such that quasars with higher ultra-violet luminosities have steeper αox values (see Figure 5). They also do not detect a significant redshift dependence of αox in their analysis, however, Bechtold et al. (2003) found that αox depends primarily on redshift (αox steepens with increasing redshift) and weakly on luminosity. We compare the average αox, −1.70 (−1.66 without HE 2149−2745), of our sample with the average αox, −1.71, of Vignali et al. (2003b), and the αox values are consistent within the observed r.m.s. dispersion. The redshift range of our quasars is 1.7 < z < 4, lower than the sample of z > 4 quasars studied in Vignali et al. (2003b). However, the consistency between the αox values from the lensed sample in this paper and the sample of z > 4 quasars studied in Vignali et al. (2003b) does not rule out a possible small evolution of αox with redshift due to our small sample size. We plotted the αox values from our lensed sample against their redshift and rest-frame 2500A˚ luminosity density in Figure 2.5(a) and (b), respectively. We performed the Spearman’s rank correlation test between αox and z and between αox and L , but found no significant correla- 2500 A˚ tion in either case. Considering the large dispersion of the αox values from the best fit αox–L relation of Vignali, Brandt, & Schneider (2003), it is not surprising that 2500A˚ no significant correlation is found in our data set because of the small sample size. We over-plotted our αox data on the αox–L relation of Vignali, Brandt, & Schneider 2500A˚ (2003) with a dispersion of 0.25 as indicated by the shaded region in Figure 2.5(b), and found that most of our data are consistent with the αox–L relation except one BAL 2500A˚ QSO data point. We also searched for possible correlations between the αox values and other properties of the quasars such as Γ and LX . The correlation results were strongly biased by the −2.1 αox value of HE 2149−2745. When we removed this data point, no significant correlation was detected.

2.6.4 Short Time Scale Variability We used the upper limits of the excess variance obtained from light-curves of bin size 1000 seconds when comparing with results for local Seyferts and other high redshift quasars. This bin size corresponds to rest-frame time scales ranging from 200 to 370 s for the quasars in our sample and is similar to the time scales used in other short time scale variability studies in Seyfert galaxies and quasars (e.g. Turner et al. 1999). We plotted 22 the excess variances of the high redshift lensed quasar sample together with the variances for Seyfert 1s (Nandra et al. 1997), NLS1s (Leighly 1999), LLAGN (Ptak et al. 1998), and high redshift (z > 2) quasars (Manners, Almaini, & Lawrence 2002) in Figure 2.6. We fitted the Seyfert 1 points with a power law and fixed the power-law index to the same value reported in Nandra et al. (1997), allowing only the normalization parameter to be free. The power-law relation is shown as a solid line in Figure 2.6. All of the upper limits of the excess variances for the high redshift lensed quasars of this paper 2 are consistent with the Seyfert 1 σrms–LX correlation. When we compare the upper limits with the NLS1s data, three of the upper limits of our sample are located below 2 the σrms–LX relation for NLS1s, which have about an order of magnitude larger excess variance than the Seyfert 1s. The consistency between the excess variance upper limits of 2 our lensed sample and the Seyfert 1s σrms–LX relation does not contradict the possible upturn in the value of the variability of z > 2 quasars for quasars with luminosities of about 1046erg s−1 as presented by Manners, Almaini, & Lawrence (2002). Most of the quasars in our sample have redshifts greater than 2, but the luminosity range of our sample is below the luminosity range of Manners, Almaini, & Lawrence (2002). The excess variance analysis that we discuss in this paper probes the shortest time-scale variability of radio-quiet quasars. There are two main interpretations that have been presented in previous studies to explain the excess variance and luminosity relation. (e.g., Nandra et al. 1997; Manners, Almaini, & Lawrence 2002). First, the more luminous sources may be physically large and lack the short time-scale variability. Second, the more luminous sources may contain more independently flaring regions and these flares contribute less to the total flux for the more luminous sources compared with the low luminous sources. There are several rapid flares observed in our light-curve sample, in particular, such flares were detected in RX J0911.4+0551, Q 2237+0305, and PG 1115+080 (Chartas et al. 2001; Dai et al. 2003, 2004b). We performed the Kolmogorov-Smirnov test to the light-curves of the individual images of the systems, RX J0911.4+0551, Q 2237+0305, and PG 1115+080, and found the light-curves are variable at the 99.8%, 97%, and 99.6% confidence levels, respectively. These observations support the second explanation where there are also flares in the high luminosity quasars, however, due to the quasar’s high luminosity, flares contribute less to the total luminosity and thus luminous quasars have smaller excess variances.

2.7 Conclusions

We presented results from a mini-survey of relatively high redshift (1.7 < z < 4) gravitationally lensed radio-quiet quasars observed with the Chandra X-ray Observatory and XMM-Newton. We demonstrated how gravitational lensing can be used to study high-redshift quasars. Our main conclusions are as follows:

1. We ﬁnd a possible correlation between the spectral slope and X-ray luminosity of the gravitationally lensed quasar sample. The X-ray spectral slope steepens as the X-ray luminosity increases. The limited number of quasars in the present sample combined with the medium S/N of several of the observations and the systematic uncertainties from the lensing magniﬁcation modeling may have led to 23

an unaccounted systematic effect. Additional observations of z ∼ 2 lensed quasars with better S/N and more detailed modeling of all the lenses in our sample will allow us to confirm this result. Such a correlation is not observed in nearby z < 0.1 quasars suggesting that quasars at redshifts near the peak of their number density may have different accretion properties than low redshift quasars. When we combined the data from other samples of radio-quiet quasars selecting quasars with redshift (z > 1.5) together with the present lensed sample, the correlation is still significant, especially in the low X-ray luminosity range between 1043−45.5 erg s−1. If this correlation is confirmed by future studies, it could provide significant information on the emission mechanism and evolution of quasars. We suggest that this correlation can be understood if we hypothesize that the quasars in our sample are fueled at rates near their Eddington limit (consistent with recent models for quasar evolution) and that the optical depth of their X-ray emitting coronae increases with black hole mass.

2. We did not ﬁnd a strong correlation between the optical-to-X-ray spectral index, αox, on either redshift or on UV luminosity in our small sample. However, most of our data points are consistent with the αox–L correlation of Vignali, Brandt, 2500A˚ & Schneider (2003).

3. Our estimated upper limits of X-ray variability of the relatively high redshift lensed quasars sample is consistent with the known correlation observed in Seyfert 1s.

Acknowledgements: We thank Steinn Sigurdsson and the anonymous referee for very helpful comments and discussions. We acknowledge the ﬁnancial support by NASA grant NAS 8-01128. 24 ation · · · · · · · · · · · · · · · · osure 60 16 · · · · · · · · 100 (ks) Exp Observ · · · · · · · · · · · · · · · · · · · · · · · · Date XMM-Newton 2002-04-28 2001-11-25 2001-11-02 ation · · · · · · · · · · · · · · osure 10 90 10 10 · · · · · · · (ks) Observ Exp a Quasars Chandr · · · · · · · · · · · · · · · · · · · · · Date Second 2001-12-08 2002-02-24 2000-11-03 2000-10-29 Radio-Quiet ation Lensed osure 10 40 20 30 49 15 10 10 10 26 30 (ks) Exp Observ a vitational Chandr Gra Date of First 2003-03-02 2000-04-19 2002-12-18 2000-09-06 2000-06-10 2000-10-14 2003-01-01 2000-11-18 2000-10-11 2000-06-02 1999-11-03 a ) H 2 − N (1990). Sample cm 1.7 1.8 3.4 5.5 4.6 2.3 3.8 2.3 3.9 3.5 3.7 20 The Galactic kman (10 c Lo 2.1. & · · · · · · · · · · · · ey · · · · · · k BAL BAL BAL BAL? able mini-BAL mini-BAL T Dic on based Redshift 2.55 3.80 3.115 1.695 2.033 2.303 2.162 1.72 2.74 3.911 2.80 is H N 0252 − 2745 1805 2130 − − − 1009 Galactic 08279+5255 Quasars J0911.4+0551 1115+080 2149 1104 0230 0818+1227 2237+0305 1208+101 1413+117 The a HE H Q Q PG LBQS HE RX APM HS HE . c ) ed ely The dels, /ν · 2 · · χ mo 0.12 0.34 0.60 0.33 0.55 0.63 0.47 0.95 0.14 0.07 0.15 (

25 ectiv observ P filter. resp The CIS ) A ν bin, ( absorption 2 ν · er · χ the el. p · 0.86(235) 0.90(22) 1.13(153) 1.15(200) 1.09(39) 1.12(168) 0.97(82) 1.57(9) 1.13(6) 0.86(19) 0.99(26) lev ts luminosites. en from ev ed) redshifted ) 1 100 − 13 13 13 13 13 14 13 13 13 14 13 13 and s confidence observ − − − − − − − − − − − − 2 and calculating tamination 10 10 10 10 10 10 10 10 10 10 10 10 eV − k 68% 15 × × × × × × × × × × × × con cm 7 3 6 3 3 0 0 8 0 1 0 1 feature, ...... when the 4 1 4 5 2 2 5 1 1 7 1 1 with the (erg ed (0.4–8 at b v X are f erties Quasars remo binned correct absorption to are are Prop errors or eV) ) k ts 46 45 45 45 45 44 46 45 45 45 45 45 1 del ed ed − 10 10 10 10 10 10 10 10 10 10 10 10 s ectra mo × × × × × × × × × × × × onen (2–10 sp 7 4 9 5 5 6 3 0 6 8 5 6 deriv ...... (erg emission 3 4 5 6 4 2 4 4 3 6 4 2 Radio-quiet Observ X all comp L CISABS and A eV) Lensed ) Gaussian eV, k 46 45 45 45 45 44 46 45 45 46 45 44 1 k tain − 10 10 10 10 10 10 10 10 10 10 10 10 XMM-Newton absorption s con × × × × × × × × × × × × 5 9 5 1 7 1 3 4 5 4 0 0 (0.2–2 0.4–8 and ...... (erg 3 2 6 8 5 1 5 4 4 1 4 9 a arious X redshifted v ectra L vitational sp er, ranges The a Gra 08279+5255. Chandr 04 04 10 08 07 06 03 03 08 02 05 02 06 04 09 10 ...... 6 3 2 2 1 2 3 3 0 0 0 0 0 0 0 0 ...... of 0 0 0 0 Γ absorb +0 − +0 − +0 − +0 − +0 +0 − − +0 − +0 − energy +0 − +0 − +0 − +0 − 08279+5255. Chandr 4 59 93 86 3 9 78 94 8 31 92 90 APM Other ...... quasar. freedom. 1 1 1 1 2 1 1 1 1 1 1 1 ed of all ectra of the ionized APM sp of and of observ w, ectrum. ectrum the sp degrees the abs, erla sp ν w to w w a o o ectrum p S/N w+zgau) w+zgau) for w w w w w+zgau) del rest-frame del magnification. o o t sp o o o o o w 2 Fits within p p p p w+zgau+zgau) w+zgau+zgau) w+zgau+zgau) a w+zgau lo abs*p χ Mo mo o o o the o p zw in ab*(p abs*(p abs*(p this lensing represen 2.2. zw en zw zw Chandr XMM-Newton erformed the giv p absori*(p absori*(p absori*(p dels exceeding the the fitting able absorption for are of T ere mo to to w y when abs ond ond fits zw Galactic 3.911 2.033 3.911 Redshift 2.55 3.8 3.115 1.695 2.162 2.303 1.72 2.8 2.74 corrected used d e bandpasses and probabilit is ectral corresp tain corresp een y sp b f the con zgau, is not The . results ) results dels statistic e v ely /ν — fit 1009-0252 luminosit fit C 08279+5255 08279+5255 2 mo ha Quasars χ J0911+0551 1115+080 absori, 2149-2745 0230-2130 1104-1805 0818+1227 ( ectiv 2237+0305 1208+101 1413+117 The The All P The The w, Note. d b a c e f APM HS Q PG APM HE HE LBQS HE H Q RX o alues p resp v 26

Table 2.3. αox Values of Gravitationally Lensed Quasars in the Sample

Optical a b c d Quasars Information f l f α 2500A˚ 2500A˚ 2keV ox HE 0230-2130 CASTLES 0.37 0.07 1.2 11. 1. −1.35 0.04 HS 0818+1227 CASTLES 1.9 0.4 8.4 9. 1. −1.65 0.05 e APM 08279+5255 E00 2.59 0.07 13. 5.4 0.4 −1.80 0.01 RX J0911+0551 CASTLES 1.2 0.2 4.9 2.3 0.3 −1.81 0.04 LBQS 1009-0252 CASTLES 3.7 0.7 15. 32. 6. −1.56 0.05 HE 1104-1805 CASTLES 3.0 0.6 10. 11.0 0.6 −1.70 0.03 f PG 1115+080 C87 1.7 0.1 4.4 11.9 0.4 −1.59 0.01 Q 1208+101 CASTLES 11. 2. 54. 60. 20. −1.62 0.06 H 1413+117 CASTLES 1.6 0.3 6.1 5. 3. −1.7 0.1 HE 2149-2745 CASTLES 7. 1. 22. 2. 1. −2.1 0.1 Q 2237+0305 OGLE 8.0 1. 22. 16. 1. −1.81 0.02

a The programs or papers where we obtained the optical magnitudes used in the αox calculation. b −27 −2 −1 −1 Rest-frame 2500 A˚ flux density, in units of 10 ergs cm s Hz . c 30 −1 −1 Rest-frame 2500 A˚ luminosity density, in units of 10 ergs s Hz . d −32 −2 −1 −1 Rest-frame 2 keV flux density, in units of 10 ergs cm s Hz . e Egami et al. (2000). f Christian, Crabtree, & Waddell (1987). 27 the ) 1 eV) of k − s 10 erg – mass (2 44 X (10 2.5 3.0 2.0 3.7 L 4.4 21.7 3.3 0.78 1.5 2.6 10.4 luminous Sample ) 1 eV) the k the − s 2 for in – erg dels (0.2 44 mo X (10 . L 3.1 3.8 1.7 4.0 45.8 2.9 3.6 0.33 0.53 12.9 2.4 Quasars ely mass ectiv Lensed Sphere resp Magnification system, 26 15 23 16 Isothermal 3.1 10 12 3.4 Flux 17 3.5 142 the vitationally c of Gra Singular of · · · · · group del · · · · · y · · · · · SIE SIE SIE SIE SIE and Mo , y nearb JF+CUSP+SIS Cusp and (1998) , b e d a · · · · · Magnification Jaffe, · · · · · · · · · · S98 C99 B02 B02 B02 T02 Lewis galaxy (2002) (2002) are & Literature (1999) 2.4. the SIS of Ivison ebster, and able opmans & , urnshek W T part T Ko & & ainis 1009-0252 dark 08279+5255 CUSP Quasars , hmidt, J0911+0551 1115+080 1104-1805 2149-2745 0230-2130 0818+1227 reu 1208+101 2237+0305 1413+117 Barv T Sc Chae JF, e d a b c LBQS APM RX HE HS PG HE HE Q H Q galaxy 28

Table 2.5. Excess Variance of Gravitational Lensed Radio-quiet Quasars

2 2 2 σrms σrms σrms −2 −2 −2 (10 ) (10 ) (10 ) Quasars Bin Size = 500 s Bin Size = 1000 s Bin Size = 2000 s HE 0230-2130 −1.7 0.7 −0.5 0.5 −0.4 0.3 HS 0818+1227 0.1 2.2 −0.6 2.0 −0.3 0.8 APM 08279+5255 −0.5 0.3 −0.3 0.2 −0.1 0.1 RX J0911+0551 −3.1 2.3 −0.7 2.3 0.9 2.9 LBQS 1009-0252 −0.5 2.6 −3.1 0.8 −1.4 0.9 HE 1104-1805 1.9 1.1 1.1 0.8 1.0 0.8 PG 1115+080 −0.2 0.5 −0.2 0.3 0.1 0.3 Q 1208+101 −6.1 1.5 −2.7 0.9 −1.2 0.8 H 1413+117 −2.4 3.5 −3.0 2.5 0.0 2.3 Q 2237+0305 −0.6 0.3 −0.3 0.1 0.0 0.2 29

Table 2.6. Excess Variance of Quasars Observed with XMM

2 2 2 2 σrms σrms σrms σrms −2 −2 −2 −2 (10 ) (10 ) (10 ) (10 ) Quasars Bin Size = 500 s Bin Size = 1000 s Bin Size = 2000 s Bin Size = 3000 s APM 08279+5255 0.4 0.2 0.1 0.2 0.1 0.2 0.1 0.1 RX J0911+0551 4.8 1.5 3.2 1.5 1.4 1.0 −0.1 0.4 PG 1115+080 0.2 0.2 0.1 0.2 0.0 0.1 −0.11 0.03 30

HE 0230−2130 HS 0818+1227

APM 08279+5255 APM 08279+5255 (XMM)

RX J0911.4+0551 LBQS 1009−0252

Fig. 2.1 Spectra of gravitationally lensed radio-quiet quasars observed with Chandra, except for the spectra of APM 08279+5255 and PG 1115+080 that were observed with XMM-Newton. (Part I) 31

HE 1104−1805 PG 1115+080 (XMM)

Q 1208+101 H 1413+117

Q 2237+0305

HE 2149−2745

Fig. 1. (continued) 32

HE 0230−2130 HS 0818+1127

RX J0911.4+0551

APM 08279+5255

Counts per Bin LBQS 1009−0252 HE 1104−1805

PG 1115+080 Q 1208+101

H 1413+117

Q 2237+0305

Time (1000 s ; observed frame)

Fig. 2.2 Light-curves of gravitationally lensed radio-quiet quasars observed with Chandra. The light-curves are binned with a bin size of 1000 s in the observed-frame. 33

(a) (b)

Fig. 2.3 Plots of (a) X-ray Luminosity vs. redshift. The squares represent 0.2–2 keV luminosities and crosses represent 2–10 keV luminosities. (b)X-ray photon index vs. redshift. (c) X-ray photon index vs. 0.2–2 keV luminosity. (d) X-ray photon index vs. 2–10 keV luminosity. 34

Fig. 2.4 Γ–LX (2–10 keV rest-frame) diagram for high redshift quasars (z > 1.5). The data shown as ﬁlled triangles are from Page et al. (2003). The data shown as ﬁlled circles are from Reeves & Turner (2000). The data shown as crosses are from George et al. (2000). The data shown as open circles are from Vignali et al. (1999). The data shown as open squares are from our own sample of lensed quasars. 35

(a)

(b)

Fig. 2.5 Plots of αox vs. redshift and UV luminosity. The crosses represent BAL QSOs and squares represent non-BAL quasars for all of the plots in this figure. (a) αox vs. redshift. (b) αox vs. rest-frame 2500A˚ luminosity. The solid line represents the best fit αox–L relation obtained from Vignali, Brandt, & Schneider (2003), and the shaded 2500A˚ region represents a dispersion of 0.25 from the best fit line. 36

Fig. 2.6 Excess variance in the 0.2–10 keV band vs. 2–10 keV luminosity. The data points representing the Seyfert 1s shown as filled triangles were obtained from Nandra et al. (1997) and are fitted with a power law (solid line). The ASCA SIS light-curves of the Seyfert 1s were binned in 128 s bins. The data points for the NLS1s shown as open circles were obtained from Leighly (1999). The ASCA SIS light-curves of the NLS1s were binned in 128 s bins. The data points for the LINERS and LLAGNs shown as squares were obtained from Ptak et al. (1998). The data points shown as filled stars were obtained from z > 2 quasars of Manners, Almaini, & Lawrence (2002). The downward arrows represent upper limits for the excess variance of the gravitationally lensed quasars from the present sample. 37

Chapter 3

Chandra Observations of Q 2237+0305

3.1 Introduction

Q 2237+0305 was1 discovered by Huchra et al. (1985) as part of the Center for Astrophysics galaxy redshift survey. Four images have been resolved (Schneider et al. 1988; Yee 1988) from this lens system. The quasar is at a redshift of zs = 1.695 and the lensing galaxy is at a redshift of zl = 0.0395. Microlensing induced by stars in the lens galaxy was proposed for this system shortly after its discovery (Kayser, Refsdal, & Stabell 1986; Kent & Falco 1988; Schneider et al. 1988; Kayser & Refsdal 1989), and was first confirmed by Irwin et al. (1989). Microlensing in Q 2237+0305 has been firmly established with extensive monitoring of this system over several years (Racine 1992; Østensen et al. 1996; Wo´zniak et al. 2000a,b). The presence of both macrolensing and microlensing in the Einstein Cross and the proximity of the lensing galaxy, an order of magnitude closer than other lensing galaxies, make it a unique laboratory to explore the structure of the different emission regions in the source quasar, and the properties of the lensing galaxy as well. During the past decades, major progress has been made in understanding the physical processes associated with Active Galactic Nuclei (AGN); however, it is beyond the capabilities of current telescopes to resolve directly the central parts of AGNs. Ob- servations of quasar microlensing events provide a means of exploring the structure of AGNs. Multi-wavelength studies of Q 2237+0305 (Falco et al. 1996; Mediavilla et al. 1998; Agol, Jones, & Blaes 2000) demonstrate that the flux ratios of the images are different in different bands, in particular, between the radio, C iii], mid-infrared, and optical. The differences of flux ratios in different wavelength bands have been interpreted as the result of microlensing. Emission regions with a size significantly less than the Einstein radius of the microlens in the source plane will be significantly magnified, whereas, emission regions with a size significantly larger than the Einstein radius will not be affected by microlensing. Studies of Q 2237+0305 indicate that the radio and mid-infrared emission regions are larger than the Einstein radius, whereas, the optical emission regions are smaller than the Einstein radius. The C iii] emission regions also extend beyond the Einstein radius but are less extended than the radio and mid-infrared regions. The analysis of light-curves of microlensing events can also constrain the source size of individual emission regions, especially in a high magnification event (HME) that may occur during a caustic crossing. Yonehara (2001) analyzed the light-curves of Q 2237+0305

1The work in this chapter has been previously published in Dai, X., Chartas, G., Agol, E., Bautz, M. W., & Garmire, G. P. (2003) Chandra Observations of Q 2237+0305. Astrophysical Journal 589:100 38 and estimated a source size of less than 2000 AU for the optical emission region in Q 2237+0305. It is desirable to study the X-ray emission of a microlensed quasar since the X-rays are thought to originate from the innermost region of the accretion disc. The X-ray light-curves of the images and the profile of the Fe Kα line during a microlensing event, especially from a HME, could constrain the X-ray emission region and possibly yield information about the mass and spin of the central black hole (Yonehara et al. 1998; Agol & Krolik 1999; Popović et al. 2002). Recently, a microlensing event in X- rays was observed by Chartas et al. (2002a) in MG J0414+0534, where an enhancement of the equivalent width of the Fe Kα line was observed in only one of the images. As mentioned earlier the proximity of the lensing galaxy of 2237+0305 has fa- cilitated its detailed study in several wave bands. In particular, Yee (1988) detected a g − i color difference between different image components which indicates differential extinction. The extinction curve for the lensing galaxy was measured by Nadeau et al. (1991). Foltz et al. (1992) measured the central velocity dispersion of the barred spiral galaxy 2237+0305 to be 215 30 km s−1. Modeling of the lens system has also provided estimates of the mass distributions of the lensing galaxy. In particular, Schmidt, Web- ster, & Lewis (1998) studied the contribution of the galaxy bar to the lens potential and 8 found a bar mass of about 7.5 × 10 M . Q 2237+0305 was first detected in X-rays with ROSAT by Wambsganss et al. (1999); however, due to the low spatial resolution of ROSAT, the individual images were not resolved. To obtain spatially resolved X-ray spectra from the individual images we performed Chandra observations of Q 2237+0305. Here, we present the results of these −1 −1 observations. We use H0 = 65 km s Mpc , Ωm = 0.3, and ΩΛ = 0.7, unless mentioned otherwise.

3.2 Observations and Data Reduction

Q 2237+0305 was observed with ACIS (Garmire et al. 2003) onboard the Chandra X-ray Observatory for ∼ 30.3 ks and ∼ 9.5 ks on 2000 September 6, and 2001 December 8, respectively. The data were taken continuously with no interruptions within each observation. Q 2237+0305 was placed at the aim point of the ACIS-S array which is on the back-illuminated S3 chip. The data were reduced with the CIAO 2.2 software tools provided by the Chandra X-ray Center (CXC). We improved the image quality of the data by removing the pixel randomization applied to the event positions in the CXC processing and by applying a subpixel resolution technique (Tsunemi et al. 2001; Mori et al. 2001). In the first and second observations of Q 2237+0305 we detected background flares with durations of ∼ 10 ks and ∼ 0.2 ks, respectively. We did not remove events collected during the background flares in either of the two observations because even at the peak of the flares, the background only contributes about 0.3% and 1% of the counts of Q 2237+0305 for the first and second observation, respectively. In the data analysis, only events with standard ASCA grades of 0, 2, 3, 4, and 6 were used. 39

3.3 Photometry and Astrometry

Totals of 2632 and 607 source events were detected from circles centered on the centroids of the sources with radii of 300 and within the 0.2-10 keV energy band during the first and second observations of Q 2237+0305, respectively. We applied a point spread function (PSF) fitting method to estimate the X-ray count rates of individual images due to the closeness of the individual images. We modeled the Chandra images of A, B , C and D with PSFs generated by the simulation tool MARX (Wise et al. 1997). The X-ray event locations were binned with a bin-size of 000.0246. The simulated PSFs were fitted to the Chandra data by minimizing the Cash C (Cash 1979) statistic formed between the observed and simulated images of Q 2237+0305. The relative positions of the images were fixed to the observed HST values obtained by the CfA- Arizona Space Telescope LEns Survey (CASTLES). The CASTLES website is located at http://cfa-www.harvard.edu/glensdata/. The total count rate and count rates of individual images for each observation are listed in Table 3.1. The total count rate of all images for the second observation dropped by (27 4)% compared to the first observation. The count rate ratios of images B and D with respect to image A are consistent within 1σ errors between the two observations, and the ratio of C/A has decreased by (16 11)% in the second observation compared to the first observation. The image of Q 2237+0305 obtained by combining the two Chandra observations is shown in Figure 3.1a. The image is binned with a binsize of 000.05 and smoothed with a Gaussian with σ = 000.05. Images B and C of Q 2237+0305 are clearly resolved in Figure 3.1a. Images A and D are not well resolved, but since image A is the brightest image, it is less contaminated by image D. Moreover, the raw binned image of D seems to have two concentrations of photons separated by about 000.3. The Lucy-Richardson deconvolution technique (Richardson 1972; Lucy 1974) was applied to the combined image in order to resolve the four images. We binned the X-ray events with binsizes of 000.1 and 000.05 for the deconvolution. The deconvolved images are shown in Figures 3.1b and 3.1c. In Figure 3.1b (image binsizes of 000.1), a total of four images are resolved, which is consistent with previous observations in other wave bands, while in Figure 3.1c (image binsizes of 000.05), five images in total are resolved. The relative X-ray positions of the different images with respect to image A are obtained from the centroids of the deconvolved images. X-ray image positions are listed in Table 3.2 together with the HST positions obtained by CASTLES. The relative positions of images B and C with respect to A as measured with the deconvolution using a 000.1 binsize are consistent with the HST positions to 000.03. The separations between image D and the remaining images, A, B, and C as measured with the deconvolution using a 000.1 binsize differ from those measured in the optical by 000.09, 000.06, and 000.07, respectively. The expected observational uncertainties of the image positions are σ = α/ S/N, where α is the spatial resolution of ACIS and S/N is the signal-to-noise ratio of the image. By p accounting for the contamination of image D by image A , we estimate the uncertainty in the position of image D to be about 000.1. Thus, the discrepancy between the optical and X-ray positions of image D relative to image A is about 1σ. 40

3.4 Spectral Analysis

Spectral analysis was carried out with the software tool XSPEC V11.2 (Arnaud 1996). The total spectrum of all images of Q 2237+0305 was extracted from a circle of 300 radius centered on the centroid of the images. The spectra of images A, B, and C were extracted from circles of 100 radii centered on the images, and the spectrum of image D was extracted from a circle of 0.600 radius centered between D1 and D2 in order to avoid the contamination from the brightest image A. The background was extracted from an annulus centered on the centroid of the images with inner and outer radii of 500 and 3000, respectively. All spectra were fitted in the 0.4–8 keV energy range assuming 20 −2 Galactic absorption of NH = 5.5 × 10 cm (Dickey & Lockman 1990). We have applied a correction to the ancillary response files to account for the use of relatively small extraction regions. We determined the corrections to the ancillary response files by simulating the spectra of point sources at the locations of the images with and without the apertures used in our analysis. For our simulations we used XSPEC to generate the source spectra and the ray-tracing tool MARX to model the dependence of photon scattering with energy. To account for the recently observed quantum efficiency decay of ACIS, possibly caused by molecular contamination of the ACIS filters, we have applied a time-dependent correction to the ACIS quantum efficiency implemented in the XSPEC model ACISABS1.1. ACISABS is an XSPEC model contributed to the Chandra users software exchange web-site http://asc.harvard.edu/cgi-gen/cont-soft/soft-list.cgi. The ACIS quantum efficiency decay is insignificant for energies above 1 keV and does not affect the main results of our analysis.

3.4.1 Simple Absorbed Power-law Models We began by fitting the spectra of the individual images and the spectrum of all images of Q 2237+0305 from each epoch with a simple power law modified by Galactic absorption and neutral absorption placed at the redshift of the lens (z = 0.0395). To obtain tighter constraints on the model parameters we fitted the spectra from both epochs simultaneously. In the case of the simultaneous fits, the model parameters, Γ and NH were kept the same between observations, whereas, the normalization parameters were allowed to vary independently. We also followed a different approach of fitting the combined spectra from both epochs. In the case of the combined spectra we weighted the ancillary response files from each observation. The spectral fitting results are listed in Table 3.3. The simultaneous fits (fits 7-11 of Table 3) and the combined fits (fits 12-16 of Table 3) to the spectra of Q 2237+0305 yield consistent results. We will use the results from the combined spectra of both epochs in the remaining analysis since they provide slightly tighter constraints. The fit to the spectrum of all images for the combined +0.05 observations yields a photon index of Γ = 1.90−0.05 and a column density of NH = +0.01 22 −2 0.02−0.01 × 10 cm . The column density is relatively low compared to that detected in other galaxies. In Figure 3.2 we show the 68% confidence contours of NH versus photon indices for all images. Absorption from gas in the lensing galaxy is marginally detected (at the 68% confidence level) towards image C. For the lines of sight towards the remaining images we can only place upper limits on the neutral hydrogen column 41 densities from the lensing galaxy. In Table 3.3 we also list the 0.4–8 keV X-ray fluxes for fits 1—6. The fluxes of individual images were normalized based on the PSF fitting results in section 3. The total 0.4–8 keV fluxes for the first and second observations +0.4 −13 −2 −1 +0.6 −13 −2 −1 of Q 2237+0305 are 4.6−0.2 × 10 erg cm s , and 3.7−0.5 × 10 erg cm s , and 0.4–8.0 keV lensed luminosities are 1.0 × 1046erg s−1, and 8.3 × 1045erg s−1, respectively. These luminosities have to be corrected by the lensing magnification in order to obtain the true luminosity of the quasar. The range of macro magnification was estimated from a few up to many hundred (Wambsganss & Paczynski´ 1994), and a recent model from +5 Schmidt, Webster, & Lewis (1998) estimated the magnification to be 16−4.

3.4.2 Features in the Spectrum of Image A Figure 3.3a shows the spectrum of image A combined from both observations of Q 2237+0305 overplotted with a simple absorbed power law model described in §3.4.1. The spectrum shows residuals in the 2–3 keV band, and the residuals are near the redshifted energy of the Fe Kα line. For a comparison in Figure 3.3b we show the combined spectrum of images B, C, and D for both observations overplotted with the best fit spectral model. In the combined spectrum of B, C, and D we detect residuals in the 2–3 keV band. However, these residuals are not as significant as those in image A and the peaks of the residuals differ between the two spectra. To model the residuals in image A we added a redshifted Gaussian line component to the absorbed power-law model and present the best fit parameters in Table 3.4. The line energy and width are free parameters during the fitting. Including a Gaussian emission line in our model for the spectrum of image A leads to a significant improvement in fit quality at the 99.99% confidence level (according to the F -test). The best-fit rest-frame energy, width, and equivalent width of the modeled emission line in the spectrum of image A are Eline +0.2 +0.30 +300 = 5.7−0.3 keV, σline = 0.87−0.15 keV, and EW = 1200−200 eV, respectively. We also modeled the combined spectrum of images B, C, and D with a redshifted Gaussian component. The improvement of the fit is significant at the 94% level based on the F -test. The rest-frame energy of the modeled Gaussian line of the combined spectrum +0.1 of images B, C, and D is Eline = 6.6−0.2 keV and its width is consistent with that of an unresolved line. Protassov et al. (2002) argued that the F-test cannot be applied to assess the significance of a line component in a spectral model because when the null values of the additional parameters (in our case these are the parameters of the Gaussian line) fall on the boundary of the allowable parameter space, the reference distribution does not follow a F-distribution in general. Protassov et al. (2002) proposed the method of posterior predictive p-value, a Monte-Carlo simulation approach, to calibrate the sample distribution of the F-statistic. We followed this approach to calibrate the sample distribution of the F-statistic for the case of the spectrum of image A combined from both observations of Q 2237+0305. The parameters of the null model (powerlaw with Galactic absorption and absorption at the lens) are well constrained from the spectrum of ∼ 1800 photons and the simple approach described in section 5.2 of Protassov et al. (2002) is used. We simulated 10,000 spectra with XSPEC from the null model with parameters fixed at their best fit value. Each simulated spectrum, was binned in the 42 same way as real data and fitted with the null model and the alternative model (which included an additional line component). The F-statistic between null and the alternative model was calculated for each simulation. The results of the Monte-Carlo simulation are displayed in Figure 3.4. The maximum value of the F-statistic from the 10,000 simulated spectra is 7.28. Therefore, the F-statistic value of 7.74 obtained from the real spectrum of image A indicates that the null model (which does not include an emission line) is rejected at the > 99.99% confidence level. In addition, we also compared the Monte- Carlo simulated sample distribution with the analytical F-distribution in Figure 3.4. The two distributions are consistent with each other in this particular case.

3.5 Discussion

Our spatial analysis of the Chandra observations of Q 2237+0305 has resolved the four lensed images A, B, C, and D, with positions in good agreement with those obtained from HST observations of Q 2237+0305, however, both the raw and deconvolved Chandra data of Q 2237+0305 hint to the presence of a fifth image near image D. In section 3.5.1 we investigate plausible mechanisms that can explain the fifth image. The analysis of the individual spectra of the images of Q 2237+0305 indicates the presence of absorption from the lensing galaxy. In section 3.5.2 we compare the column densities obtained from our X-ray analysis with the column densities inferred from the g − i color changes of the images. This comparison is used to estimate the dust-to-gas ratio in the lensing galaxy. In section 3.5.3 we compare the optical and X-ray image flux ratios. An exciting finding of our spectral analysis was the identification of a broad emission line near the energy of the redshifted Fe Kα line in only image A. In section 3.4.2 we performed Monte Carlo simulations to show that the line in image A is significant at the 99.99% level. In section 3.5.4 we rule out possible instrumental effects that could mimic such a line and discuss possible origins of the broad Fe Kα line. We discuss the variability of the source in section 3.5.5

3.5.1 An Additional Image? The Chandra observations of Q 2237+0305 indicate an additional image when the data are binned with a binsize of less than 000.07 both in the raw image and in the deconvolved image. The total number of photons detected in both images D1 and D2 combining the two observations of Q 2237+0305 is ∼ 340, thus the apparent image splitting could be the result of poor photon statistics. The difference between the optical and X-ray positions of image D is larger than that measured in the other images. This large difference in image D may be the result of the significant contamination of this image by the brighter image A. Considering the 000.3 separation of D1 and D2, their X-ray fluxes, and the fact that the additional images only show up in the X-ray band, it would be extremely difficult to interpret this result, if the images D1 and D2 are real. Here we briefly investigate possible origins (other than the mentioned statistical interpretation) for the discrepancy between the optical and X-ray image configuration of Q 2237+0305. 43

(a) Spatially distinct X-ray flares in the source plane. X-rays are generated in the inner most region of the accretion disc. X-ray variability studies of quasars indicate that the size of the X-ray continuum emission region is of the order of ∼ 1 × 10−4 pc (e.g., Chartas et al. 2001). If we were to attribute the additional X-ray image to macrolensing or microlensing of two distinct X-ray flares the implied distance between flares would be about 2 kpc in the source plane, considerably larger than the expected size of the X-ray emitting region. The flares would also have to vary over time-scales shorter than the time-delay between the images since only one additional image is observed if we attribute it to macrolensing. (b) An additional X-ray source in the lens plane. The luminosity of the additional image would be ∼ 1041erg s−1 if the source producing the image were located in the lensing galaxy, and this is over two orders of magnitude brighter than the Eddington limit for X-ray binaries. This luminosity, however, lies at the upper end of the luminosity range (1039−41erg s−1, e.g., Roberts et al. 2002) of ultraluminous X-ray (ULX) sources. (c) An X-ray jet component extending from image A. This is unlikely based on VLA observations that indicate (Falco et al. 1996) Q 2237+0305 being a radio quiet quasar with no jet. (d) A source in our Galaxy. The X-ray luminosity of the additional image would be ∼ 1036erg s−1 if it were located in the Galaxy, and any object with such a large X-ray luminosity would have been detected by HST. (e) A fifth image produced by the lensing galaxy. In principle, a gravitational macrolens could generate an odd number of images if the lens potential is non-singular. But the anticipated position of the central image should lie within the central core of the lens potential and be greatly demagnified, which is not consistent with the Chandra observations of Q 2237+0305. (f) Microlensing by solar-mass stars in the central bulge of the lensing galaxy. The image separation produced by a microlens of mass M is given by the expression −3 1/2 α0 ≈ 3 × 10 M/M (DOL/kpc) arcsec (Schneider et al. 1992), where DOL is the angular diameter distance between observer and lens. The interpretation of the 000.3 image p splitting of image D as a microlensing event would require a microlens mass of at least 8 ∼ 10 M . The Einstein radius of the microlens at the source plane is proportional to the square-root of the mass of the microlens, specifically for this system, RE = 17 1/2 −1/2 1.1 × 10 (M/M ) h cm. The optical and radio images should also show this splitting if such a large “microlens” were present, unless the optical and radio emission regions are far more extended than the Einstein radius. This could possibly be true for the radio emission, but studies of microlensing of Q 2237+0305 showed that the optical emission region is within 1 pc of the accretion disc of the central engine (Yonehara 2001), which make the above interpretation highly improbable.

3.5.2 Absorption at the Lensing Galaxy In the appendix of Agol, Jones, & Blaes (2000), the extinctions for the images of Q 2237+0305 were estimated based on the g − i color changes between the images 44

(Yee 1988), and the correlation between the g − i color change and the lens galaxy surface brightness (Racine 1991). The hydrogen column densities can be inferred from the extinction by assuming an extinction law of R = 3.1 0.9 from the Milky Way and 21 −1 −2 employing a dust-to-gas ratio of NH= 5.9 × 10 EB−V mag cm (Bohlin, Savage, & Drake 1978). A comparison between NH obtained from our spectral fits to the Chan- dra data of Q 2237+0305 and the inferred values from the extinctions is presented in Table 3.5. The comparison shows that the column densities inferred from the extinction values are systematically larger than the column densities obtained from our X-ray analysis by about 2.1σ, 2.5σ, 2.6σ, and 2.7σ for images C, B, A, and D, respectively. The ratio of the column densities obtained from our X-ray analysis to those inferred from the extinction values are about 20%, 13%, 6%, and 5% for image C, B, A, and D, respectively. The estimated large value for NH inferred from the extinction measurements could arise from a problem with one of our two assumptions; the extinction law and the gas-to-dust ratio taken to be that of the Milky Way. The extinction law of the lensing galaxy 2237+0305 has been measured by Nadeau et al. (1991) assuming A(K)/A(V ) = 0.11, where A(K) and A(V) are the extinctions in the K band and V band, respectively. They find that the resulting extinction law in Q 2237+0305 is in good agreement with that of the Milky Way. Thus, we are left with the possibility that the dust-to-gas ratio of the lensing galaxy 2237+0305 is significantly larger than that of the Milky Way. It is also possible that gas may be ionized because it is in the central bulge of the galaxy. The dust-to-gas ratios for several gravitational lenses are discussed by Falco et al. (1999). They found that the dust-to-gas ratios are small for the systems B0218+357 and PKS 1830-211, which is opposite to what we observed in Q 2237+0305.

3.5.3 Image Flux Ratios It is well established from optical monitoring that Q 2237+0305 is being microlensed as mentioned in the introduction section. We compared the X-ray flux ratios of Q 2237+0305 with the optical V band flux ratios from the Optical Gravitational Lensing Experiment (OGLE) monitoring data obtained only four days prior to our first observation. An optical flux close to our second observation was not available. The OGLE website is at http://bulge.princeton.edu/~ogle. The extinction for the optical data is corrected based on the method described in the appendix of Agol, Jones, & Blaes (2000). To compute the X-ray flux ratios we used the 2–8 keV band to avoid the complication of absorption which may affect the soft energy band to a greater degree. The results from this comparison are presented in Table 3.6. The X-ray and optical V band flux ratios of images B, C, and D relative to image A are consistent. Since the optical fluxes are influenced by microlensing the agreement between X-ray and optical V band flux ratios implies that the X-ray fluxes are also magnified by microlensing. We also listed the 2–8 keV flux ratios, with larger error bars though, for the second observation in Table 3.6.

3.5.4 Broad Fe Kα Line Our spectral analysis indicates the presence of significant residuals between energies of 2–3 keV in image A. This energy region is near the energy of the red-shifted Fe Kα 45 line. Unfortunately, these residuals fall near a sudden change of the HRMA/ACIS effective area caused by the iridium M absorption edges of the Chandra mirrors. To ascertain any systematic calibration uncertainties near the mirror edge we have fitted the spectra of several test-sources2 with expected smooth power-law spectra near the 2 keV iridium edge. Since χ2 residuals depend on the statistics, we filtered the test-source data in time to produce spectra with a total number of counts equal to that observed in the second observation of Q 2237+0305. Typical residuals for these test-sources near the mirror edge are less than ∼ 1σ indicating that the observed consecutive 2σ residuals near 2 keV in the spectrum of image A are real and not due to systematic errors in the calibration of the effective area of the Chandra mirrors. We also note that the residuals are more significant in image A (at the 99.99% confidence level) than the combined spectrum of images B, C, and D (at the 94% confidence level). Furthermore, the energies and widths of the lines in image A and the remaining images differ significantly. It is unlikely that the residuals are caused by pile-up. We simulated, using the software tool LYNX (see appendix A of Chartas et al. 2000), a piled-up spectrum with input model parameters taken from fit 2 of Table 3 and using the observed count rate in image A of 0.16 counts per frame. We find no evidence that the residuals are due to pile up. To further test whether pile up is the cause of the observed residuals, we excluded events from the core of image A. After the removal of the core, the remaining spectrum of image A still shows residuals between 2 and 3 keV. We conclude that a broad Fe Kα line is present in the spectrum of image A. The presence of a broad Fe Kα line in image A and not in the other images is indicative that microlensing may be enhancing the redshifted emission near the black hole. Observational and theoretical arguments rule out interpretations other than microlensing. First, strong and broad Fe Kα lines detected in several low luminosity Seyfert galaxies are rarely observed in quasars. This fact is further supported by the observed anti-correlation between the luminosities of AGN and the equivalent widths of Fe Kα lines detected in these AGN (Iwasawa & Taniguchi 1993; Nandra et al. 1995) and by theoretical estimates of the properties of Fe Kα lines in quasars (Fabian et al. 2000). Recently, Fe Kα lines with equivalent widths of ∼ 1 keV were observed in the quasars H 1413+117 (Oshima et al. 2001; Chartas et al. 2003) and MG J0414+0534 (Chartas et al. 2002a). However, these quasars are both gravitationally lensed and these relatively large equivalent widths were interpreted as the result of microlensing (Chartas et al. 2002a; Popović et al. 2002; Chartas et al. 2003). Second, an interpretation suggesting that the broad line in image A of Q 2237+0305 is being emitted by an X-ray flare which is only seen in image A is not supported by the Chandra observations. In particular, the predicted time-delays between images A and B, A and C, and A and D are ∼ 2, 16, and 5 hours, respectively (Schmidt, Webster, & Lewis 1998). If the flare duration is longer than a few days, we would have detected a similar enhanced and broadened Fe Kα line in the spectrum of the combined images of B, C, and D, since the relative time-delays are less than a day. For a flare duration of less than ∼ 8.4 hours we would

2The test-sources observed with ACIS S3 are the supernova remnant G21.5-0.9 observed on 2001 March 18, the millisecond pulsar J0437-4715 observed on 2000 May 29 and the radio-loud quasar Q0957+561 observed on 2000 April 16. 46 have detected significant variability of the strength and shape of the Fe Kα line during the first observation. We did not detect such variability during the first observation, and therefore, rule out flares with durations of less than 8.4 hours as being responsible for the broad Fe Kα line detected in image A only. In the following arguments we assume that the difference between the spectrum of image A and the combined spectrum of images B, C, and D is produced by microlensing, which magnifies the inner part of the accretion disc. The broadening and the observed redshift of the Fe Kα line in the spectrum of image A imply that the emission originates near the center of the black hole where special and general relativistic effects are important. The broad and redshifted profile of the Fe Kα line and its large equivalent width also indicate that the microlensing caustic should be located near the broad Fe Kα line emission region. The broad Fe Kα line emission region where special and general relativistic effects are important is expected to be very small ∼ 10 rg and the magnification of this relatively small emission region close to a fold caustic scales approximately as the inverse square root of its distance to the caustic. This microlensing event is funda- mentally different from those discussed in theoretical studies of optical and UV broad emission lines (e.g. Popović, Mediavilla, & Munõz 2001; Abajas et al. 2002) in that the locations and sizes of the emission regions and the line broadening mechanisms are all different. Popović et al. (2002) discussed the influence of microlensing on the shape of the Fe Kα line in AGN. A qualitative comparison between the profile of the observed broad Fe Kα line in image A and the theoretical predictions of Popović et al. (2002) also indicates that the microlensing caustic should be located near the broad Fe Kα line emission region. The microlensing interpretation has to explain the following facts indicated by the comparison of the optical and X-ray observations of Q 2237+0305. First, the OGLE pho- tometric data show no peak in the V band light-curve of image A during the September 2000 observation. The V band light-curve of image A shows a microlensing event that peaked about ten months earlier than the first Chandra observation. Delays between the peaks of the X-ray and optical light-curves have been predicted to occur in caustic crossings in the case where the X-ray and optical emission regions differ significantly (Mineshige, Yonehara, & Takahashi 2001). As we mentioned earlier the estimated size of the X-ray broad Fe Kα line region where special and general relativistic effects would produce the observed distortion of the Fe Kα line is ∼ 10 rg, whereas, the size of the < 15 14 optical and X-ray continuum emission regions are ∼ 6 × 10 cm and ∼ 1 × 10 cm, respectively. The size of the X-ray continuum region is based on the observed X-ray variability of the continuum in image A of about ∼ 3000 sec (proper time) which corresponds to a size of about ∼ 1 × 1014 cm (see section 5.5 for more details). The optical < 15 emission region has been constrained to be ∼ 6 × 10 cm (Wyithe et al. 2000). These sizes of emission regions are similar to those assumed in the simulations performed by Mineshige, Yonehara, & Takahashi (2001) that showed significant delays in the peaks of the magnification light-curves originating from different emission regions. We note that the radiation mechanisms assumed for the emission regions in the simulations of Mineshige, Yonehara, & Takahashi (2001) may differ from those in Q 2237+0305, however, the main contribution to the simulated delays in the peaks arises from the different sizes of the emission regions. Second, the optical and X-ray continuum flux ratios are 47 consistent within 1σ at the time of the first Chandra observation. This is possible since both the X-ray and optical continuum regions are much larger than the Fe Kα line emission region, as we discussed above, and they are both comparable in size with the Einstein radius of a typical 0.1 M microlens. The simulations of Mineshige, Yonehara, & Takahashi (2001) also showed that the flux magnifications for the X-ray and optical extended emission regions are not significantly different during the microlensing event. Detailed modeling of a caustic crossing that includes both the optical and X-ray constraints of Q 2237+0305 are needed to accurately interpret the microlensing event in Q 2237+0305. However, such an analysis is beyond the scope of this paper.

3.5.5 Variability We investigated the long term variability of Q 2237+0305 by comparing the fluxes of the two Chandra observations with the flux observed in the previous ROSAT observation. The 0.4–8 keV and 0.1–2.4 keV fluxes of Q 2237+0305 are 4.6×10−13erg cm−2 s−1 and 2.3 × 10−13erg cm−2 s−1, respectively, for the first Chandra observation. The 0.1– 2.4 keV flux detected with the first Chandra observation is consistent with that previously detected with ROSAT (Wambsganss et al. 1999). A comparison between the two Chan- dra observations of Q 2237+0305 shows that the total 0.4–8 keV flux has decreased by about 20% in the second observation. It is not clear from the present Chandra data if this decrease in X-ray flux is caused by intrinsic variability of the quasar or by microlensing.

3.6 Conclusions

1. Chandra observations of Q 2237+0305 have resolved the system into at least four X-ray images. A possible ﬁfth image could be the result of poor photon statistics and the contamination from the brightest image A. A longer Chandra observation of Q 2237+0305 is needed to resolve this issue.

2. The X-ray flux ratios of images B, C, and D with respect to image A are consistent with the V band flux ratios observed only four days prior to our first Chandra observation. This indicates that the X-ray fluxes are also magnified by microlensing as expected since the X-rays are thought to originate from the inner most regions of the accretion disc.

3. The hydrogen column densities of images A, B, C, and D measured from the Chandra observations of Q 2237+0305 are signiﬁcantly lower than the column densities inferred from extinction measurements of these images in the optical and infrared bands. This diﬀerence is suggestive of a higher value of the dust-to-gas ratio in the lensing galaxy compared to the Galactic value.

4. Our spectral analysis indicates the presence of a broad Fe Kα line in image A +0.2 with a rest-frame energy, width, and equivalent width of Eline = 5.7−0.3 keV, σline +0.30 +300 = 0.87−0.15 keV and EW = 1200−200 eV, respectively. The enhancement of the emission line in image A is possibly caused by microlensing since the combined spectrum of the other three images does not show such a signiﬁcant feature. The 48

redshift and broadening of the line may be the result of the Doppler eﬀect and special and general relativistic eﬀects.

5. Q 2237+0305 exhibits variability both over long and short time scales from the Chandra observations. The X-ray flux has dropped by 20% between the two observations, and the Kolmogorov-Smirnov test showed that image A is variable at the 97% confidence level within the first observation. A possible time-delay of +0.5 2.7−0.9 hours between images A and B with image A leading is detected in the first Chandra observation.

Acknowledgments: We would like to thank Pat Broos for providing the TARA software package, Koji Mori for providing subpixel correction software, and the anonymous referee for providing many useful comments and suggestions. We acknowledge the financial support by NASA grant NAS 8-01128. 49 of 1 and − . s source 2 5” ely troid − 4 2 e . . ) of 0 0 00 the cen ( ectiv Bkg of ts R 0 5 . . the radii cn 4 4 resp 6 on troid − outer 10 cen fitting, tered 7 the and 0 . . 0 cen 1 on D PSF R 6 1 . inner eV. . k the a 8 circle 10 tered a with cen 2 8 after . . 1 0 0.2–10 from C ulus R circle 1 0 een . . 2237+0305 a ann w 12 19 et obtained Q 1 an b − D 6 s of 9 . extracted . within 0 0 ts B from and cn R 0 3 . 3 . energies C, ations 7 − images 10 e v B, 10 kground all ha 0 3 . . A, bac extracted 2 1 of d Observ A and a R the 1 3 . . images 36 47 kground of 6 7 Chandr . . c 0,2,3,4,6 bac subtracted) 2 1 including of otal rates T ts the 6 9 t . . R 3.1. en of 63 86 ev grade 2 coun kground of able b ts T net er (bac b arcsec otal 608 ASCA 2635 T the Coun er um 3”. rate p n t of are the D rate R coun is standard s osure t 9538 radius ts 30287 of 3”. net . and a Exp coun , are of ely coun C the R ts the with , is en is ectiv B ation total radius ev ,R otal a A Date T Bkg resp source The R All R R a b c d e 2001-12-08 2000-09-06 Observ 30”, with the 50 04 . with with 04 . 0 0 ...... D2 ttp://cfa- 67 arcsec . 46 (h binned binned . 0 0 − a 04 . 04 . 0 0 ebsite Images 2237+0305 2237+0305 w ...... D1 Q Q 93 arcsec . 46 . 0 of of 0 − image image 03 003 2237+0305 . . 03 003 . . 0 0 ed ed 0 0 CASTLES Q olv D olv ...... v v of 78 arcsec . 49 866 . . 0 528 . 0 0 − 0 the − decon decon ositions the the P 02 02 02 02 003 003 of of ...... y 0 0 0 0 0 0 from C X-ra arcsec troids troids 21 21 63 62 . . . . 210 635 1 1 0 0 . . tml). 1 0 cen cen and A the the obtained 02 02 003 . . . 02 02 003 . . . 0 0 0 0 0 0 from from image Optical B e to 67 68 arcsec . . are 72 73 673 e . . 0 0 . 697 . 1 1 0 − − 1 − obtained obtained Relativ relativ are are 0 0 0 0 0 0 A are ositions 3.2. arcsec p ositions ositions able p p ositions T a a RA RA RA p DEC DEC DEC Offset HST 0.05”. 0.1”. c d ard.edu/glensdata/Individual/Q2237.h e of of a a b image Chandr Chandr HST The The The The elescop a b c d binsize binsize Chandr Chandr T www.harv a a 51

Table 3.3. Results of Fits to the Chandra Spectra of Q 2237+0305a

b c 2 2 d Fit Epoch Image Γ NH(z = 0.0395) Flux χν(ν) P (χ /ν) 20 −2 −13 −1 −2 10 cm 10 erg s cm +0.06 +1 +0.4 1 I Total 1.90−0.05 2−2 4.6−0.2 1.22(124) 0.05 +0.07 +2 +0.2 2 I A 1.81−0.07 1−1 2.5−0.2 1.25(76) 0.07 +0.15 +0.1 3 I B 1.70−0.12 < 3 0.5−0.1 1.11(15) 0.34 +0.07 +3 +0.1 4 I C 1.93−0.08 5−4 1.0−0.1 0.87(35) 0.68 +0.18 +0.1 5 I D 1.78−0.12 < 3 0.7−0.1 0.75(12) 0.70 +0.12 3 +0.6 6 II Total 1.88−0.12 3−3 3.7−0.5 1.26(33) 0.14 +0.06 +1 7 I+II simultaneous Total 1.90−0.06 2−2 ... 1.22(159) 0.03 +0.07 +2 8 I+II simultaneous A 1.81−0.07 1−1 ... 1.31(96) 0.02 +0.14 9 I+II simultaneous B 1.69−0.11 < 2 ... 1.10(18) 0.34 +0.14 +4 10 I+II simultaneous C 1.90−0.14 4−3 ... 0.83(41) 0.78 +0.16 11 I+II simultaneous D 1.83−0.13 < 3 ... 0.70(15) 0.78 +0.05 +1 12 I+II combined Total 1.90−0.05 2−1 ... 1.02(149) 0.40 +0.06 +1 13 I+II combined A 1.79−0.07 1−1 ... 1.06(94) 0.32 +0.12 14 I+II combined B 1.73−0.10 < 2 ... 1.26(20) 0.20 +0.08 +3 15 I+II combined C 1.91−0.07 5−3 ... 0.89(41) 0.68 +0.14 16 I+II combined D 1.86−0.13 < 2 ... 1.13(16) 0.32

− a × 22 2 All models include Galactic absorption with a column density of NH = 0.055 10 cm . All derived errors are at the 68% confidence level. b The spectral fits were performed within the energy range 0.4–8 keV c Flux is estimated in the 0.4–8 keV band d 2 2 P (χ /ν) is the probability of exceeding χ for ν degrees of freedom. 52 , b ) /ν 2 energy χ ( P 0.87 0.85 0.38 0.75 line e ) F ν ( 2 ν B, χ The 0.82(70) 0.81(55) 1.04(73) 0.87(58) 200 200 1990). Images +300 − +300 − ...... eV EW of 400 1200 kman del c 15 30 Lo Mo . . 0 30 ectrum . − +0 & σ eV 0 ...... Sp k line 87 < . ey 0 e k F 3 2 2 1 bined . . . . (Dic an 0 0 2 − − +0 +0 line eV ...... − 7 6 k . . E Com 5 6 cm 20 the without 10 2 − 01 00 02 02 01 02 02 02 0395) ...... × and . 0 0 0 0 and 0 5 cm +0 +0 +0 +0 − − − − . A freedom. 5 = 01 00 03 03 22 . . . . of = 0 0 0 0 (z with 10 H H 695). N . Image N 1 of of = degrees 07 06 13 08 06 07 07 09 ...... z 0 0 0 0 ( ν +0 +0 +0 +0 − − − − Γ 80 98 2237+0305 83 00 for . . . . 1 1 1 2 2 ectrum alues Q v χ Sp absorption of D a the frame w w del to o o and exceeding p p rest Galactic Mo of C, w+Gaussian w+Gaussian Fits are o o y p p fixed, 3.4. width t A A probabilit include able Image alen T B+C+D B+C+D the fits is h I I I I equiv c ) del o /ν I+I I+I I+I I+I 2 mo Ep and χ ( P All 3 2 4 1 a b Fit width, 53

Table 3.5. Hydrogen Column Densities in Q 2237+0305 Images

A B C D − − − − 1021 cm 2 1021 cm 2 1021 cm 2 1021 cm 2 a +0.1 +0.3 Chandra 0.1−0.1 < 0.2 0.5−0.3 < 0.2 b +0.6 +0.6 +0.9 +0.8 Converted Value 1.7−0.6 1.6−0.6 2.5−0.9 2.2−0.8

aColumn densities are obtained from the spectral modeling of the Chandra observations bColumn densities are converted from the extinction through an extinction law and a dust-to-gas ratio 54

Table 3.6. X-ray and Optical Flux Ratio in Q 2237+0305

Band Date A B C D Va 2000 Sep 2 1 0.24 0.07 0.54 0.19 0.29 0.09 X-Rayb 2000 Sep 6 1 0.23 0.05 0.38 0.06 0.27 0.06 X-Ray 2001 Dec 8 1 0.27 0.19 0.42 0.22 0.19 0.10

aThe V band data are provided by OGLE (http://bulge.princeton.edu/õgle/ogle2/huchra.html). bThe X-ray flux ratios relative to image A are estimated from 2–8 keV in order to avoid the complication of the differential absorption in the soft energy band 55

Fig. 3.1 (a) The raw image of the combined observations of Q 2237+0305 binned with a binsize of 000.05 and smoothed with a Gaussian of 000.05 (top). (b) The deconvolved image binned with a binsize of 000.1 (bottom left). (c) The deconvolved image binned with a binsize of 000.05 (bottom right). The green circles in each image are the corresponding HST image positions provided by CASTLES (http://cfa- www.harvard.edu/glensdata/Individual/Q2237.html). 56

Fig. 3.2 68% conﬁdence contours of photon index and neutral absorption at the lens (z = 0.0395) for images A, B, C, and D of the combined spectra from both observations. The shaded region represents the overlapping region of the four conﬁdence contours. 57

Fe Kα

Fig. 3.3 (a) Spectrum of image A combined from both observations (top). (b) Combined spectrum of images B, C, and D from both observations (bottom). 58

Fig. 3.4 To evaluate the significance of the emission feature in image A, we determined the distribution of the F-statistic (shown as histogram) using a Monte-Carlo simulation. We also overplotted for comparison the analytical curve for the F-distribution (shown as dashed curve). The vertical line indicates the F value obtained from the real spectrum of image A. The simulation shows that the detection of the broad emission line is significant at the > 99.99% confidence level. 59

Chapter 4

Detecting Time-delays in Gravitational Lensing Systems in X-Rays

4.1 Introduction

The1 time-delays in a gravitational lens system provide important constraints on the lensing system in addition to the constraints provided by the image positions and image flux ratios. Even before the discovery of the first gravitational lens by Walsh, Carswell, & Weymann (1979), Refsdal (1964a,b) proposed that the time-delays could be used to measure the Hubble constant. This method is independent of the distance ladder and provides a means of determining a global value for the Hubble constant. The time-delays in a gravitational lens system are difficult to measure. Only a small fraction of known gravitational lenses have measured time-delays. The difficulty of measuring time-delays arises for several reasons. First, the source needs to be variable in order to detect a time-delay between different images. Second, time-delays can be of order months to years for most of the lens systems. Therefore, extensive monitoring of gravitational lenses is needed to measure long time-delays. In addition, light-curves of lensed images can be easily contaminated by variations caused by microlensing events which have similar variability time scales. In Table 4.1 we list time-delays of several gravitational lenses measured in the optical and radio bands. The currently measured time-delays listed in Table 4.1 all have relatively long time scales (more than a few days at least). However, there are lenses whose images are predicted by lens models to have short time-delays (of order a day). For example, the time-delays of the quadruple image lens Q 2237+0305 are all predicted to be of order a day (e.g., Schmidt et al. 1998). These short time-delays are even more difficult to measure in the optical band because the quasar variability time-scale in the optical band is typically longer than a day. In addition, the sampling of optical light-curves are typically separated by at least a day, which makes it practically impossible to detect time-delays shorter than a day. Since the advent of Chandra, it is possible to resolve the individual lensed quasar images of more than ∼ 0.35 arcsec apart in X-rays. In the

1The work in this chapter contains material published in Chartas, G., Dai, X., Gallagher, S. C., Garmire, G. P., Bautz, M. W., Schechter, P. L., & Morgan, N. D. (2001) Chandra Detects a Rapid Flare in the Gravitationally Lensed Mini-Broad Absorption Line QSO RX J0911.4+0551, Astrophysical Journal 558:119, Dai, X., Chartas, G., Agol, E., Bautz, M. W., & Garmire, G. P. (2003) Chandra Observations of Q 2237+0305, Astrophysical Journal 589:100, Chartas, G., Dai, X., & Garmire, G. P. (2004) Chandra and XMM-Newton Results on the Hubble Constant from Gravitational Lensing, Measuring and Modeling the Universe, from the Carnegie Observatories Centennial Symposia, Carnegie Observatories Astrophysics Series, Edited by W. L. Freedman, 2004, Pasadena: Carnegie Observatories, and Dai et al. (2004) in preparation. 60

Table 4.1. Time-Delays Measured Through Optical and Radio Observations

GL systems Images Time-Delay References B 0218+357 A, B 10.5 0.4 days 1 RX J0911.4+0551 A, B 146 8 days 2 Q 0957+561 A, B 417 3 days 3 HE 1104-1805 B, A 0.73 years 4 PG 1115+080 B, C 23.7 3.4 days 5, 6 SBS 1520+530 A, B 130 3 days 7 B 1600+434 A, B 51 4 days 8 Q 1608+656 A, C 31.5 days 9 PKS 1830-211 A, B 26 5 days 10

References. — (1) Biggs et al. (1999); (2) Hjorth et al. (2002); (3) Kundic et al. (1997); (4) Wisotzki et al. (1998); (5) Schechter et al. (1997); (6) Barkana (1997); (7) Burud et al. (2002); (8) Burud et al. (2000); (9) Fassnacht et al. (2002); (10) Lovell et al. (1998)

X-ray band, quasar flares produce small time-scale variations shorter than the time-delay itself. These short flares make it possible to detect the time-delays in X-rays. In this chapter, we discuss the detections of such short time-delays in several lenses observed with Chandra and XMM-Newton. As mentioned earlier, time-delays can be used to constrain the Hubble constant or, alternatively by combining the Hubble constant determined from the HSTKP (Freedman et al. 2001) and W MAP (Spergel et al. 2003) projects to constrain the mass profiles of the lensing galaxies. The detection of time-delays in X-rays will not only provide a new time-delay detection method for all lenses, but also complement the studies of gravitational lenses in optical and radio bands because they are suitable for measuring time-delays of different time-scales. The short time-delays are particularly important in lens systems where long time-delays have been measured previously (e.g., the lens system PG 1115+080). The additional time-delays could in principle serve as additional constraints to lens models and reduce the number of allowable mass profiles in lens models of these systems.

4.2 Chandra Observation of RX J0911.4+0551

RX J0911.4+0551 was detected in the ROSAT All-Sky Survey (Bade et al. 1997) and was resolved to have four images with follow up optical observations (Burud et al. 1998). The source quasar is at a redshift of z = 2.8, and the main lens of the system is at a redshift of z = 0.769 (Falco, Davis & Stern, 1999, private communication). A cluster of galaxies has been detected at about 38 arcsec SW from RX J0911.4+0551 at the same mean redshift of 0.769 0.004 (Kneib, Cohen, & Hjorth 2000) and is thought to contribute to the lensing of the quasar. This object was observed with ACIS onboard 61

Chandra for ∼30 ks on November 3, 1999. The X-ray image and a deconvolved image of RX J0911.4+0551 are presented by Morgan et al. (2001).

4.2.1 Timing Analysis of RX J0911.4+0551 The combined light-curve of images A1 and A2 shows a significant variation of the X-ray flux within a period of about 2 ks. The images A1 and A2 are separated by ∼0.48 arcsec, which is just within the capabilities of the Chandra/ACIS combination. To determine whether the variation observed in the combined light-curve of images A1 and A2 originates from individual images, we extracted light-curves from rectangular regions with sides of length ∆R.A. = 2 arcsec and ∆dec = 0.8 arcsec centered on the centroids of the images as determined from the deconvolution analysis described in Morgan et al. (2001). The deconvolved image and the light-curves of images A1 and A2 are displayed in Figure 4.1. The time resolution for this observation is 3.241 sec. The light-curves in Figure 4.1 are binned in 1166.76s intervals, and are corrected for background events. Background is estimated by extracting events from a neighboring source-free region. The binned light-curves show a flare occurring in image A2 and not image A1. Two consecutive data points in the light-curve of image A2 lie at ∼ 3σ above the mean value. The duration of the X-ray flare is ∼ 2000 s and the count-rate changed from ∼ 5 counts per bin to ∼ 15 counts per bin. The background flares that occur at several intervals during the observation do not coincide with the 2000 s interval where we detect variability in A2. The background rate during the X-ray flare is ∼ 6 × 10−6 events s−1 pixel−1 (including only events with ASCA grades 0,2,3,4,6 and with energies within 0.5-8 keV). For the A2 source region the number of background counts expected during the 2000 s X-ray flare in A2 is ∼ 0.007 counts. More appropriate and unbiased tests for unbinned data are the Kolmogorov- Smirnov (K-S) and Kuiper (a variant of K-S) tests. In Figure 4.2 we show the cumulative probability distribution versus exposure time for the light-curves of A1 and A2. We find a significant deviation in A2, with a chance probability of about 1.8 × 10−3 for the K-S test applied to the entire duration of the observation. Results for the Kuiper test are similar and are presented in Table 4.2. We applied the K-S test over the entire observation of A2, and expect it to be unbiased with respect to time filtering. We also applied to K-S test over several narrower time intervals containing the flare. The results are shown in Table 4.2. The K-S probabilities for these time intervals range from 3.2 × 10−4 to 2.3 × 10−5 and indicate a high significance for the presence of a flare in image A2 but not in image A1.

4.2.2 Lens Modeling of RX J0911.4+0551 To obtain more accurate estimates of the short time delays in RX J0911.4+0551, we modeled these using the χ2 minimization method of Kayser et al. (1990) and Kochanek (1991). To account for the presence of a cluster of galaxies centered ∼ 38 arcsec SW of RX J0911.4+0551 we have included a shear component in our models. Shear measures the anisotropic stretching of the image and is due to mass residing out- side the beam (Weyl focusing). 62

Table 4.2. Tests of Variability of RX J0911.4+0551

Statistics Chance Probability Test Time Interval A2 A1 A2 A1 − K-S 0—29.6 ks 0.18 0.05 1.8 × 10 3 0.78 − Kuiper 0—29.6 ks 0.23 0.09 3.9 × 10 4 0.57 − K-S 1—28.6 ks 0.20 0.05 3.2 × 10 4 0.81 − Kuiper 1—28.6 ks 0.23 0.10 5.7 × 10 4 0.46 − K-S 2—27.6 ks 0.23 0.07 5.2 × 10 5 0.43 − Kuiper 2—27.6 ks 0.25 0.11 1.2 × 10 4 0.27 − K-S 3—26.6 ks 0.25 0.06 2.7 × 10 5 0.59 − Kuiper 3—26.6 ks 0.26 0.12 2.1 × 10 4 0.29 − K-S 4—25.6 ks 0.26 0.08 2.3 × 10 5 0.44 − Kuiper 4—25.6 ks 0.27 0.14 2.7 × 10 4 0.10

The adopted two-dimensional projected potentials are,

2 γ 2 ψ (θ~) = b lnr + r cos[2(θ − θ )] (4.1) P MXS 2 γ γ 2 ψ (θ~) = br + r cos[2(θ − θ )] (4.2) ISXS 2 γ ~ ψISEP (θ) = br + γbr cos[2(θ − θγ)] (4.3) where PMXS represents a point mass with external shear model, ISXS describes an isothermal sphere with external shear model, and ISEP considers an isothermal elliptical potential model. In the equations above, r and θ are polar coordinates of the image with respect to the galaxy, γ is the shear, θγ is the orientation of the shear (measured from North to West), and b is the strength of the lens.

Dls 2 b = 4π 2 vG0 (4.4) c Dos where vG0 is the velocity dispersion of the galaxy, D are the angular diameter distances, and the subscripts l, s, and o refer to the lens, deﬂector and observer (see Schechter et al. 1997 and references therein for more details on these lens models). The time delay between an image at a position θ~ and an unlensed light path is

(1 + z ) D D 1 2 τ(θ~) = d d s [ (θ~ − β~) − ψ(θ~)] c Dds 2 where β~ is the source position. The observable constraints are the positions of the lensed images and deflector galaxies taken from the CfA-Arizona Space Telescope LEns Survey (CASTLES) of gravitational lenses website. The best fit parameters obtained by minimizing the χ2 statistic formed between observables and their modeled values are 63 listed in Table 4.3. We find that the best fit model (model ISXS in Table 4.3) yields a time-delay value of 0.65h−1days between images A1 and A2 and 0.46h−1days between images A1 and A3. The detection of a flare in A2 and not in A1 constrains the time- delay between these images to be greater than 23 ks, consistent with our model results. The best fit value for the position angle of the external shear for the ISXS model is PA = 187 ◦. This is close to the observed position angle of PA ∼ 197 ◦ of X-ray emission from the lensing cluster (see Morgan et al. 2001). Considering the additional complexity introduced by the presence of a cluster of galaxies in the lens plane further detailed modeling of this system is needed. Although, we only measured a lower limit of the time-delay between images A2 and A1 in RX J0911.4+0551, it is the first time that we realized that it was possible to measure the time-delay between the lensed images in a single X-ray observation. We continued the search of time-delays in other lens systems and we succeeded in detecting two time-delays in gravitational lenses Q 2237+0305 and PG 1115+080. 64 to del, and /ν 2 ν mo χ A3 0.50/3 5.11/3 7.88/3 deflector North A2, shear B . and from M 1.78 1.09 1.50 A1, 3 of images A external M -2.78 -0.72 -1.88 images (measured dels with du/glensdata/ 2 lensed A d.e Mo lensed M shear 8.41 1.60 4.43 the sphere of the the 1 Lens A of of M -6.51 -2.42 -5.85 for ositions p ys tation isothermal da 1 an The orien A1-B − . es h -105.86 -147.92 -149.19 http://cfa-www.harvar magnifications the is ys the galaxy γ describ ebsite Magnifications da θ 1 w for − A1-A3 h 0.46 1.78 1.19 and ISXS lensing shear, alues v ys ys del, the the fit da to mo CASTLES is 1 J0911.4+0551 − γ A1-A2 est h -0.65 -0.92 -0.53 ect b the shear RX del. Time-dela resp the from γ mo ts θ (deg) en 173.00 172.64 172.23 with tial external tak oten γ represen are p 0.31 0.5 0.15 with source arameters, M P the mass of del t lens. b elliptical oin (arcsec) 1.108 1.028 1.368 Mo the parameters p a of ositions ts lens p 4.3. y fit the isothermal (arcsec) 0.047 0.064 0.069 e est strength an able represen b T deriv the the x is to b PMXS are -0.433 (arcsec) -0.649 -0.666 considers y — used and del and ISEP x Note. est), Mo ISEP ISXS PMXS galaxies W B. and 65

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Fig. 4.1 This ﬁgure is a composite of the deconvolved X-ray image of the gravitational lens RX J0911.4+0551 (top panel) and the light-curves of the lensed images A2 (left panel) and A1 (right panel). Chandra clearly resolves the four lensed images of the distant quasar. A rapid ﬂare that lasted for about 2000s was recorded in image A2 whereas image A1 does not show any variability. 66

Fig. 4.2 Cumulative probability distribution versus exposure number for image A2 (left panel) and image A1 (right panel) compared to the cumulative probability distribution of a constant source. 67

4.3 Q 2237+0305

The Chandra observations of Q 2237+0305 are presented in Chapter 3. Here, we focus on the timing analysis of the target. We explored the variability of Q 2237+0305 within each Chandra observation. The light-curves of the combined images and the individual images A, B, C, and D for the first and second observation are displayed in Figure 4.3. We performed Kolmogorov-Smirnov (K-S) tests to the unbinned light-curves of each image. In Table 4.4 we list the results of the K-S test. These results indicate that the light-curve of image A for the first observation is variable at the 97% confidence level. The K-S plot of the cumulative probability distribution versus the exposure number for image A of the first observation is illustrated in Figure 4.4. The light-curve of the combined images for the first observation also shows some variability according to the K-S test, however, at a lower ∼ 90% confidence level. In this light-curve we identified two possible flux enhancements. A comparison between the light-curve of all images and that of image A indicated that the first enhancement in the total light-curve corresponds to the bump detected at a similar time in the light-curve of image A. The correspondence of the second flux enhancement of the total light-curve with bumps in individual light- curves is less clear than the first bump. It is possible that the second bump arises in image B. We performed an auto-correlation of the total light-curve for the first observation and obtained a lag of 5 bins (1 bin = 1944.6 seconds) which yields a maximum auto-correlation coefficient of 0.40. The probability of obtaining this auto-correlation coefficient by chance is 0.06. We tested the sensitivity of the computed lag-time to the selected bin size of the total light-curve by performing the auto-correlation over a range of bin sizes. In all cases we recovered lag-times similar to the one obtained above. Our simple auto- +0.5 correlation analysis indicated a possible time-delay of 2.7−0.9 hours in the total light- curve of Q 2237+0305 for the first Chandra observation. The errors of this time-delay are dominated by the different choices of the bin size. A comparison between the total light-curve and those of the individual images indicates that the measured time-delay most likely corresponds to the time-delay between images A and B with image A leading. This is consistent with recent modeling of (Schmidt, Webster, & Lewis 1998) that predict +0.4 −1 a time-delay between images A and B of 2.0−0.3 h75 hours with image A leading.

4.3.1 Discussion The detection of the time-delay is tentative; if confirmed however, it would have significant implications. The gravitational lens Q 2237+0305 is unique among the gravitational lenses in several ways. First, it is the closest gravitational lens to us. The redshift of the lensing galaxy is z = 0.0395. The relatively close proximity of the lens enables us to observe and model the luminous part of the lensing galaxy much better than other lenses. Second, this system is among the most studied lenses and the target has been observed in almost all wavelength bands. The lens system has been modeled in detail by several groups. Third, the lensing galaxy is a spiral galaxy and gravitational lensing is produced by the central bulge of the galaxy. This provides us a plausible method to test whether the inner slope of the dark matter profile is cuspy or cored. 68

Furthermore, recently Metcalf et al. (2004) reported the detection of dark matter sub-structure in this system. An important prediction of the CDM model from both numerical and analytical simulations is the presence of dark matter substructure (e.g., Moore et al. 1999). Such dark matter substructure will lead to “milli-lensing”, which will produce an anomalous flux magnification of one of the images, if the dark matter substructure lies along a line of sight of one of the lensed images. However, this effect is similar to micro-lensing that is induced by stars in the lensing galaxy. One way to distinguish between these two effects is to observe different emission regions of the source. If the Einstein ring of the milli-lens or micro-lens in the source plane is much smaller than the source emission region, the flux magnification would not be affected by the milli or micro-lensing. Therefore, by observing a source region large enough compared with the Einstein ring of a micro-lens, the effect of microlensing can be excluded. Metcalf et al. (2004) were able to use this method and detected the anomalous flux ratio of the narrow line region (NLR) of Q 2237+0305, which is large enough so that it is not affected by microlensing. Metcalf et al. (2004) attributed the anomalous NLR flux ratio to milli- lensing. The authors also modeled the amount of dark matter substructure by fitting the anomalous flux ratio. However, they found that the amount of dark matter substructure is coupled with the slope of dark matter when fitting the NLR flux ratios. With our preliminary time-delay measurement between images A and B of ∼ 2.7 hr and assuming a Hubble constant of 72 km s−1 Mpc−1 (as determined from HSTKP), Metcalf et al. (2004) constrained the dark matter mass profile. With this information, the authors were able to constrain the amount of dark matter sub-structure, which turned out to be too much compared to CDM predictions. By confirming the time-delay measurement between images A and B, the mass profile in the lensing galaxy can be constrained, and the uncertainty in fitting the NRL flux ratio in this system solely resides in the properties of dark matter substructure. In addition, if time-delays between other images are also measured, the mass profile in the lensing galaxy can be constrained even better. We applied a simple lens model to the Q 2237+0305 using Keeton’s gravlens software to test this issue. We modeled the mass surface density of the lensing galaxy α as a simple powerlaw, κ = κ0r , and allowed the powerlaw index, α, to vary. We also −1 −1 adopted H0 = 72 km s Mpc in the modeling. The time-delays between the images are calculated as functions of the powerlaw index of the surface mass density in the lensing galaxy (Figure 4.5). With our tentative time-delay measurement between images +0.3 A and B, the surface density powerlaw index is constrained to be α = −1.0−0.2. This result is consistent with that of Metcalf et al. (2004). It is important to confirm and better constrain this time-delay measurement. In addition, a slightly longer observation will possibly allow us to constrain other time- delays in this system which are all within a day. The additional time-delay, most proba- bly between images A and C, could serve as an additional constrain to the lens models. Assuming a Poisson distribution for the occurrence of flares and considering that one flare was observed in 30 ks Chandra observation, the probability of observing at least one, two, and three flares in a 100 ks observation are 96.4%, 84.5% and 64.7%, respectively. We note that the flare amplitudes and occurrence frequencies are described by the power spectrum, which is a powerlaw. We used the Poisson distribution as an approximation here. We simulated the light-curves of the images for a 100 ks observation 69 assuming that three flares would occur (Figure 4.6). We performed cross correlations to the simulated light-curves and Monte Carlo simulations to evaluate the error-bars. These techniques are the same as those used in our tentative time-delay measurements in GL systems Q 2237+0305 and PG 1115+080 (Dai et al. 2003; Chartas, Dai, & Garmire 2004). We predict that a 100 ks Chandra observation is sufficient to measure the time- delays between images A and C, and images A and B with 2%, and 5% uncertainties, respectively.

Table 4.4. Kolmogorov-Smirnov Test of Variability for Q 2237+0305

Epoch Chance Probabilitya Total A B C D I 0.11 0.03 0.80 0.95 0.08 II 0.97 0.70 0.15 0.86 0.49

aThe probability that the tested light- curve is drawn from a constant distribution. 70

Epoch I Epoch II 2000 Sept 6 2001 Dec 8 Counts

Bin ( 1 bin = 1944.6 s )

Fig. 4.3 The full band (0.2–10 keV) light-curves of the sum of all images and images A, B, C, and D, separately, for the ﬁrst and second Chandra observations of Q 2237+0305. The data were taken continuously within each observation. 71

Fig. 4.4 Cumulative probability distribution vs. exposure number for image A of the ﬁrst observation of Q 2237+0305 compared to the cumulative probability distribution of a constant source. 72

Fig. 4.5 Time-delay constraints of the slope of the mass proﬁle of the lensing galaxy of gravitational lens Q 2237+0305. The shaded region indicates the error range of the tentative time-delay between images A and B in Q 2237+0305 measured with Chandra. 73 Counts

Bin (1 bin = 2000 s)

Fig. 4.6 Simulated 100 ks Chandra light-curve for image A of Q 2237+0305. 74

4.4 PG 1115+080

PG 1115+080 is the second gravitational lens and the first quadruple image lens discovered (Weymann et al. 1980). The source quasar is at a redshift of z = 1.722 and the lensing galaxy is at a redshift of z = 0.31. The time-delay between images A, B, and C in this system have been measured with optical observations (Schechter et al. 1997). The time-delay between images C and B is τCB = 23.7 3.4 days (68% confidence) and the time-delay between images C and A, A and B are about 9.4 and 14.3 days, respectively (the time-delay between images A1 and A2 is very short). Barkana (1997) re-analyzed the light-curves and obtained τCB = 25.0 3.5 days (95% confidence) and +0.18 τAC /τBA = 1.13−0.17 (68% confidence). The time-delays of this system, as measured in the optical band, received tremen- dous attention and detailed modeling of this system was performed to obtain the Hubble constant. In addition to the accurately measured image positions and well constrained flux ratios obtained with HST and KECK observations, an infra-red Einstein ring image of the quasar has also been detected in this system. The lens of this system is relatively simple and contains only one major lensing galaxy. However, even in this system the mass profile of the lensing galaxy could not be constrained. If the lensing galaxy is assumed to be dominated by dark matter that has an isothermal profile, a Hubble constant of about 50 km s−1 Mpc−1 is obtained (e.g., Schechter et al. 1997; Impey et al. 1998). If a constant mass-to-light (M/L) ratio is assumed for the lensing galaxy, a Hubble constant around 65 km s−1 Mpc−1 is obtained (e.g., Impey et al. 1998). It is desirable to measure the time-delay between images A1 and A2, which will add an additional constrain to the system.

4.4.1 Timing Analysis of Chandra Observations of PG 1115+080 PG 1115+080 was observed with ACIS onboard Chandra on June 2, 2000 and November 3, 2000 for 26.8 and 10 ks, respectively. The light-curves of images A (A1 and A2 combined), A1, A2, B, and C are extracted from both PG 1115+080 observations. The light-curves of images B, and C are extracted in circular regions, and the light-curves of the close images A1 and A2 (0.4800 apart) and their combined image A are extracted from rectangular regions. A rectangular extraction region is used for the close image pairs in order to avoid the contamination from the other image as much as possible. The background light-curves are extracted in annuli around the center of the images in both observations. The backgrounds have low count rates for the two observations and they are subtracted from the light-curves during the timing analysis.

4.4.1.1 Variability The Kolmogorov-Smirnov (K-S) test is performed on each of the unbinned light- curves extracted to test the variability with respect to a constant source model. The light-curve of images A (A1 and A2 combined) and A1 in the 26.8 ks observation of PG 1115+080, and the light-curve of image A1 in the 10 ks observation of PG 1115+080 are signiﬁcantly variable under the K-S test. Figures 4.7, 4.8, and 4.9 are the light-curves and the cumulative plots of the above mentioned signiﬁcantly variable light-curves. The 75

K-S test results for variability are listed in Table 4.5. The variability found in the second 10 ks PG 1115+080 observation is in the full energy band (0.3 – 8 keV), while the variability found in the ﬁrst 26.8 ks PG 1115+080 observation is in a narrow energy band around 2.0–3.0 keV. By adjusting the energy ﬁlter of the light-curve of image A of the 26.8 ks observation, the K-S chance probability could become as low as 0.002.

4.4.1.2 Time-Delay Between Images A1 and A2 in PG 1115+080 The significantly variable light-curve A (A1 and A2 combined) of the 26.8 ks observation of PG 1115+080 shows two peaks. The light-curve of the individual images A1 and A2 are shown in Figure 4.10. The light-curve of image A1 is presented again with the light-curve of image A2 together for comparison. The light-curve of image A1 is also significantly variable and it clearly shows one peak corresponding to the first peak in the combined light-curve of image A. Although the light-curve of image A2 is not significantly variable under the K-S test, it does show a peak (at about the 1 σ level) at the second peak of the combined light-curve of image A. The variability and the correspondence of the peaks in the combined and individual light-curves may serve as a first indication of the time-delay effect between images A1 and A2 in PG 1115+080. We applied cross-correlations between the individual light-curves and auto-correlations to the total combined light-curve, respectively. The result is displayed in Figure 4.11. Both the cross-correlation and the auto-correlation plots showed significant peaks at the time lag of eight bins which corresponds to 0.16 days. The cross-correlation coefficient has a peak value of 0.67 and the auto-correlation coefficient has a peak value of 0.43. A Monte Carlo simulation was performed to determine the significance level of these correlation coefficients. We simulated random light-curves from Poisson distributions with averages of the simulated light-curves set to be the same as the observed light- curves of images A1, A2 and A. The chance probability of getting a cross-correlation coefficient of 0.67 for two random light-curves is 0.019, and the probability is 0.036 for an auto-correlation coefficient of 0.43. Therefore, we conclude that we have detected the time-delay between images A1 and A2 of PG 1115+080 to be about 0.16 days. This time-delay is detected in a narrow energy band. We changed the energy filter and performed the cross correlations to the filtered light-curves and the chance probability can reach as low as 0.007 by adjusting the energy filter appropriately. Another Monte Carlo simulation was performed to estimate the uncertainty of the time-delay measurement. The bin-size of the light-curves, ∼0.01 days, used in this simulation is chosen as a compromise between a more accurate time-delay measurement and a higher detection confidence level. 1,000 light-curves were simulated for each image A1 and A2. Each simulated light-curve has the same number of bins as the observed light-curves and the photon counts in each bin were generated randomly within the error bar of the observed light-curves. Another constraint was added so that the sum of the simulated light-curves of images A1 and A2 is within the error-bar range of the observed combined light-curve of image A. The error-bars of the observed light-curves are calculated using Gehrels’s statistics (Gehrels 1986) for data points with small number of events. The cross correlation was performed to each pair of the simulated light-curves of images A1 and A2, and the lag of the maximum cross-correlation coefficient was 76 considered as the time-delay between images A1 and A2. The result of the simulation is shown in Figure 4.12(a). The Monte Carlo simulation showed that the time-delay +0.02 between images A1 and A2 in PG 1115+080 is ∆τA1A2 = 0.162−0.01 days with image A1 leading, and the result is significant at the 69% confidence level which corresponds to 1σ in Gaussian statistics. Image A1 is significantly variable in the second 10 ks PG 1115+080 observation. We also performed the cross correlation analysis to the combined light-curve of images A1 and A2 of the second observation in different energy bands and no strong correlation signal was obtained. This is consistent with our ∼ 0.162 days time delay detected in the long observation because the variation of the light-curve of image A2 has not been observed yet in the short observation of PG 1115+080.

4.4.1.3 Discussion There are no apparent background flares in the 10 ks observation made with the S3 chip in the full energy band; however, there are some background flares present in the 26.8 ks observation. The background flares in the 26.8 ks observation are in the full energy band while the light-curve of image A is variable in an energy band around 2.1–3.1 keV, where the background flares are not significant. The background count rates are low for both of the observations, 4.79×10−7 and 5.43×10−7 counts pixel−1 s−1 for the 26.8 ks and 10 ks observations respectively. The microlensing explanation for the variability is also excluded because of the predicted long time-scale of such an event. Therefore, the variability must be intrinsic to the quasar. The variability and the time-delay detected in the 26.8 ks observation of PG 1115+080 was detected in a narrow energy band around 2.1–3.1 keV. We changed the energy filter slightly and performed the K-S test and cross-correlation to the new light-curves as mentioned in the previous section. The maximum cross correlation coefficient is recovered at the same time lag (0.16 days) in most of the energy bands. The time-delay analysis of PG 1115+080 was mainly carried out with the cross correlation technique. We also determined the discrete correlation function (DCF) (Edel- son & Krolik 1988) of the light-curves of images A1 and A2 as an independent test. The result of Monte Carlo simulations of the DCF method is shown in Figure 4.12(b). The result is similar to that obtained from the cross correlation method. As mentioned in the introduction, extensive fitting of various mass models to the lensing galaxy of PG 1115+080 have been performed with the goal of constraining the Hubble constant. Most of these lens models have used the measured long time-delay between images B and C (e.g., Impey et al. 1998). One of the problems of this approach is that two groups of models fit the observable constrains but predict very different values for the Hubble constant. A possible approach of breaking this degeneracy is to include the short time-delay between images A1 and A2 as an additional constraint. A predicted time-delay between images A1 and A2 is not listed in the literature. We therefore modeled this system using the SIE+SIS and de Vaucouleurs+SIS models in Impey et al. (1998) available in Keeton’s gravlens software package (Keeton 2001a), (Keeton 2001b). Our fitting results are in good agreement with the parameters listed in Impey et al. (1998) and our predicted time-delay between images A1 and A2 is 77

+0.01 +0.011 0.162−0.01 days for the SIE+SIS model and 0.183−0.012 days for the de Vaucouleurs+SIS model. Both models predict time delays that lie within the observed error range of the +0.02 time delay of ∆τA1A2 = 0.162−0.01 days measured with Chandra, however the SIE+SIS model is slightly preferred. Due to the close prediction of the two models and the low signal to noise ratio of the Chandra observation we could not distinguish between the two groups of models.

Table 4.5. K-S Test Results of Chandra PG 1115+080 Light-Curves

QSO Exposure time (ks) Image Energy band (keV) K-S probability

PG 1115+080 26.8 A 2.1–3.1 0.044 PG 1115+080 26.8 A1 2.1–3.1 0.0007 PG 1115+080 10.0 A1 fulla 0.004

aThe full energy band is 0.3–8 keV. 78

Fig. 4.7 Light-curve and cumulative distribution of image A (A1 and A2 combined) of the 26.8 ks observation of PG1115+080 in the 2.1–3.1 keV energy band. 79

Fig. 4.8 Light-curve and cumulative distribution of image A1 of the 26.8 ks observation of PG 1115+080 in the 2.1–3.1 keV energy band. 80

Fig. 4.9 Light-curve and cumulative distribution of image A1 of the 10 ks observation of PG 1115+080 in the full energy band ( 0.3-8 keV). 81

Fig. 4.10 Light-curves of images A1 and A2 of the 26.8 ks PG1115+080 observation in the 2.1-3.1 keV energy band. 82

Fig. 4.11 (a) Cross correlation between the light-curves of images A1 and A2 of the 26.8 ks PG1115+080 observation in the 2.1–3.1 keV energy band. (b) Auto correlation of the light-curve A12 of the 26.8 ks PG1115+080 observation in the 2.1–3.1 keV energy band. 83

Fig. 4.12 (a) Error estimation of cross correlation results based on Monte-Carlo simulation. (b) Error estimation of DCF results based on Monte-Carlo simulation. 84

4.4.2 XMM-Newton observation of PG 1115+080 PG 1115+080 was observed with XMM-Newton on November 25, 2001 for 62.6 ks. The XMM-Newton image of the system and the combined light-curve of all images of PG 1115+080 in the 0.6–1.7 keV band are shown in Figure 4.13. The spatial resolution for XMM-Newton is ∼1000, which does not allow us to resolve the individual images of PG 1115+080. The larger effective area of XMM-Newton compared to that of Chandra resulted in an increased S/N of the XMM-Newton observation of PG 1115+080. In addition, the XMM-Newton observation of PG 1115+080 was longer than the Chandra one, thus, increasing the probability of detecting a time-delay between images A1 and A2. We applied the auto-correlation (AC) technique to the combined light-curve of all images of PG 1115+080 to determine the time-delay between images A1 and A2. The resolved Chandra image showed that images A1 and A2 are much brighter than images B and C. In addition, the time-delay between images A (A1 and A2), B, and C are measured to be of the order of days. Therefore, if a strong AC signal is present in the light-curve of the 62.6 ks XMM-Newton observation, it cannot be attributed to time-delays from other images. Such a strong AC signal could only be explained as a time-delay signal between images A1 and A2 or intrinsic variability of the source. A light-curve needs to be significantly variable to obtain a tight constraint of the time-delay. Unfortunately, there were no large flares during the XMM-Newton observation. Considering the weak nature of the X-ray flares in the XMM-Newton observation of PG 1115+080, we used the following techniques to determine the time-delay in this system. We first obtained a background subtracted light-curve of the combined images A1,A2, B and C of the XMM-Newton observation of PG 1115+080. AC of the X-ray light-curves were performed over a range of energy bands to determine AC lag-times. We created a histogram of the time-delays that correspond to the maximum values of the AC coefficients. This histogram is filtered for light-curves that meet a set of criteria. In our case the filtering criteria were (a) the K-S chance probability of variability of a light-curve be less than 0.1 and (b) the probability of obtaining the maximum AC coefficient by chance in a light-curve be less than 0.1. Monte-Carlo simulations were performed to evaluate the errors in the time-delay. We also investigated the sensitivity of the derived time-delay to the selected bin size of the light-curve. This error has been included in the error analysis of the time-delay. In Figure 4.14 we show the histogram of the AC lag times corresponding to the maxima of the AC coefficients with K-S chance probabilities of variability in each light-curve of less than 0.1 and Monte-Carlo chance probabilities of obtaining each AC coefficient of less than 0.1. We find that a time-delay between images A1 and A2 of ∆tA1A2 = 0.149 0.006 days.

4.4.2.1 Discussion

The values for H0 derived from present measurements of long time-delays depend strongly on the assumed mass profiles of the lenses (e.g., Impey et al. 1998, Kochanek −1 −1 2002a, 2002b). Isothermal lens models predict H0 ∼ 40–50 km s Mpc , whereas con- −1 −1 stant M/L ratio models predict H0 ∼ 60–80 km s Mpc . We investigated whether the accurate X-ray measurement of the time-delay ∆tA1A2 in PG1115+080 can discriminate 85 between mass models. We used Keeton’s gravitational lensing software gravlens 1.04 to produce a range of lens models, fitted these models to the observables and predicted the time-delays for each model. We essentially reproduced the models described in Impey et al. (1998) and Treu & Koopmans (2002). In Table 4.6 we show the predicted time-delays and resulting values for the Hubble constant for three different lens models. The first model consists of a singular isothermal ellipsoid (SIE) model to represent the principal lensing galaxy and a singular isothermal sphere model to represent the galaxy group that is known to contribute to the lensing of this system. For the second model we assumed a de Vaucouleurs profile for the main galaxy and a SIS model for the galaxy group. The de Vaucouleurs profile approximates a constant mass-to-light lens model for the main galaxy. Finally, for the third model we assumed a Pseudo Jaffe model for the luminous component of the main galaxy, a cuspy model for the dark matter component of the main galaxy, and a SIS model for the galaxy group. The third model is based on the lens model of Treu & Koopmans (2002) that includes both lensing constraints (image positions, main lens position and flux ratio) and kinematic constraints ( mass fraction and slope of dark matter density profile of lens). The estimates in Table 4.6 assume a time-delay between images B and C of 25 days. We note that all models predict time-delays between images A1 and A2 that are larger than the X-ray measured value. Our measured time-delay between images A1 and A2 combined with the third model of Table 4.6 imply a time-delay between images B and C of about 22 days which is consistent with the Schechter et al. (1997) value of ∆tBC = 23.7 3.4 days (1σ errors) but only marginally consistent at the 95% confidence level with the Barkana et +3.3 al. (1997) value of ∆tBC = 25.0−3.8 days (95% confidence levels). If we scale the third model that contains the additional constraints on the mass fraction and slope of the dark matter component from Treu & Koopmans (2002) to have ∆tA1A2 = 0.149 hours +13 −1 −1 we obtain a Hubble constant of H0 = 67−8 3 km s Mpc (systematic + random errors). The large systematic error originates from the uncertainty of the amount dark matter in the lensing galaxy. If we use the Hubble constant of 725 km s−1 Mpc−1 determined from the W MAP project (Spergel et al. 2003) as a constraint, the mass of the dark matter component needs to be less than 20% of the total mass within the Einstein ring of the lensing galaxy in order to obtain the short time-delay measured from XMM-Newton in PG 1115+080. This is consistent with recent studies suggesting that the dark matter content in some elliptical galaxies is small (e.g. Romanowsky et al. 2003).

4.5 Conclusions

We used gravitational lenses as tools to constrain cosmological parameters or the mass proﬁles of the lensing galaxies. These constraints are derived by measuring the time-delays in a sample of gravitational lenses observed with Chandra and XMM- Newton. To determine the time-delays we applied cross correlation and auto correlation techniques to the X-ray light-curves of the gravitational lenses. The time-delays between some of the images are predicted to be short (of the order of a few hours). We have measured two time-delays and one lower time-delay limit. 86

1. In RX J0911.4+0551, we have detected a ﬂare only in image A2 and not in image A1 constraining the time-delay between the two images to be greater than 23 ks. Although, we did not measure the time-delay in this system it was realized for the ﬁrst time that short time-delays can be measured in single X-ray observations.

2. In a Chandra observation of the Q 2237+0305, we detected a tentative time-delay +0.5 of 2.7−0.9 hours between images A and B with image A leading. This time-delay is important in constraining the mass proﬁle of the lensing galaxy and the amount of dark matter substructure in the lensing galaxy. With our tentative time-delay measurement between images A and B, the surface density powerlaw index is con- +0.3 −1 −1 strained to be α = −1.0−0.2, assuming a Hubble constant of 72 km s Mpc .

3. In a Chandra observation of PG 1115+080, we detected a time-delay of ∆τA1A2 = +0.02 0.162−0.01 days with image A1 leading. Furthermore, the analysis of an XMM- Newton observation of PG 1115+080 also yields a time-delay of 0.149 0.006 days, which is consistent with the time-delay between images A1 and A2 measured from the Chandra observation. Combining this time delay with other constraints +13 −1 −1 in the system, a Hubble constant of H0 = 67−8 3 km s Mpc is obtained. Inversely, if we use the Hubble constant of 725 km s−1 Mpc−1 determined from the W MAP project (Spergel et al. 2003) as a constraint, the mass of the dark matter component needs to be less than 20% of the total mass within the Einstein ring of the lensing galaxy in order to obtain the short time-delay measured from XMM-Newton in PG 1115+080. 87

Table 4.6. Predicted Time-Delays Between Images A1 and A2 of PG 1115+080 and Resulting Values of the Hubble constant.

Lens Model A1 A2 B C δtA1A2 h

SIE + SIS 14.0640 14.2265 25. 0 0.162 0.4528 de Vaucouleurs + SIS 14.0806 14.2546 25. 0 0.174 0.6809 JF + Cusp + SIS 14.1597 14.3291 25. 0 0.169 0.5962

Note. — SIE is a singular isothermal ellipsoid model, SIS is a singular isothermal sphere potential used to model the nearby group of galaxies that contributes to the lensing of PG 1115+080, de Vaucouleurs is a constant mass-to-light lens model, JF is a Pseudo Jaffe model for the luminous component of the lensing galaxy, Cusp is a cuspy model for the dark matter component of the lensing galaxy. The third model in Table 4.6 is based on lens model of Treu & Koopmans (2002) that includes both lensing constraints (image positions, main lens position and flux ratio) and kinematic constraints (mass fraction and slope of dark matter density profile of lens). All time-delays are in units of days and computed with respect to image C. The time-delay between images B and C for these simulations has been set to the estimated time-delay of 25 days by Barkana et al. (1997) based on −1 −1 the observations of Schechter et al. (1997). h = H0/(100 km s Mpc ) 88

Fig. 4.13 Left panel: XMM-Newton image (taken with the PN instrument) of the PG 1115+080 ﬁeld, Right panel: Light Curve of PG 1115+080 in the 0.6 - 1.7 keV band taken with the PN instrument onboard XMM-Newton 89

Fig. 4.14 The histogram of the auto correlation (AC) lag times of the XMM-Newton light- curves of different X-ray bands of the combined images of PG 1115+080 corresponding to the maxima of the AC coefficients with K-S chance probabilities of variability in each light-curve of less than 0.1 and Monte-Carlo chance probabilities of obtaining each AC coefficient of less than 0.1. 90

Chapter 5

Conclusions

5.0.1 Constraints on AGNs In our survey of high redshift lensed radio-quiet quasars, we used the flux magnification provided by gravitational lensing to obtain high S/N quasar spectra and light- curves. We reached the following conclusions. 1. We find a possible correlation between the spectral slope and X-ray luminosity of the gravitationally lensed quasar sample in the redshift range of 1.7 to 4. The X- ray spectral slope steepens as the X-ray luminosity increases. The limited number of quasars in the present sample combined with the medium S/N of several of the observations and the systematic uncertainties from the lensing magnification modeling may have led to an unaccounted systematic effect. Additional observations of z ∼ 2 lensed quasars with better S/N and more detailed modeling of all the lenses in our sample will allow us to confirm this result. Such a correlation is not observed in nearby z < 0.1 quasars suggesting that quasars at redshifts near the peak of their number density may have different accretion properties than low redshift quasars. When we combined the data from other samples of radio-quiet quasars selecting quasars with redshift (z > 1.5) together with the present lensed sample, the correlation is still significant, especially in the low X-ray luminosity range between 1043−45.5 erg s−1. If this correlation is confirmed by future studies, it could provide significant information on the emission mechanism and evolution of quasars. We suggest that this correlation can be understood if we hypothesize that the quasars in our sample are fueled at rates near their Eddington limit (consistent with recent models for quasar evolution) and that the optical depth of their X-ray emitting coronae increases with black hole mass. 2. We did not find a strong correlation between the optical-to-X-ray spectral index, αox, on either redshift or on UV luminosity in our small sample. However, most of our data points are consistent with the αox–L correlation of Vignali, Brandt, 2500A˚ & Schneider (2003). 91

3. Our estimated upper limits of X-ray variability of the relatively high redshift lensed quasars sample is consistent with the known correlation observed in Seyfert 1s.

Our analysis of the Chandra observations of Q 2237+0305 indicates the presence of an X-ray microlensing event. The conclusions from this analysis are summarized as follows.

3. Our spectral analysis indicates the presence of a broad Fe Kα line in image A +0.2 with a rest-frame energy, width, and equivalent width of Eline = 5.7−0.3 keV, σline +0.30 +300 = 0.87−0.15 keV and EW = 1200−200 eV, respectively. The enhancement of the emission line in image A is possibly caused by microlensing since the combined spectrum of the other three images does not show such a significant feature. The redshift and broadening of the line may be the result of the Doppler effect and special and general relativistic effects. It is likely that the broad iron line region that is affected by the GR and SR effects is smaller than the X-ray continuum region.

5.0.2 Constraints on Cosmology We used gravitational lenses as a tool to constrain cosmological parameters. Our method was based on constraining time-delays in our sample of gravitational lenses observed with Chandra and XMM-Newton. We performed cross correlation and auto correlation techniques to the X-ray light-curves of the gravitational lenses. The time- delays between some of the short separation systems images are predicted to be short of the order of several hours. We have measured two time-delays and one lower limit on a time-delay.

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Research Experience Doctoral Research The Pennsylvania State University 1999–2004 Thesis Advisor: Dr. Gordon P. Garmire & Dr. George Chartas We analyze data obtained from X-ray observations of gravitational lenses. We use gravitational lensing as a tool to study the properties of quasars and cosmology. Graduate Research The Pennsylvania State University 2003–2004 Research Advisor: Dr. Bing Zhang This research involves testing the Gamma-ray burst jet structures. Graduate Research The Pennsylvania State University 2002–2004 Research Advisor: Dr. Gordon P. Garmire We search for serendipitious X-ray sources in C handra cluster ﬁelds. Teaching Experience Teaching Assistant The Pennsylvania State University 1998-2000 I was the teaching assistant for Dr. Donald P. Schneider for Astro 291/292.