The Hot Interstellar Medium in Normal Elliptical Galaxies

THE HOT INTERSTELLAR MEDIUM IN NORMAL ELLIPTICAL GALAXIES

A dissertation presented to

the faculty of

the College of Arts and Sciences of Ohio University

In partial fulﬁllment

of the requirements for the degree

Doctor of Philosophy

Steven Diehl

August 2006 This dissertation entitled

THE HOT INTERSTELLAR MEDIUM IN NORMAL ELLIPTICAL GALAXIES

STEVEN DIEHL

has been approved for

the Department of Physics & Astronomy

and the College of Arts and Sciences by

Thomas S. Statler

Associate Professor of Physics & Astronomy

Benjamin M. Ogles

Dean, College of Arts and Sciences DIEHL, STEVEN, Ph.D., August 2006, Physics & Astronomy

THE HOT INTERSTELLAR MEDIUM IN NORMAL ELLIPTICAL GALAXIES

(250 pp.)

Director of Dissertation: Thomas S. Statler

I present a complete morphological and spectral X-ray analysis of the hot interstellar medium in 54 normal elliptical galaxies in the Chandra archive. I isolate their hot gas component from the contaminating point source emission, and adaptively bin the gas maps with a new adaptive binning technique using weighted Voronoi tesselations.

A comparison with optical images and photometry shows that the gas morphology has little in common with the starlight. In particular, I observe no correlation between optical and X-ray ellipticity, contrary to expectations for hydrostatic equilibrium.

Instead, I ﬁnd that the gas in general appears to be very disturbed, and I statistically quantify the amount of asymmetry. I see no correlations with environment, but a strong dependence of asymmetry on radio and X-ray AGN luminosities, such that galaxies with more active AGN are more disturbed. Surprisingly, this AGN– morphology connection persists all the way down to the weakest AGN, providing strong morphological evidence for AGN feedback in normal elliptical galaxies. I conclude that the hot gas in elliptical galaxies is generally not in hydrostatic equilibrium; instead, it is continually disturbed by intermittent outbursts of the central AGN.

I extract radial temperature proﬁles, revealing surprisingly complex structures with positive and negative gradients, or even combinations of both. I ﬁnd that the outer temperature gradient is determined by galaxy environment, while the inner

temperature proﬁles shows a strong correlation with radio luminosity and a weaker

with stellar mass. While our data are consistent with compressive heating in cooling

ﬂow models or supernova heating, AGN feedback is a more likely explanation. I

suggest that the change of sign for the temperature gradient indicates either how

localized diﬀerent AGN heat, or where AGN heating becomes unimportant.

Despite the disturbed gas morphology, I also report on the discovery of a tight

correlation, the X-ray gas fundamental plane (XGFP), linking temperature, half-light

0.28 0.22 radius, and average surface brightness as TX ∝ RX IX , reducing the large scatter in

the closely related luminosity-temperature relation. The XGFP has a small intrinsic

width of only 0.07 dex, and represents a new constraint on the hydrodynamic history of the gas.

Approved:

Thomas S. Statler

Associate Professor of Physics & Astronomy Preface

I would like to note that each chapter, except for chapter 1 (Introduction) and chapter 7 (Conclusions), is an individual paper by Diehl & Statler. These papers are either already published, submitted or to be submitted very soon. As a result of our collaboration, the introduction to chapter 2 was written by my adviser Thomas

Statler, and is not my own work. As each chapter was designed to be primarily published in a paper, we will not reference back to diﬀerent chapters, but rather quote the appopriate paper. In addition, chapters 4, 5, and 6 are published as a series, which is why we usually refer back to Paper I, II and III of the series.

To avoid confusion, here are the appropriate references for each individual chapter, along with their typically used “shortcuts”:

- Chapter 2 (Diehl and Statler 2005):

S. Diehl and T. S. Statler. A Fundamental Plane Relation for the X-Ray Gas

in Normal Elliptical Galaxies. ApJ, 633:L21-L24, November 2005.

- Chapter 3 (Diehl and Statler 2006a):

S. Diehl and T. S. Statler. Adaptive binning of X-ray data with weighted

Voronoi tessellations. MNRAS, 368:497-510, May 2006a.

- Chapter 4 (Paper I, Diehl and Statler 2006b):

S. Diehl and T. S. Statler. The Hot Interstellar Medium in Normal Ellipti- cal Galaxies I: A Chandra Gas Gallery and Comparison of X-ray and Optical

Morphology. ApJ, submitted, 2006b.

- Chapter 5 (Paper II, Diehl and Statler 2006c):

S. Diehl and T. S. Statler. The Hot Interstellar Medium in Normal Elliptical

Galaxies II: Morphological Evidence for AGN feedback. ApJ, to be submitted,

2006c.

- Chapter 6 (Paper III, Diehl and Statler 2006d):

S. Diehl and T. S. Statler. The Hot Interstellar Medium in Normal Elliptical

Galaxies III: The Thermodynamic Structure of the Gas. ApJ, to be submitted,

2006d. To my wife Anke Acknowledgments

First of all, I would like to thank my adviser Tom Statler, who has not only been an exceptional mentor, but has also become a good friend during the last ﬁve years.

Without his guidance, this project would have been impossible. He has inspired me from the beginning with his enthusiasm for teaching and his concise analytic skills.

He left me the space to explore in my own ways, but always kept me ﬁrm on target.

I would also like to thank Christopher Fryer to give me the opportunity to visit the Los Alamos National Laboratory twice during my time as a graduate student, and to oﬀer me the chance to continue the collaboration after my PhD.

I am also indebted to the other astronomy professors in our department, Joe

Shields, Brian McNamara and Markus B¨ottcher, who always had an open door for questions and greatly helped in many situations. A great deal of gratitude is also due for the members of my dissertation committee, who stayed patient with me near the end, when I was short on time.

I also owe a special note of gratitude to our system administrator Don Roth, who kept my computer alive, no matter how hard I tried to break it. In that sense, I would also like to thank all of my colleagues Justin, Swati, Manasvita, Myriam, Nick, Anca,

Tom and Mangala, whose computers were crunching my data for extended periods of time, without them complaining. There are also many friends back home in Germany, that I simply want to thank for keeping in contact, despite the long distance: Kersten, Torsten, Sven, Andreas,

Jens, Michael, Holger, and Frank.

Of course, I am also grateful to my friends at Ohio University, Rocco, Karthik,

Manasvita, Justin, Jack, Christina, Swati, Eric, Greg, Nick, Stu, Anca, Chris, Ozan, and Zach, who were always there to help, or just to talk and keep me from working too much.

Finally, I’d like to thank my family.

From the beginning, my parents Rosi and Reiner, encouraged me to go after the chance to study in the U.S., well knowing that I may not make it back soon. I would also like to thank my grand-mothers Trude and Ilse, who have accepted my decision to leave Germany to study without trying to hold me back. My brother Bj¨orn and my sister Annika were always there, when I needed someone to talk. All of them always supported my decisions and have stood by my side whenever I needed them most, which I will be always thankful for.

But most of all, I would like to thank my wife Anke, who took a chance before we got married, and followed me to Ohio after one year of a long-distance relationship.

She left her family and a good job behind to be with me, without ever looking back afterwards or regretting her decision. This took a lot of courage and I will be forever in her debt for taking this leap of faith for me. 10 Table of Contents Page

Abstract ...... 3

Preface ...... 5

Dedication ...... 7

Acknowledgments ...... 8

List of Tables ...... 13

List of Figures ...... 14

1 Introduction ...... 21 1.1 Structural and Photometric Properties of Normal Elliptical Galaxies . 21 1.2 X-ray Observations of Elliptical Galaxies ...... 23 1.2.1 Historical Background ...... 23 1.2.2 The Importance of Understanding the Point Source Component 24 1.3 The Hot Interstellar Medium ...... 25 1.3.1 Origin ...... 25 1.3.2 Evolution ...... 26 1.3.3 Hydrostatic Equilibrium ...... 28 1.4 The Role of the Central AGN in Clusters ...... 30 1.5 Open Questions for Normal Elliptical Galaxies ...... 32 1.6 Outline of the Project ...... 33

2 A Fundamental Plane Relation for the X-Ray Gas ...... 36 2.1 Introduction ...... 36 2.2 Data Reduction and Analysis ...... 38 2.2.1 Chandra Archive Sample and Pipeline Reduction ...... 38 2.2.2 Isolating the Gas Emission ...... 38 2.2.3 Physical Parameters for the Gas ...... 40 2.3 The X-Ray Gas Fundamental Plane ...... 44 2.4 Discussion ...... 46 2.4.1 Relation to Known Scaling Laws ...... 46 2.4.2 Independence of the XGFP and the SFP ...... 48

3 Adaptive Binning of X-ray data with Weighted Voronoi Tesselations ... 51 3.1 Introduction ...... 51 3.2 Existing Adaptive Binning Algorithms ...... 53 11

3.2.1 Quadtree Binning ...... 53 3.2.2 Voronoi Binning ...... 54 3.3 Adaptive Binning with Weighted Voronoi Tesselations ...... 57 3.3.1 Introduction to Weighted Voronoi Tesselations (WVT) .... 57 3.3.2 Adaptive Binning Algorithm ...... 58 3.4 Performance ...... 61 3.4.1 Comparison with Quadtree ...... 61 3.4.2 Comparison with VT ...... 64 3.5 Applications to X-ray data ...... 68 3.5.1 Intensity Maps ...... 68 3.5.2 Hardness Ratio Maps ...... 70 3.5.3 Maps of Temperature (or other Spectral Parameters) ..... 71 3.5.4 Isolation of Diﬀerent Components ...... 77 3.6 Adaptive Binning vs. Adaptive Smoothing ...... 78 3.6.1 Adaptive Smoothing in X-ray astronomy ...... 78 3.6.2 Comparison with XMM-asmooth ...... 80 3.6.3 A Cautionary Note on CIAO’s csmooth ...... 83 3.7 Availability of the Code ...... 87 3.8 Conclusions ...... 89

4 A Chandra Gas Gallery and Comparison of X-ray and Optical Morphology 91 4.1 Introduction ...... 91 4.2 Data ...... 96 4.2.1 Sample Selection and Pipeline Reduction ...... 96 4.2.2 Isolating the X-ray Gas Emission ...... 99 4.2.3 X-ray Gas Luminosity ...... 107 4.2.4 X-ray Ellipticity and Position Angle Proﬁles ...... 108 4.2.5 Optical Data ...... 109 4.3 Results ...... 115 4.3.1 X-ray vs. Optical Luminosity ...... 115 4.3.2 X-ray vs. Optical Morphology ...... 122 4.3.3 Rotational Support ...... 128 4.4 Discussion ...... 131 4.4.1 Implications for Hydrostatic Equilibrium ...... 131 4.4.2 Implications for Rotational Support ...... 133 4.5 Conclusions ...... 136

5 Morphological Evidence for AGN feedback ...... 138 5.1 Introduction ...... 138 5.2 Data Analysis ...... 142 5.2.1 Summary of Paper I and Preliminary Analysis ...... 142 5.2.2 Quantifying Asymmetry ...... 148 12

5.2.3 X-ray AGN Luminosities ...... 154 5.2.4 Radio AGN Luminosities ...... 158 5.2.5 The Galaxy Environment ...... 160 5.3 Results ...... 162 5.3.1 X-ray Ellipticity and Asymmetry ...... 162 5.3.2 Environmental Inﬂuence on Morphology ...... 163 5.3.3 Gas Morphology and the Central AGN ...... 165 5.4 Discussion ...... 169 5.4.1 Causes and Consequences of Disturbances in the Gas Morphology169 5.4.2 Implications for Interactions with the Intergalactic Medium .. 173 5.5 Conclusions ...... 174

6 The Thermodynamic Structure of the Gas ...... 176 6.1 Introduction ...... 176 6.2 Data Analysis ...... 180 6.2.1 Summary of Papers I+II and Preliminary Analysis ...... 180 6.2.2 Projected Radial Temperature Profiles ...... 187 6.2.3 Two-Dimensional Temperature Maps ...... 188 6.2.4 Deprojected Density Profiles ...... 189 6.3 The Temperature Structure of Elliptical Galaxies ...... 191 6.3.1 Radial Temperature Profiles ...... 191 6.3.2 The Inner Temperature Gradient α02 ...... 194 6.3.3 The Outer Temperature Gradient α24 ...... 199 6.3.4 Two-dimensional Temperature Maps ...... 200 6.4 Density and Cooling Time Profiles ...... 210 6.5 Entropy Profiles ...... 210 6.5.1 Effects on the L-T diagram ...... 215 6.6 Discussion ...... 216 6.6.1 Implications for Cooling Flows ...... 216 6.6.2 Implications for Supernova Feedback ...... 219 6.6.3 Implications for AGN feedback ...... 221 6.6.4 What is so special about ∼ 0.6 keV? ...... 224 6.7 Conclusions ...... 225

7 Conclusions ...... 229 7.1 Summary ...... 229 7.1.1 Morphological Evidence for AGN Feedback ...... 229 7.1.2 Toward a Solution of the Cooling Problem ...... 231 7.1.3 Feedback and the X-ray Gas Fundamental Plane ...... 233 7.2 Open Questions ...... 235

Bibliography ...... 238 13 List of Tables 2.1 Physical parameters for the X-ray gas ...... 43

4.1 Chandra X-ray properties ...... 104 4.2 Optical properties ...... 111

5.1 Gas morphology, AGN properties and environment ...... 145

6.1 Chandra X-ray luminosity and temperature profile parameters. ... 182 6.2 Optical, radio, and environmental parameters ...... 184 6.3 Correlations involving inner and outer temperature gradients. .... 199 14 List of Figures 2.1 Face-on (top) and edge-on (bottom) views of the X-ray Gas Funda- mental Plane. Axis labels indicate eigenvector components. Symbol sizes roughly indicate the relative positions into and out of the page. Error bars indicate 1σ-projections of the covariance matrices. Arrows illustrate the sense of view relative to the fundamental measured parameters...... 45 2.2 Exponents a and b, describing the orientation of the XGFP according to equation (2.4). Cross and ellipses indicate best-fit values and confidence regions, respectively. Diagonal line marks combinations of a and b corresponding to pure luminosity-temperature correlations of the form L ∝ T n...... 46

3.1 A normal VT (left) and a WVT (right) with identical bin generators zi (crosses). The numbers attached to the bins are the associated scale lengths δi. The dashed lines connect neighboring bin generators. Note how the bin boundaries are always perpendicular to them. For a normal VT, the bin boundaries are the perpendicular bisectors; for a WVT, the dashed lines are divided proportional to the bins’ respective scale lengths...... 59 3.2 Comparison between Quadtree (left column) and WVT binning (right column); Middle Panels: Logarithmically scaled, binned intensity images. The square indicates the region of the zoom-in shown in the upper panels. Each bin has been outlined to emphasize the diﬀerence in the binning structure. Note the darker “stranded” bins on the left; Lower panels: Absolute fractional diﬀerence between the model surface brightness and the binned simulated data...... 65 3.3 Upper panels: area per bin vs. radius for quadtree (left) and WVT (right), the solid line indicates the theoretical prediction to produce a constant S/N of 20 per bin for our test model. Lower panels: corresponding S/N per bin; note the jumps in S/N due to the discrete bin sizes for the quadtree binning, which is completely absent in WVT; the solid line shows the target S/N, the dashed lines indicate the natural scatter of ∼ 2 in quadtree and the 3σ rms scatter in WVT...... 66 3.4 Comparison of quadtree (left) and WVT binning (right); Both panels show adaptively binned hardness ratio maps of the core of the Perseus cluster, with dark colors indicating regions of higher temperature and/or lower photoelectric absorption. Note how quadtree binning leads the eye into identifying two ring structures, due to the strong jumps in the S/N where the bin area suddenly quadruples. .. 67 15

3.5 Final result after application of the CC03’s Voronoi binning code (left) and the WVT algorithm (right) to the SAURON data of NGC 2273. After completion of the binning process, the bins have been projected onto a finer grid to make it easier to identify differences in the shape of the bins...... 68 3.6 Comparison of bin compactness between Voronoi binning (open circles) and WVT binning (filled circles). The dashed line indicates the theoretical limit for a perfect circle...... 74 3.7 Top: Flux-calibrated Chandra image of Cassiopeia A with an exposure time of 1 ks (left) and the same data adaptively binned with WVT to a target S/N of 5 (right); Bottom: Cassiopeia A with the full exposure of 50 ks (left) and the same image binned to a S/N of 20 (right). .. 75 3.8 Temperature map of NGC 4636. Temperatures are scaled linearly from 0.55 to 1.0keV, as indicated by the color bar. The relative 1σ uncertainties, in percent, of the fitted values are shown in right panel. The error distribution is not completely uniform in this case owing to a combination of different levels in background contribution, degradation of the instrument response for large off-axis angles, and differences in the spectral shape for varying temperatures...... 76 3.9 Upper left: Model surface brightness distribution for unresolved point sources; Upper right: Model surface brightness distribution for the hot, isothermal gas; Lower left: Simulated Poisson image for the full band, including contributions of both point sources and gas; Lower right: Reconstruction of the gas surface brightness distribution with the help of WVT binning...... 79 3.10 A comparison of WVT binning with adaptive smoothing. Upper left: Model surface brightness distribution; The other three panels show the simulated counts image, adaptively binned image with WVT binning (upper right), adaptively smoothed with CIAO’s csmooth (lower left) and XMM-asmooth (lower right). In the csmoothed image, note the radial “fingers”, the annulus of deficient emission (deep purple) and the boundary effects in the corners...... 81 3.11 Histogram of relative errors, compared to the model surface brightness, for the example of Figure 3.10. The WVT binning (solid line) and XMM-asmooth (dashed line) histograms are consistent with the target S/N value of 5 (i.e. they approximate a Gaussian with a width of 20%). Note that the adaptively smoothed image is not a statistically better representation of the true surface brightness. The histogram of csmooth results (dotted line) is very irregular with a wide range of positive and especially negative errors, demonstrating the failure of this algorithm. 84 16

3.12 Comparison between XMM-asmooth (left) and WVT binning (right): the simulated counts data was derived from a flat Poisson distribution with a count rate of 1 cts pix−1, with a spatially variable background “ramp” increasing linearly from 0 cts pix−1 at the bottom to 5 cts pix−1 at the top of the image...... 85 3.13 Left panel: Relative error distribution for the csmoothed image in the lower right panel of Fig. 3.10; note the large-scale spatially dependent error distribution which leads to the identification of spurious features. Right panel: The csmooth scale map, indicating the spatial distribution of the smoothing kernel size. Note how smaller kernel sizes translate into stronger positive deviations in the error distribution; in particular, note the correspondence between the transition to the largest smoothing kernel and the sharp edge in the error distribution that leads to the annulus of deficient emission...... 88

4.1 Adaptively binned Chandra X-ray gas surface brightness maps (right) and optical DSS R-band images (left). The objects are ordered by 2MASS K band luminosity, starting with the most luminous galaxy on the top left of the page, and decreasing to the right and then to the next row. The physical scale of each image is 50 kpc × 50 kpc, except where indicated by an individually attached scale bar. The color range of the X-ray gas distribution is scaled logarithmically between 5×10−11 and 3×10−7 photons sec−1cm−2 arcsec−2. The x and y-axes are labelled according to right ascension and declination (2000), respectively. .. 116 4.2 Total X-ray gas luminosity in erg s−1 as a function of absolute blue 32 −1 luminosity in units of blue solar luminosity (LB, = 5.2 × 10 erg s ) taken from LEDA. The dashed line shows the best fit by O’Sullivan et al. (2001), which they statistically correct for the expected contribution from unresolved point sources. Our data is consistent with their relation...... 123 4.3 Radial isophotal ellipticity and position angle profiles for the subset of 36 elliptical galaxies containing sufficient signal. Large filled circles with error bars denote X-ray gas profiles; other symbols denote optical profiles as indicated in the figure. The 2MASS ellipticity and position angle are marked with arrows at the right border. The vertical dashed lines mark the 2MASS J-band effective radius...... 125 4.4 X-ray gas ellipticity vs. optical ellipticity, both evaluated between 0.8 − 1.2 RJ. There is no correlation, contrary to what what would be expected if the gas were in hydrostatic equilibrium in a stellar-mass- dominated potential...... 127 17

4.5 Histogram of absolute diﬀerences between the 2MASS J-band position angle PAJ and the X-ray gas position angle (PAX) between 0.8−1.2RJ. The error bars indicate the 1σ uncertainties per bin. Gas and stellar major axes have a tendency to be aligned, at the 97% conﬁdence level. 129 4.6 X-ray ellipticity as a function of rotational stellar velocity between 0.8 − 1.2 RJ. No correlation is present, contrary to what is expected if the hot gas would be due to stellar mass-loss and subsequently settle into a cooling disk...... 130

5.1 Left panel: Gas X-ray surface brightness (in photons s−1 cm−2 arcsec−2), ellipticity and position angle profile for NGC 4649. Solid lines indicate the Chebychev polynomial fits. Right panel: Adaptively binned gas map of NGC 4649 with the fitted elliptical isophotes overlaid. .... 150 5.2 Gas surface brightness maps for three elliptical galaxies, showing the range in asymmetry index η; Left: NGC 6482 (η < 0.032); Center: NGC 4472 (η = 0.077); Right: NGC 4374 (η = 0.478). Colors depict gas surface brightness levels with the color scale ranging from 5 × 10−10 to 10−6photons s−1 cm−2 arcsec−2. The x and y-axes are labelled according to right ascension and declination (2000), respectively. ... 151 5.3 One-dimensional cut through our adopted two-dimensional simulated “bubble depressions“, demonstrating the fractional depression strength of the bubble with respect to its radial extent. The bubble has negative surface brightness deviations within the bubble radius RBubble , and slightly enhanced rims around it. The profile shape is chosen such that the integrated deviations integrate to 0 over all radii...... 154 5.4 Results of testing the asymmetry index against models with simulated bubble-like depressions (see Fig. 5.3). The asymmetry index η is sensitive to the number of simulated bubbles (left), the relative strength of the depression (middle) and the effective exposure time, characterized by the total number of counts (right). The dashed lines mark the expected behavior for perfect data...... 155 5.5 Radial X-ray surface brightness profiles for the inner 600 of NGC 4261 (left) and NGC 6482 (right). Solid grey lines indicate Sèrsicmodel fits, solid black lines show β model fits, including a PSF model for the central AGN. Dashed lines show the same model fits without the AGN component. NGC 4261’s AGN is detected on a 7σ level, NGC 6482 profile reveals no AGN signature. For NGC 6482, the AGN flux yielded by the Sérsicmodel fit is so small that the black dashed line is invisible, as it is covered by the black solid line...... 159 5.6 The X-ray asymmetry index η as a function of X-ray ellipticity X. The observed positive correlation suggests a common underlying cause for both the large measured X-ray ellipticities and the asymmetries. ... 162 18

5.7 X-ray ellipticity X (top) and asymmetry index η (bottom) as a function of projected galaxy density ρ2MASS. Both plots indicate that environment is not the driving factor causing the high ellipticities and asymmetries...... 164 5.8 X-ray AGN luminosity vs. 20 cm continuum radio luminosity with data taken from NVSS within 3 optical radii (left) and from FIRST (right) within a 3000 radius. Arrows indicate 3σ upper limits. The slope of the relationship between radio and X-ray luminosity is close to be linear, as indicated by the solid lines. Thus, X-ray and radio luminosities are likely caused by the same underlying phenomenon, and are independent measures of AGN activity...... 166 5.9 Asymmetry index η as a function of X-ray AGN luminosity LX,AGN (left) and 20 cm radio continuum power LNVSS taken from NVSS (right). Both plots indicate that the central AGN luminosity is positively correlated with the observed asymmetry in the gas, with the correlation extending all the way down to the weakest AGN...... 170 5.10 Histogram of absolute diﬀerences between optical (2MASS J-band, PAJ), radio (NVSS 20cm continuum, PANVSS), and X-ray gas (PAX) position angles. The grey shaded histogram with dotted contours shows that there is a clear tendency for galaxies to have X-ray and optical isophotes aligned (reproduced from Diehl and Statler 2006b). The solid line shows an anti-correlation between optical and radio position angles, and the dashed line an anti-correlation between radio and X-ray position angles, providing support for the idea that the radio source is responsible for producing the X-ray–optical alignment. ... 171

6.1 Combined plot of all projected temperature profiles, as a function of radius scaled by the J-band effective radius RJ. Error bars are omitted for clarity; for typical error estimates, refer to Figure 6.2. The profiles are colored according to the luminosity weighted average temperature of the galaxy within 3 optical radii TX, as indicated by the color scale bar. Note how the temperature gradient changes continuously from positive gradients at the top to isothermal and hybrid profiles to negative gradient profiles at the bottom, along with the average temperature...... 195 6.2 Examples of different projected temperature profiles as a function of radius. Temperature profile types can be divided into 4 major groups (top to bottom rows): (1) Positive gradient (outwardly rising) at all radii; (2) Negative gradient (outwardly falling) at all radii; (3) Hybrid, negative gradient in the core and positive gradient at larger radii; (4) Quasi-isothermal, no apparent temperature change with radius. ... 196 19

6.3 Inner temperature gradient within 2 RJ as a function of the luminosity weighted temperature within 3 optical radii. The dashed line indicates the best fit...... 203 6.4 Inner temperature gradient within 2 RJ as a function of 20 cm NVSS radio luminosity (left) and absolute K magnitude (or stellar mass, right). The dashed lines indicate the best-fit correlations. Note the increased scatter in the MK plot, compared to the stronger correlation. 204 6.5 Projected galaxy number density ρ2MASS vs. outer (α24, top panel) and inner (α02, bottom panel) temperature gradients. Note how α02 is completely unaffected by the environment, whereas α24 depends strongly on the presence of hot ambient gas...... 205 6.6 Identical to Figure 6.1, but colors now indicate NVSS 20 cm continuum radio luminosity within 3RJ, as indicated by the colorbar. Note how the radio luminosity changes smoothly, as one works its way down from positive to negative temperature gradients...... 206 6.7 Projected temperature maps (right), together with their gas maps (left) for the 12 brightest galaxies in our sample. The temperature maps are scaled logarithmically, with their individual temperature ranges indicated by the color bars. Black areas denote regions outside the field of view, or bins for which the spectral fit did not converge. All gas images are scaled on the same logarithmic scale, ranging from 5×10−11 to 3× 10−7 photons sec−1cm−2 arcsec−2. Note how disturbed both gas images and temperature maps are, and how disturbances in the gas map often are often associated with the asymmetries in the temperature distribution...... 207 6.8 Combined plot of all electron density profiles as a function of physical radius. Each plot is colored according to the galaxy’s X-ray gas luminosity. X-ray faint galaxies tend to have generally lower densities and are less extended, which may be a sign that X-ray fain galaxies have lost a significant fraction of their gas through winds...... 211 6.9 Combined plot of all cooling time profiles as a function of physical radius. Each plot is colored according to the galaxy’s X-ray gas luminosity. X-ray faint galaxies tend to have longer cooling times at large radii, due to their lower electron densities. The cooling times reach values as low as only 10Myr in the centers...... 212 20

6.10 Combined plot of all circularly averaged entropy profiles as a function of physical radius. The profiles are colored according to the galaxy’s X- ray gas luminosity, revealing a slightly higher entropy levels for fainter galaxies due to their lower densities. The solid circles show the average of all profiles, obtained from binning all profiles into radial segments and averaging over the data points. The combined profiles shows a slope of ∼ 0.61 within 1 kpc, which steepens to ∼ 0.98 between 5 − 25 kpc. All profiles exhibit similar shapes and none show evidence for an “entropy floor” in their cores. The dashed line indicates a slope of 1.1, a prediction of shock-heated accretion models, developed for galaxy clusters...... 214 6.11 The Logarithm of the X-ray temperature as a function of X-ray luminosity. Black, filled diamonds are our X-ray data for elliptical galaxies. The grey symbols are group data (circles) from Helsdon and Ponman (2000) and cluster data (triangles) from (Wu et al. 1999), reproduced from a review by Mulchaey (2000). Clusters, groups and normal elliptical galaxies form a continuous relation, with groups and galaxies dropping off from the best-fit for the cluster data (solid line, adopted from Wu et al. 1999), continuously steepening the LX–TX relation at lower luminosities...... 217 21 Chapter 1

Introduction

1.1 Structural and Photometric Properties of Nor-

mal Elliptical Galaxies

8 13 Normal elliptical galaxies have stellar masses of ∼ 10 − 10 M and absolute

B magnitudes ranging from −15 to −23. Their characteristic red colors are caused by an old stellar population, in which the blue high-mass stars have already died through type II supernovae and dispersed their mass and gas into the interstellar medium. The stellar surface brightness profiles of elliptical galaxies are generally well approximated by the deVaucouleurs profile, also known as the r1/4 law. A better description is given by the slightly more complex Sérsicprofile, defined as I(r) =

1/n I(Re) exp −bn (r/Re) − 1 , where bn ≈ 1.999 − 0.327. This proﬁle is fully

described by a set of three parameters: the eﬀective radius Re, the surface brightness

at this radius I(Re) and the S´ersicparameter n, which produces “cuspy” central

proﬁles for large n and more of a “core” structure at larger radii for small values of

Several important scaling relations have been found that systematically link pho-

tometric and structural parameters for elliptical galaxies. An example is the Faber- 22

Jackson relation, which relates the galaxy luminosity L to the velocity dispersion σ

(Faber and Jackson 1976). This relation has been found to be the nearly edge-on view of a very tight 2-dimensional plane in a 3-dimensional parameter space, spanned by the mean surface brightness Ie, the eﬀective radius Re, and σ (e.g. Bernardi et al.

2003). This important correlation is called the fundamental plane and usually under-

stood as a consequence of the virial theorem, modiﬁed by non-homology and changes

in the stellar populations (Trujillo et al. 2004), and is one of the main tools to study

the structure and origin of elliptical galaxies.

As their name already implies, the isophotal structure of elliptical galaxies is gen-

erally well-described by ellipses with diﬀerent major and minor axes a and b. The

ellipticity = 1 − b/a is the most basic structural parameter to characterize the gen-

eral shape of elliptical galaxies. The true, intrinsic 3-dimensional shape is thought to

cover the whole range from prolate to oblate, and even triaxial objects. The origin of

the ellipticity can be attributed to two diﬀerent mechanisms. The ﬁrst is rotational

support, which is important for fainter elliptical galaxies with −18 < MB < −20.5 and results in a “disky” appearance of their isophotes. Brighter elliptical galaxies on the other hand are solely pressure supported by their velocity dispersion and the anisotropy in the velocity dispersion is responsible for the apparent ellipticity. How- ever, stellar rotation is still common in these galaxies, but no longer has a signiﬁcant inﬂuence on the shape, which can generally be described as being slightly “boxy”. 23 1.2 X-ray Observations of Elliptical Galaxies

1.2.1 Historical Background

Before the launch of the Einstein Space Observatory in 1978, little was known

about X-ray emission of elliptical galaxies, which were thought to be simple gas-free

stellar systems. But with the help of this ﬁrst X-ray imaging satellite, astronomers

soon started to discover substantial extended emission (e.g. Forman et al. 1985). Un-

fortunately the low sensitivity of the Einstein High Resolution Imager (HRI), leading

usually to a total of less than ∼ 200 detected X-ray photons, made it hard to clearly

identify the origin of the X-ray emission.

Twelve years later its follow-up, the Röntgensatellite (ROSAT) made this possible for the first time. The collaboration of Germany, US and UK represented a significant improvement in imaging, spectral resolution, and sensitivity. The X-ray spectra could be modelled in a more sophisticated way and two major spectral components could be separated: a harder component thought to originate from stellar sources and a softer component from the hot interstellar medium (e.g. Fabbiano et al. 1994), although the

relative contributions of each component were still quite unconstrained.

In 1999 a new era in X-ray astronomy began with the launch of two new X-ray

satellites: the Chandra X-ray Space Observatory and XMM-Newton. Both observa-

tories have unique capabilities which are actually quite complementary. While XMM

has exquisite spectral resolution and a large collecting area, Chandra is the ﬁrst X-ray 24 imaging satellite with sub-arcsecond spatial resolution. The work in this dissertation will exclusively rely on Chandra observations of 54 normal elliptical galaxies, but we note the potential of a similar study with XMM to study the metallicity distribution in the hot gas in more detail.

1.2.2 The Importance of Understanding the Point Source

Component

Thanks to the excellent spatial resolution of the Chandra telescope it is now possible to resolve a large fraction of the X-ray emission in normal ellipticals into discrete point sources, leaving a cleaner view of the diﬀuse gas emission. An analysis of the spatial distribution of the point sources suggests that most of them are of stellar origin, and a spectral analysis identiﬁes them as low-mass X-ray binaries (LMXBs; e.g.

Sarazin et al. 2003). Another small fraction of the point sources are also believed to be supernova remnants, in addition to some background objects comprised of distant

AGN.

It is very important to understand the nature of these point sources, as not all of them are resolved. A signiﬁcant fraction is simply too faint and still below Chandra’s detection limit. Thus, one has to exert caution when interpreting the spectra or the spatial distribution of the diﬀuse emission, as the hot gas emission may still be severely contaminated by unresolved LMXBs. A prime example is the historical “Iron- discrepancy” problem in elliptical galaxies: spectral analyses of X-ray observations of 25

elliptical galaxies with the spectrographs on ASCA or ROSAT yielded consistently

low metal abundances, at odds with the solar or even super-solar values expected from

wind models (Ciotti et al. 1991). A recent study by Humphrey and Buote (2006) has resolved this long-standing problem with high-resolution Chandra data. They ﬁnd solar abundances for most of their sample, and claim that a signiﬁcant part of this new result is due to the fact that they were able to resolve and then exclude many point sources from their data.

For a spatial analysis of the hot gas, things are equally bad, because the diﬀuse emission is a superposition of two diﬀerent components, often of comparable strengths.

We will present a new technique in chapter 2, that spatially disentangles these two

contributions, using the spectral properties of the hot gas and the unresolved point

sources, leaving a clear, uncontaminated view of the gas alone for the ﬁrst time.

1.3 The Hot Interstellar Medium

1.3.1 Origin

The hot gas in elliptical galaxies is thought to have two main sources: (1) stellar

mass-loss and (2) external accretion.

The arguments for the importance of stellar mass-loss are based on the prevalence

of an old stellar population in elliptical galaxies. Stellar evolution models predict

that stars in the asymptotic giant branch lose up to ∼ 0.3M by driving stellar 26

winds. The ejected gas is then heated through collisions and shocks to the virial

temperature around ∼ 106 − 107K. The integrated stellar mass-loss rate for old

−1 11 stellar populations is believed to sum to an average of ∼ 1.3M yr per 10 LB (e.g.

Mathews and Brighenti 2003a), which can easily add up to the observed amounts of

8 11 gas (10 − 10 M ) over the lifetime of the galaxy. Thus, stellar mass-loss is thought

to be one of the main sources of the hot interstellar medium in X-ray faint elliptical

galaxies.

On the other hand, elliptical galaxies are primarily found in dynamically active

environments, such as groups and clusters. While this fact in itself already argues

for the presence of an extragalactic source of gas, the intergalactic medium, it also

increases the chances of interactions or even mergers with neighbor galaxies, during

which signiﬁcant amounts of hot gas can be accreted (e.g. Statler and McNamara

2002).

1.3.2 Evolution

The hot interstellar medium in elliptical galaxies is believed to undergo several

stages of evolution. In the early days, when young stars are still present in the

galaxies, the kinetic energy injected by type II supernovae is more than suﬃcient to

drive a galactic wind (e.g. Ciotti et al. 1991). This wind is believed to essentially

evacuate all the gas in the galaxy and fuel a circumgalactic gas reservoir (Brighenti 27

and Mathews 1998), which may be also ﬁlled by gas accreting from the cosmological

ﬂow (Mathews and Brighenti 2003a).

Depending on the strength of the gravitational potential, this gas may or may not be accreted back on to the galaxy at a later time. If the galaxy is in a group or cluster environment, the circumgalactic gas gets gravitationally heated in the deeper potential to temperatures well above the virial temperature for the galaxy. This hotter ambient gas reservoir is then also thought to be responsible for creating the positive temperature gradients commonly observed in luminous elliptical galaxies.

While the SN driven wind phase ends after a few Gyrs for massive elliptical galaxies, the energy input by type Ia SN may still be sufficient to drive a wind in many nearby X-ray faint galaxies even today. For the more massive systems, the gas is thought to settle down after the wind has ceased, and some of the expelled gas ac- cretes back onto the galaxy. The gas is then thought to enter a quasi-hydrostatic phase. Radiative cooling becomes energetically very important, as the density rises and the cooling time drops, allowing the gas close to the galaxy center to radiate significant fractions of its kinetic energy in only a few 100 Myr. Thus, the central regions lose pressure support and the outer gas starts to subsonically flow inward, developing a slow galactic cooling flow. 28

1.3.3 Hydrostatic Equilibrium

From the very beginning of X-ray studies of elliptical galaxies, it has been one

of the main assumptions that the hot gas is in hydrostatic pressure equilibrium with

the underlying gravitational potential (Forman et al. 1985). The main argument for

this assumption was mainly the fact that X-ray emission from elliptical galaxies was

observable at all. If the galaxy were driving a wind, the densities would generally

be much lower, and the galaxy’s X-ray luminosity signiﬁcantly lower. Thus, it was

assumed that the more massive galaxies are in the last evolutionary stage that we laid

out in the last section. The gas ﬂow would therefore be highly subsonic and the gas

would be in hydrostatic equilibrium, at least to a good approximation. Over time the

assumption of hydrostatic equilibrium has been widely accepted and only relatively

little work has been devoted to prove or disprove this assumption. Nevertheless, the

little work that has been done has been rarely in favor of hydrostatic equilibrium

(e.g. Ciotti and Pellegrini 2004; Mathews and Brighenti 2003b; Pellegrini and Ciotti

2006; Statler and McNamara 2002). Unfortunately, these analyses have usually been

restricted to the in-depth analysis of individual objects, which is why they have

been largely disregarded as general statements. Still the presumption persists that

hydrostatic equilibrium holds in the majority of early-type galaxies (e.g. Humphrey

et al. 2006; Fukazawa et al. 2006).

This simple assumption of hydrostatic equilibrium has far reaching consequences, as the internal pressure gradient of the hot gas is predicted to exactly balance the 29

inward gravitational pull of the potential. Thus, one can study the radial structure

of the total mass distribution according to the following relationship (Forman et al.

1985): k d log ρ d log T M(r) = −rT (r) + , (1.1) Gµmp d log r d log r

which relies only on the knowledge of the observable density and temperature gradi-

ents. Alternatively, Buote and Canizares (1994) use the shape of the X-ray emission to infer the shape of the underlying potential. Based on hydrostatic equilibrium, these X-ray derived mass proﬁles have been among the strongest supporters of dark matter halos around normal elliptical galaxies (e.g. Forman et al. 1985; Killeen and

Bicknell 1988; Paolillo et al. 2003; Humphrey et al. 2006; Fukazawa et al. 2006).

Detailed comparisons with independently derived mass proﬁles have been rather rare and often inconclusive. Fukazawa et al. (2006) make a systematic comparison of their X-ray mass measurements with various optical measurements and ﬁnd reasonable agreement, with typical discrepancies on the order of ∼ 30% being the norm.

However, they also ﬁnd 3 galaxies, which diﬀer by a factor of ∼ 2 and one galaxy,

NGC 3379, that is even oﬀ by a factor of ∼ 7. Nevertheless, they still conclude that their measurements are generally reliable and hydrostatic equilibrium holds in general. In a follow-up study on the large discrepancy for NGC 3379, Pellegrini and

Ciotti (2006) model the X-ray proﬁle with a non-hydrostatic wind, and can easily reconcile their model with the X-ray data, while staying consistent with the mass proﬁle derived from stellar kinematics. 30

The standard assumption of hydrostatic equilibrium may not be so well-founded after all. In chapter 4, we will provide a morphological test for hydrostatic equilibrium, based on a comparison between X-ray gas morphology and stellar distribution for our large galaxy sample.

1.4 The Role of the Central AGN in Clusters

Mainly due to the exquisite spectral resolution of XMM-Newton we now know that the cooling ﬂow model is ﬂawed, at least for the more massive clusters of galaxies.

XMM spectra show no evidence for the massive amounts of gas cooling from X-ray temperatures, as predicted by standard cooling ﬂow models (Peterson and Fabian

2006). There are several ideas on how to save the cooling ﬂow scenario. In principle, it is possible to “hide” the emission of the cooling gas by absorption through cold gas.

However, this would require massive amounts of cold gas, which should be detectable at other wavelengths, but have never been observed so far (Mathews and Brighenti

2003a; Bregman et al. 2006). The other possibility is to prevent the gas from cooling altogether by invoking the presence of a heat source.

High-resolution Chandra images of clusters have revealed such a possible heat source: the central active galactic nucleus (AGN). Massive cD galaxies in the centers of clusters are known to harbor supermassive black holes in their centers, which can power energetic radio jets, extending well beyond the optical extent of the galaxy itself. Chandra is able to capture the direct interaction of the jet with the hot in- 31

tracluster medium, which is apparently subsonically inﬂating “bubbles” of hot gas,

pushing the intracluster medium aside (e.g. McNamara et al. 2000). These bubbles

are believed to eventually detach from the radio source and to buoyantly rise in the

cluster gas, leaving depressions in the surface brightness distribution without obvious

radio counterparts, nicknamed “ghost cavities” (McNamara et al. 2001).

While it is clear that the luminosities of typical AGN have the potential for oﬀ-

setting cooling in clusters, it is still unclear how this energy is actually transferred

to the hot gas. A systematic analysis of the mechanical pdV work needed to inﬂate these bubbles by (Bˆırzanet al. 2004) shows that their mechanical energies range from

∼ 1060 erg for rich clusters to ∼ 1055 erg in galaxies and groups. This may be suﬃcient

to quench the cooling by “eﬀervescent heating” as the bubbles rise in the potential

and expand (Roychowdhury et al. 2004), at least for short periods of time. The dis-

covery of ripples in the intracluster gas of Perseus (Fabian et al. 2006), may provide

a means to distribute heat into the gas by sound waves over an extended region. And

last but not least, heat conduction may also play an important role (Voigt and Fabian

2004).

These are just some of the main theories for AGN feedback in clusters of galaxies,

and the list is in no way complete and growing by the day. It is still quite controversial

if or how the AGN is able to prevent the hot gas from cooling. 32 1.5 Open Questions for Normal Elliptical Galaxies

The cooling ﬂow problem also exists in normal elliptical galaxies, where the cooling gas has also not been observed in the predicted amount (Bregman et al. 2006). Thus, the question arises again of what can heat the gas and prevent it from cooling. SN feedback is a possible source of energy, but neither do the observed radial metallicity gradients match predictions, nor are the wind models able to reproduce the typical

X-ray properties over long periods of time (Mathews and Brighenti 2003a). Only very X-ray faint elliptical galaxies have properties that are consistent with SN driven winds (e.g. Pellegrini and Ciotti 2006). Compressive heating during the cooling inﬂow may provide another source of heat, but is insuﬃcient to explain the lack of cooling in the rather shallow cores of X-ray bright elliptical galaxies.

The only other explanation left is the central AGN. But normal elliptical galaxies reside in a very diﬀerent mass regime than clusters. Their total masses are lower by orders of magnitude, as are the gas fractions, and also the masses of the black holes residing in their centers. The luminosities of the radio sources that they power are accordingly much lower. Only very few galaxies actually have powerful jets that resemble those seen in cluster cDs, and most of them are consistent with small, unresolved central point sources, if they are detected at all at radio wavelengths.

Is AGN feedback generally important for normal elliptical galaxies? Or are their eﬀects restricted to a few individual objects with extended radio jets, such as the well-known galaxy NGC 4374 (Finoguenov and Jones 2001)? If not, what else could 33

be reheating the gas? If they are important, which eﬀects do they have on the gas

morphology and overall properties of the gas? And in that sense, what is actually the

hydrodynamic state of the gas? Is it truly in hydrostatic equilibrium, the common

assumption?

In this work, we will address these important questions through a morphological

and spectral analysis of 54 elliptical galaxies in the Chandra public archive.

1.6 Outline of the Project

The work presented in this dissertation is the result of the ﬁrst comprehensive

morphological and spectral analysis of the hot gas in a sample of 54 normal elliptical

galaxies, exploiting the unique capabilities of the Chandra satellite.

In chapter 2, we will start out with a general characterization of the hot gas struc-

ture through global parameters: the eﬀective radius RX, the average surface bright-

ness IX within RX, and the average X-ray gas temperature TX. We ﬁnd that these parameters form a tight 2-dimensional relationship, akin to the optical fundamental plane relation. Accordingly, we name this new relation the “X-ray Gas Fundamental

Plane”, or XGFP. We will show that the XGFP is extremely tight, in fact as tight as the optical fundamental plane and discuss its connection and implications for the important LX,gas–TX relation.

Chapter 3 describes a new adaptive binning technique, based on Weighted Voronoi

Tesselations. This new analysis method, which we call “WVT binning” has been 34 developed to enable a quantitative morphological analysis of our galaxy sample. We describe the principles of the algorithm, test results, and discuss sample applications to various types of data, including X-ray images, color maps, and temperature maps.

We also point out the shortcomings of adaptive smoothing techniques, a standard visualization technique commonly used in X-ray astronomy.

The new WVT binning method makes the morphological analysis in chapter 4 possible. Here, we isolate the hot gas emission with an innovative isolation technique and adaptively bin the image to present the Chandra gas gallery for elliptical galaxies.

We use optical images and publicly available optical photometry to show that the shape of the hot gas emission and of the starlight have surprisingly little in common and that the gas cannot be in hydrostatic equilibrium with the gravitational potential.

We reject rotational support of the gas as the underlying cause and ﬁnd instead, that the hot gas is generally disturbed and asymmetric. We end this chapter by discussing the severe implications of our ﬁndings for dark matter mass estimates, that are based on the assumption of hydrostatic equilibrium.

In chapter 5, we go after the origin of the asymmetries in the hot gas. We introduce a new statistical measure for asymmetry and ﬁnd that it is strongly correlated with the radio and X-ray power of the central AGN. We ﬁnd that the asymmetries are further completely unrelated with galaxy environment and conclude that the AGN is the only dominant factor to shape the gas morphology. The most striking result is that this

AGN–morphology connection persists down to the weakest AGN luminosities. This 35

discovery suggests that AGN feedback may be important in preventing the hot gas

from cooling, even for rather low-lumiosity elliptical galaxies.

Chapter 6 describes the analysis of radial temperature, density and entropy profiles and their implications for cooling flows, supernovae heating, and AGN feedback. Our radial temperature profiles show the standard positive temperature gradients, but also reveal a new class of negative temperature gradients with warmer centers. We also find evidence for hybrid cases with a small warm central region, and a positive temperature gradient at larger radii. We interpret these findings by analyzing the inner and outer temperature gradient separately, and correlate them with various properties of our galaxies. We find that the outer temperature gradient is defined by environmental influences, while the inner temperature profiles shows a strong correlation with radio luminosity and a weaker correlation with stellar mass. We find that our data are consistent with compressive heating in cooling flow models, but that AGN feedback is the most likely explanation.

We then ﬁnish in chapter 7 with a short summary of our results and their implications for the role of AGN feedback in normal elliptical galaxies. We discuss the current state of the ﬁeld and lay out the major gaps in the current knowledge. 36 Chapter 2

A Fundamental Plane Relation for

the X-Ray Gas

2.1 Introduction

Elliptical galaxies lie on a two-dimensional locus, known as the fundamental plane

(FP), in the space deﬁned by the optical eﬀective radius Re, optical surface brightness

Ie, and stellar velocity dispersion σ0 (Djorgovski and Davis 1987; Dressler et al. 1987).

The FP is understood to be a consequence of the virial theorem, modiﬁed by stellar

population variations and structural nonhomology for systems of diﬀerent luminosity

(Trujillo et al. 2004, and references therein). FP-like scaling relations have been found

for other types of systems as well, including galaxy clusters (Schaeﬀer et al. 1993).

Several authors have pointed out “cluster fundamental plane” relations involving either optical parameters alone (Adami et al. 1998) or mixtures of X-ray and optical parameters (Fritsch and Buchert 1999; Miller et al. 1999). Because the baryonic mass in clusters is dominated by intracluster gas at temperatures & 1 keV, X-rays are a

better tracer of ordinary matter than starlight. Fujita and Takahara (1999b) show the existence of a cluster FP purely in X-ray parameters (see also Annis 1994), which they show can be consistent with simple spherical collapse (Fujita and Takahara 1999a). 37

An “X-ray fundamental plane” for elliptical galaxies—actually a relation between

stellar dispersion, X-ray luminosity, and half-light radius—has been suggested by

Fukugita and Peebles (1999). But in normal ellipticals,1 the mass of X-ray gas is

typically only a few percent of the stellar mass (Bregman et al. 1992). Much of the

X-ray ﬂux comes from low-mass X-ray binaries (LMXBs); if not accounted for, this

guarantees a correlation between X-ray and optical luminosity. Normal ellipticals are

thought to lose most of their gas in supernova-driven winds (Ciotti et al. 1991), and

high-resolution observations using Chandra show that many appear disturbed, sug-

gesting redistribution of gas through shocks, nuclear activity, mergers, or interaction

with the intergalactic medium (e.g Finoguenov and Jones 2001; Jones et al. 2002a;

Machacek et al. 2004; Statler and McNamara 2002). Thus, the visible hot gas is

only a tenuous leftover of a complex hydrodynamical history, and may be far from

equilibrium.

Nonetheless, in this Letter we report the discovery of a fundamental plane relation

for the X-ray gas alone. We show that the X-ray Gas Fundamental Plane (XGFP) is

distinct from—but as tight as—the stellar fundamental plane (SFP). Unlike the SFP,

the XGFP is not a simple consequence of the virial theorem. In fact, the XGFP is

almost completely decoupled from the SFP, and thus constitutes a new constraint on

the evolution of normal elliptical galaxies.

1For our purposes, normal ellipticals are those that are not at the centers of cluster potential wells. 38 2.2 Data Reduction and Analysis

2.2.1 Chandra Archive Sample and Pipeline Reduction

We analyze a sample consisting of 56 E and E/S0 galaxies having non-grating

ACIS-S exposures longer than 10 ks in the Chandra public archive. Brightest cluster

galaxies and objects with AGN-dominated emission are excluded. All observations

are uniformly reprocessed using version 3.1 of the CIAO software and version 2.28 of

the calibration database. Flares are removed by iteratively applying a 2.5σ threshold.

For the quiescent background, intervals more than 20% above the mean count rate

are excised, to match the blank sky background ﬁelds. We restrict photon energies

to the range 0.3–5 keV, further divided into soft (0.3–1.2 keV) and hard (1.2–5.0 keV)

bands. Monoenergetic exposure maps are created in steps of 7 in PI (∼ 100 eV). An

image is extracted for each 14.6 eV-wide PI channel, and divided by the energeti-

cally closest exposure map to create a photon-ﬂux-calibrated “slice.” The slices are

summed to produce the calibrated photon ﬂux images. Full details of the analysis

and results, along with data products, will be presented in future papers (Diehl and

Statler 2006b,c).

2.2.2 Isolating the Gas Emission

Point sources are identiﬁed in each band by CIAO’s wavdetect tool. Regions en-

closing 95% of the source ﬂux are removed and the holes ﬁlled with counts drawn 39

from a Poisson distribution, whose pixel-by-pixel expectation value is determined by

adaptive interpolation using the asmooth tool in the XMMSAS package. A uniform

background is determined from ﬁts to the radial surface brightness proﬁle, and sub-

tracted.

To remove the contribution of unresolved point sources, we use the fact that the

hot gas and LMXBs contribute diﬀerently to the soft and the hard bands. Let S and

H represent the background-subtracted soft and hard images. We can express both

in terms of the unresolved point source emission P , the gas emission G, and their

respective softness ratios γ and δ:

S = γP + δG (2.1)

H = (1 − γ)P + (1 − δ)G. (2.2)

The uncontaminated gas image is then given by

1 − γ γ G = S − H . (2.3) δ − γ 1 − γ

Assuming that resolved and unresolved LMXBs share spatially independent spec-

tral properties, we can use the resolved sources to determine the constant γ. We

00 take sources between 5 and 5Re from the center, excluding high luminosity sources

(> 200 counts). For systems with > 10 sources meeting these criteria, we ﬁt an absorbed power law model to the combined point source spectrum, with hydrogen column density ﬁxed at the Galactic value for the line of sight. Integrating the model over the soft and hard bands yields γ. For other galaxies, we exploit the universal 40

nature of the LMXB spectrum (Irwin et al. 2003). A simultaneous power-law ﬁt to

37 −1 all low-luminosity (LX ≤ 5 × 10 erg s ) point sources in our sample gives a photon

index of 1.603. This model is used to derive γ for the source-poor galaxies.

The coeﬃcient δ is determined similarly, from the ﬁt of an APEC thermal plasma

model (Smith et al. 2001) to the hot gas emission (see § 2.2.3). This approach assumes

isothermal gas throughout the galaxy. In case of a temperature gradient, one would

have to account for the spatial dependence of δ, but this approach is beyond the scope of this Letter.

2.2.3 Physical Parameters for the Gas

To produce a radial proﬁle, we adaptively bin the gas image G into circular annuli.

In 12 cases there is insufficient signal to fit the spatial profile. We fit the remaining profiles with Sérsicmodels to derive X-ray half-light radii RX and mean enclosed

2 surface brightnesses IX . We discard 14 objects with RX larger than the size of the

observed ﬁeld. The ﬁnal sample of 30 objects has B absolute magnitudes in the range

−22.5 < MB < −19. Twenty-one are group members, and 14 are brightest group galaxies (Garcia 1993). Eight of the 14, plus 3 additional objects, are central members of X-ray-bright groups in the GEMS survey (Osmond and Ponman 2004). We ﬁnd

that up to 55% (typically 10–30%) of the diﬀuse emission in the ﬁnal sample comes

from unresolved LMXBs. 2Fits using β and double-β models are unphysical in more than half the cases, implying divergent ﬂuxes at large radii. 41

The spectrum of the diﬀuse emission between 0.3 and 5 keV is extracted from

a circular region 3Re in radius, excluding resolved point source regions. We ﬁt the

spectrum using the SHERPA package, adopting a single temperature APEC thermal

plasma model for the hot gas and a power law for the unresolved LMXBs. The

normalizations of both components, the gas temperature TX , and (in most cases) gas

metallicity are allowed to vary. The redshift is set to the value given in the Lyon–

Meudon Extragalactic Database (LEDA; Paturel et al. 1997). For low signal-to-noise

spectra, the abundances are held ﬁxed at the solar value. The photon index of the

power law component is determined by a simultaneous ﬁt to the spectrum of the

lowest luminosity resolved point sources (§ 2.2.2). Single-temperature APEC models are poor ﬁts (reduced χ2 > 2) to 12 objects. In these cases the temperature should be interpreted as an emission weighted average. Excluding these galaxies from the sample does not change the results.

All errors are assumed to be Gaussian, described by a covariance matrix. Sta- tistical errors on RX , IX , and TX are obtained from the ﬁtted models. We adopt

distances and errors obtained from surface brightness ﬂuctuations (Tonry et al. 2001)

where available; otherwise we use LEDA values3 and assume errors of 15%. We adopt a 10% uncertainty in γ from the galaxy-to-galaxy scatter in the photon indices ﬁtted to the composite point-source spectra, and a 5% uncertainty in δ from a comparison of values obtained from the spectral ﬁts and from direct integration of gas-dominated

3 LEDA distances are obtained from a B-band Faber-Jackson relation of the form MBT = −6.2 log σ − 5.9. 42

spectra over the hard and soft bands. We measure the eﬀect on RX and IX by repeating the spatial ﬁts with altered values of γ and δ.

−1 −2 −2 Table 2.1 lists the base-10 logarithms of RX (kpc), IX ( erg s cm arcsec ) and TX ( keV) for the ﬁnal sample of 30 galaxies, and the corresponding non-zero elements of the covariance matrix. 43

Table 2.1. Physical parameters for the X-ray gas

ID log log log CRR CII CTT CRI 4 4 6 4 RX IX TX ×10 ×10 ×10 ×10

I1459 0.93 −16.73 −0.318 276.3 48.4 259.5 −29.2 I4296 0.35 −15.18 −0.055 59.3 32.8 56.2 −12.1 N193 1.34 −16.79 −0.114 44.9 20.0 43.3 −0.6 N315 0.62 −15.77 −0.196 60.5 58.1 75.4 −12.4 N533 0.73 −14.99 −0.009 53.1 90.0 11.4 −13.6 N720 0.96 −16.46 −0.247 48.0 41.3 36.9 −20.0 N741 0.64 −15.27 −0.016 84.0 91.5 72.8 −30.5 N1316 0.43 −15.60 −0.210 59.2 43.4 35.9 −9.2 N1404 0.52 −15.31 −0.234 17.5 40.7 7.6 −1.6 N1407 0.56 −15.61 −0.061 29.8 32.5 6.4 −1.4 N1553 1.02 −17.10 −0.392 88.2 1236.5 190.2 2.1 N2434 1.16 −17.42 −0.273 362.9 29.7 621.3 −79.1 N3923 0.23 −15.32 −0.322 47.0 24.1 217.4 −7.2 N4125 1.09 −16.82 −0.356 61.2 38.0 57.6 −6.2 N4261 0.22 −15.27 −0.110 21.0 46.2 56.4 −5.4 N4374 0.28 −15.30 −0.151 6.1 65.0 15.4 −0.9 N4526 0.58 −16.71 −0.450 405.6 95.5 1328.8 −89.2 N4552 0.01 −15.20 −0.245 9.0 545.0 20.1 −2.2 N4621 1.29 −18.05 −0.629 456.5 74.8 2359.7 −133.9 N4636 0.76 −15.60 −0.160 73.1 1092.3 0.9 −98.1 N4649 0.35 −15.08 −0.096 15.8 39.4 2.0 −7.3 N4783 1.14 −16.57 0.053 479.8 114.8 878.3 −105.1 N5044 1.07 −15.24 −0.041 34.1 55.8 1.5 −3.1 N5846 0.91 −15.74 −0.152 17.3 40.0 4.3 −0.5 N6482 1.54 −16.34 −0.131 286.8 118.1 21.3 −67.3 N7052 1.08 −16.13 −0.278 1323.9 507.3 626.0 −209.1 N7618 1.59 −16.34 −0.095 73.8 27.2 35.4 −6.8 44 2.3 The X-Ray Gas Fundamental Plane

The distribution of galaxies in the parameter space (log RX , log IX , log TX ) is nearly planar. This is seen clearly in Figure 2.1, which shows face-on and edge- on views of the XGFP. We determine the intrinsic distribution in this space by ﬁtting a probability density in the form of a tilted slab with ﬁnite Gaussian width, taking correlated errors into account.

We can express the XGFP in the form

a b TX ∝ RX IX , (2.4) where a and b determine the orientation of the plane. The best-ﬁt values are a = 0.28 and b = 0.22 (Figure 2.2). The formal 1-dimensional errors in a and b are 0.045 and

0.037, respectively; but as the figure shows, the errors are correlated. The intrinsic width of the XGFP is very small, with a value of 0.068 ± 0.012 dex, which is identical to that of the SFP (Bernardi et al. 2003) to within the errors. The fit is robust and not sensitive to the choice of model for the surface brightness profile. Excluding the brightest group galaxies or galaxies with bad single-temperature fits results in a and b values within the 68.3% confidence ellipse in Figure 2.2. 45

Figure 2.1: Face-on (top) and edge-on (bottom) views of the X-ray Gas Fundamental Plane. Axis labels indicate eigenvector components. Symbol sizes roughly indicate the relative positions into and out of the page. Error bars indicate 1σ-projections of the covariance matrices. Arrows illustrate the sense of view relative to the fundamental measured parameters. 46

Figure 2.2: Exponents a and b, describing the orientation of the XGFP according to equation (2.4). Cross and ellipses indicate best-ﬁt values and conﬁdence regions, respectively. Diagonal line marks combinations of a and b corresponding to pure luminosity-temperature correlations of the form L ∝ T n.

2.4 Discussion

2.4.1 Relation to Known Scaling Laws

If a and b obeyed the relation a = 2b, the XGFP would be equivalent to a simple

2/a luminosity–temperature relation of the form LX,gas ∝ TX , indicated by the solid line in Figure 2.2. The model ﬁt rules out a pure LX,gas–TX relation at > 99.7%

conﬁdence. The LX,gas–TX relation represents a nearly edge-on view of the XGFP,

analogous to the Faber-Jackson relation (Faber and Jackson 1976) for the SFP. As 47

in the optical case, the XGFP accounts for much of the intrinsic scatter (0.091 dex)

4 in the LX,gas–TX relation. For a given TX , galaxies with more extended gas emission

are more luminous than compact objects.

The LX –TX relation most nearly consistent with the XGFP is given by LX,gas ∝

8.5 T (Figure 2.2). A naive principal component analysis in the LX,gas–TX plane yields

4.8±0.7 a shallower exponent of 5.9. O’Sullivan et al. (2003) ﬁnd LX,tot ∝ TX for their complete sample, and a steeper exponent of 5.9 ± 1.3 when they exclude galaxies with prominent temperature gradients. However, their X-ray luminosities include unresolved LMXBs, the removal of which would steepen the LX –TX relation.

A comparison can also be made with the LX –σ relation for ellipticals. Mahdavi

10.2+4.1 and Geller (2001) ﬁnd LX,tot ∝ σ −1.6 , and predict this relation to steepen to LX,gas ∝

12±5 σ if LX is restricted solely to the hot gas. Using the temperature-dispersion

0.56 correlation σ ∝ TX (O’Sullivan et al. 2003), we can approximate our closest LX –TX

15 relation as LX,gas ∝ σ , which is consistent with the earlier result.

Fujita and Takahara (1999b) obtain a result vaguely similar to ours for clusters of

galaxies. They ﬁnd an X-ray cluster FP connecting core radius, central density, and

mean cluster temperature. Assuming a constant value of β = 2/3 for their surface

brightness profile fits, we can translate their cluster FP to our parameters, finding

0.57 0.32 TX ∝ RX IX . Their relation is significantly inclined to our XGFP, and is close to 4Gas luminosities are obtained by summing the observed flux in the field of view and using the fitted Sérsic law to account for the flux at larger radii. 48

the relation L ∝ T 3. However, the cluster FP deviates from a pure L–T relation in a

manner similar to that of the XGFP.

Fukugita and Peebles (1999) suggest a galaxy fundamental plane with mixed X-

2 ray and optical parameters, LX , RX and σ . Their sample consists of 11 galaxies with ROSAT, Einstein or ASCA observations. We do not reproduce their result with

our larger Chandra sample. The reason for this discrepancy may be that their X-

ray luminosities are corrected neither for light outside the ﬁeld of view nor for the

contribution of point sources.

2.4.2 Independence of the XGFP and the SFP

The virial theorem connects a system’s total mass M with its characteristic radius

RM and dispersion σM . This relation produces an observable SFP because mass maps

to luminosity by way of the mass-to-light ratio, and the stellar Re and σ are surrogates

for RM and σM . For the XGFP to be another manifestation of the virial theorem,

one would require similar mappings from mass parameters into X-ray observables.

One example is hydrostatic equilibrium, which links RX and TX for a given potential.

Others might connect gas mass to total mass or to a measure of gas retainability

2 such as σ /TX . However, these relations would be identiﬁable in correlations between

optical and X-ray parameters. Only the known TX –σ relation (e.g. O’Sullivan et al.

2003) and an additional, very weak TX –Re relation are supported by the data. X-ray

gas masses are uncorrelated with MB and other optical properties. 49

If the SFP and XGFP were linked, then each plane would represent a projec-

tion of a higher dimensional, more fundamental hyperplane into the corresponding

3-parameter subspace. We test this hypothesis by analyzing the (log RX , log IX ,

2 log TX , log Re, log Ie, log σ ) space with principal component analysis (PCA). In this

space our sample is reduced to 25 objects with reliable X-ray and optical param-

eters. We deﬁne the 3-vectors nX and nO to be the normals to the fundamental

planes in X-ray and optical parameters, respectively. From the SFP we have nO =

[0.69, 0.51, −0.51] (Bernardi et al. 2003) and from the XGFP, nX = [0.26, 0.21, −0.94].

If the planes are completely independent, the eigenvectors corresponding to the

p 2 two smallest eigenvalues will have the form N1 = [µ nX, 1 − µ nO] and N2 =

p 2 [ 1 − µ nX, −µ nO]. Here, N1 and N2 are 6-vectors, and µ can be any number between −1 and 1, depending on the relative scatter in the two planes. We obtain N1 =

[−0.21, −0.16, 0.84, 0.20, 0.15, −0.39] and N2 = [0.01, 0.03, −0.38, 0.79, 0.38, −0.28].

This result is not far from the above prediction with µ = −0.40. Furthermore,

the scatter about both planes is not reduced by going to higher dimensions. Both

results point to, at most, weak coupling of the subspaces.

Optical and X-ray parameters are known to be coupled through the observed

2 TX –σ relation. We test whether this coupling could have a measurable eﬀect on

the eigenvectors, using Monte Carlo simulations of 25-object samples following the

ﬁtted SFP and XGFP relations. We take the SFP and XGFP to be independent,

2 except for an intrinsic linear correlation between log TX and log σ with a variable 50 amount of scatter. We consider three coupling strengths: none, weak, and strong.

2 Weak coupling reproduces the observed width (0.10 dex) of the TX –σ relation and, by way of the SFP, the somewhat weaker TX –Re relation; strong coupling reduces

2 the TX –σ width by a factor of 3. We perform PCA on the simulated 6-d data and measure the alignment of the best 2 eigenvectors with those obtained from the real data. All 3 cases reproduce the eigenvectors to within the Poisson noise, showing

2 that the observed TX –σ relation does not change the relation between a decoupled

XGFP and SFP at a level that can be resolved with a 25-object sample.

The data are thus consistent with the XGFP and SFP being almost completely independent. The XGFP cannot be understood as a simple consequence of the virial theorem or hydrostatic equilibrium. Instead, the XGFP represents a new constraint on the hydrodynamic evolution of elliptical galaxies. 51 Chapter 3

Adaptive Binning of X-ray data with Weighted Voronoi

Tesselations

3.1 Introduction

X-ray data are generally very sparse in nature. To deal with this problem, astronomers are often forced to either bin or smooth their data. The most commonly used techniques are simply binning to square blocks of a fixed size or convolving with a fixed kernel. However, due to the large dynamic range in many extended objects, ordinary binning and smoothing techniques are never able to capture structure on large scales without masking detail on smaller scales. This deficiency is the motivation for spatially adaptive algorithms.

With the advent of the two major X-ray satellites, Chandra and XMM-Newton, it is now possible to resolve ﬁne morphological structures in extended X-ray emitting sources, such as galaxies, clusters, or supernova remnants. This calls for new techniques to reliably extract spatial information. Sanders and Fabian (2001, hereafter

SF01) were the ﬁrst to answer with a 2-dimensional adaptive binning algorithm, ap- 52 plicable to background-corrected intensity images and hardness ratio maps. However, this algorithm is restricted to a limited set of bin sizes, which prevents it from being fully adaptive and from adjusting its resolution so as to keep the signal-to-noise ratio

(S/N) constant. This creates jumps in S/N of a factor of ∼ 2, which, along with its quadrilateral bin shapes, can lead the eye and suggest structure that is not there.

Motivated by the diﬀerent problem of analyzing 2-dimensional optical integral

ﬁeld spectroscopic data, Cappellari and Copin (2003, hereafter CC03) developed an innovative adaptive binning technique using Voronoi tesselations. Their algorithm is able to smoothly adjust the bin size to the local S/N requirements and does not impose a Cartesian geometry on the image. Unfortunately, it can be used only with strictly positive, Poissonian or optimally weighted data whose S/N is guaranteed to add in quadrature. This prevents it from being useful in even simple situations in

X-ray astronomy, involving data corrected for exposure map eﬀects or background, or in creating hardness ratio maps.

In this paper, we generalize CC03’s Voronoi binning technique so that it can be used with any type of data. The generalized algorithm makes use of Weighted

Voronoi Tesselations (WVT), and combines the virtues of both CC03’s and SF01’s techniques. It is as robust as, and even more versatile than SF01’s code, yet retains the advantage of CC03’s ﬂexible bin sizes. The algorithm produces smoothly varying binning structures that are geometrically unbiased and do not lead the eye. 53

In section 3.2 of this paper, we review the two binning techniques of SF01 and

CC03 in more detail, pointing out their advantages and drawbacks. In §3.3, we

explain the functionality of the generalized WVT binning technique, and compare its

performance to the two older algorithms in section 3.4. Section 3.5 then demonstrates

the utility of WVT binning in creating X-ray intensity images, hardness ratio maps,

and temperature maps, and in disentangling the diﬀuse gas emission in elliptical

galaxies from the contribution of unresolved point sources. Finally, §3.6 quantitatively

compares WVT binning to commonly used adaptive smoothing algorithms, before

commenting on the availability of the code in section 3.7 and ending with conclusions

in §3.8.

3.2 Existing Adaptive Binning Algorithms

3.2.1 Quadtree Binning

The pivotal work on spatial binning of sparse X-ray data is that of SF01, who

produce surface brightness and color maps for the analysis of X-ray cluster images.

Their algorithm starts with the smallest possible bin size of 1 × 1 pixel and calculates

the S/N for each bin. Each bin with a S/N higher than the user supplied minimal

1 value (S/N)min is marked as binned , its pixel members are removed from the pixel list,

and ignored for the rest of the binning process. In the next iteration, the unbinned

1Sanders and Fabian’s criterion of “maximal fractional error” is equivalent to a “minimal S/N” threshold. 54 pixels are rebinned with square bins of double the side length. The S/N of each bin is computed, and those exceeding the threshold are marked. This process is repeated until either all pixels are binned or the bin size exceeds the image size. Thus, the bins are generally square, with areas of 4n pixels, except for regions at the transition between two binning levels. There, some pixels may have already been binned on a previous level and removed. The resulting bin shapes can be rectangular, L-shaped, or more complicated. Even non-contiguous bins are common.

Owing to its hierarchical structure, which resembles a quadratic tree commonly used in N-body simulations, we refer to this method as “quadtree” binning. Although slightly diﬀerent implementations are conceivable, we take SF01’s version as representative. In section 3.4.1, we make a rigorous quantitative comparison between this algorithm and WVT binning.

3.2.2 Voronoi Binning

Motivated by the need to optimally bin integral-ﬁeld spectroscopic data, CC03 present a method to spatially bin two-dimensional images using Voronoi Tesselations.

The goal is again to obtain a uniform S/N per bin over the entire image, while keeping each bin as compact as possible.

A Voronoi Tesselation (VT) is a partitioning of a region, deﬁned by a set of points called the generators. Each point in the region, or in this case, each pixel in the image, is assigned to the generator to which it is closest. As a consequence of this 55

scheme, the boundary between two adjacent bins is always the perpendicular bisector

of the connecting line between the two generators (Figure 3.1).

A subset of VTs, called Centroidal Voronoi Tesselations (CVTs), has the addi-

tional property that the generators coincide with the centroids of the bins. CVTs

are meaningful when there is a density, ρ, deﬁned over the region to be binned, and

the generators are the density-weighted bin centroids. Since the centroids cannot be

calculated before the bins themselves are constructed, it is necessary to construct a

CVT by iteration. A helpful tool is the Lloyd algorithm (Lloyd 1982), which itera-

tively constructs CVTs with generators at each iteration taken as the centroids from

the previous step. The Lloyd iterations have the desirable eﬀect of moving generators

into regions of higher density, thereby creating smaller bins. For a uniform density,

this algorithm tends to create hexagonal lattice structures (Du et al. 1999).

In binning an image, one generally works with a signal Sk per resolution element

2 k (“pixel” from now on) and the associated noise per pixel, σk. One can compute

the S/N of a bin Vi as P S k∈Vi k (S/N)i = q . (3.1) P σ2 k∈Vi k For pure Poisson statistics, or certain forms of optimal weighting, the (S/N)2 is

additive (CC03). With this restriction, one can make use of a property of the Lloyd

algorithm known as Gersho’s conjecture: applying the Lloyd algorithm to the square

of the density tends to produce a conﬁguration with equal mass per bin (Gersho

2For integral ﬁeld spectroscopy, this is the averaged signal over a ﬁxed wavelength interval. 56

1979). CC03 exploit this conjecture by applying the Lloyd algorithm to the quantity

(S/N)2, thus producing a CVT with a constant S/N per bin.

In order for the Lloyd algorithm to converge, a good initial set of generators is necessary. CC03 solve this problem with a “bin-accretion” algorithm. Starting from the pixel with the highest S/N in the input image, one grows a bin by accreting nearest neighbors until the bin reaches a minimum S/N or violates an imposed “roundness” criterion. Then the next bin is started from the pixel closest to the weighted centroid of all previously binned pixels. This method is guaranteed to generate compact bins within the desired S/N range. Bins that do not meet both of these criteria are marked as “bad” and their pixels are reassigned to the next closest bin. The centroids of the resulting bins are then used as the initial set of generators for the Lloyd algorithm.

By deﬁnition, a Voronoi tesselation can produce neither gaps in the data nor non- contiguous bins. The tesselation adjusts to uneven boundaries smoothly, and the

CC03 algorithm generally converges to a solution with small, spatially independent scatter around the target S/N. The bins are usually very compact, but can get more elongated or ragged close to the boundaries, or in regions with very strong S/N gradients. The principal drawback of CC03’s algorithm lies in its applicability. The algorithm works only for data in which S/N adds in quadrature, as the iterative part is based on Gersho’s conjecture. This precludes the possibility of applying the code to background-corrected or exposure-corrected data, hardness ratios, or other types of 57

data where (S/N)2 is not additive.The bin-accretion algorithm can be used without

this restriction (Sanders et al. 2005, 2004; Fabian et al. 2003)

3.3 Adaptive Binning with Weighted Voronoi Tes-

selations

3.3.1 Introduction to Weighted Voronoi Tesselations (WVT)

As described above, a normal VT assigns each pixel k to the generator zi to which

it is closest; i.e., one ﬁnds the bin to which the pixel belongs by minimizing its distance

to the generator |xk −zi| over all bins i. In order to make this deﬁnition more ﬂexible,

we use a generalization known as a Weighted Voronoi Tesselation (e.g., Møller 1994).

In a WVT, each bin i has an associated scale length δi in addition to its generator zi, and a pixel k is assigned to the bin that minimizes |xk −zi|/δi. One can picture δi as a factor that stretches or compresses the metric inside the bin i. An intuitive analogy is simultaneous crystal growth, with the generators representing the seeds and the scale length representing the growth rate (Møller 1994). A WVT is completely described by its set of generators and scale lengths and can therefore be stored very eﬃciently.

Figure 3.1 illustrates the appearance of a WVT (right) with a simple example of bins with diﬀerent relative scale lengths, and compares it to an unweighted VT with the same generators (left). Note how the bin boundaries move closer to the generators with the smaller associated scale lengths, making their bins rounder and 58 more compact. For WVTs, the boundaries b between two bins i and j always fulﬁll the equation |b − zi|/δi = |b − zj|/δj, implying that the ratio of the bin radii is equal to the ratio of scale lengths. This property is used below to modify the bin sizes by manipulating their relative scale lengths and letting the generator locations adjust.

This replaces the Gersho prescription which changes the bin sizes by explicitly moving the generators.

3.3.2 Adaptive Binning Algorithm

In the following discussion, we assume that there is some general way to combine the signal and noise of various pixels to calculate the resulting S/N for the bins. We emphasize that the details of how the S/N is actually calculated are irrelevant for the functionality of the WVT binning algorithm.

Our algorithm creates a weighted Voronoi tesselation, choosing the scale lengths δi such that the bins have a near-uniform S/N distribution, with the least possible scatter around the target signal-to-noise (S/N)T. To ﬁnd the appropriate scale lengths, it is useful to consider the quantity µi, deﬁned by

(S/N)i µi = , (3.2) Ai

where Ai is the bin area and (S/N)i is the S/N ratio in bin i. The algorithm is aiming for a conﬁguration where the bins have a S/N equal to the target value, (S/N)T. In 59

Figure 3.1: A normal VT (left) and a WVT (right) with identical bin generators zi (crosses). The numbers attached to the bins are the associated scale lengths δi. The dashed lines connect neighboring bin generators. Note how the bin boundaries are always perpendicular to them. For a normal VT, the bin boundaries are the perpendicular bisectors; for a WVT, the dashed lines are divided proportional to the bins’ respective scale lengths. 60

this conﬁguration, we should have, approximately,

(S/N)T µi = 2 , (3.3) q δi

where q is a dimensionless constant that depends weakly on bin shape (for circular bins, q = π). Combining equations (3.2) and (3.3) gives a rule for setting the scale

length at each iteration: s s (S/N)T Ai (S/N)T δi = = · . (3.4) q µi q (S/N)i

Since the binning depends only on the ratio of the scale lengths, the value of q is

unimportant. We show below that good results are obtained taking q = const for

all bins, regardless of shape. This prescription replaces the Gersho-Lloyd procedure

which, at each iteration, moves the generators to the (S/N)2 weighted centroids. Such weighting is superﬂuous in our algorithm, so we adopt the geometric bin centers as the new generators.

The WVT binning procedure thus proceeds as follows:

(i) Start with an initial WVT.

(ii) For each bin i, evaluate the signal to noise (S/N)i, the area Ai and the geometric

centers zi.

(iii) Calculate the scale length δi for each bin according to equation (3.4).

(iv) Reassign all pixels according to the new WVT with generators zi and scale

lengths δi. 61

(v) Return to step (ii) until the bins stop changing signiﬁcantly.

A binning with constant S/N across the field is a natural stable fixed point of this p iteration scheme, as it satisfies the relation δi/δj = Ai/Aj.

As in ordinary Voronoi binning, this algorithm requires a good set of initial genera-

tors. We adopt CC03’s solution of “bin accretion” with a few modiﬁcations for speed,

relaxing some acceptance criteria to suit sparse and not strictly positive data (e.g.

background subtracted X-ray images). We also employ a soft lower S/N boundary

for accepting bins, in which the S/N has no longer to be larger than the ﬁxed target

S/N. Instead, accretion terminates if the addition of another pixel would increase the

scatter around the target S/N. This modiﬁcation keeps the average S/N closer to the

target value.

3.4 Performance

3.4.1 Comparison with Quadtree

While the simplicity of the quadtree binning algorithm makes it easy to understand

and apply, there are several disadvantages, which we illustrate in this section using

simulated X-ray data. A suitable model for the surface brightness proﬁles I(r) of a

galaxy or galaxy cluster is the circular β–model (Sarazin 1988):

" #0.5−3β r 2 I(r) = I0 1 + + IBg, (3.5) rc 62

where I0 is the central surface brightness, rc is the core radius, β is a slope parameter, and IBg is an additive, ﬂat background. We adopt the same parameters used by SF01:

−1 the image size is set to 512 × 512 pixels, rc is 128 pixels, I0 is 100 cts pix , β is 0.67

−1 and IBg is 20 cts pix . The simulated X-ray image is obtained by populating the image with counts according to a Poisson distribution. For the quadtree algorithm, √ a minimum S/N limit of 14 (∼ 20/ 2) produces an average S/N of 19.92 in the test image and is therefore chosen as the equivalent to a target S/N of 20 for the comparison with the WVT algorithm.

The results of the quadtree and WVT binning algorithms are shown on the left and right sides of Figure 3.2, respectively. The middle panels show the full images; the upper panels zoom in on a small region to emphasize the differences between the binning structures. Note that the quadtree algorithm regularly forms non-contiguous bins and can leave single pixels or small sets of pixels “stranded”. In a few cases, these pixels can be directly picked out as isolated dark spots in the image, since a larger binning level usually also corresponds to a lower average flux per bin. This effect occurs predominantly in regions where neighboring pixels have already been binned on a previous binning level. SF01 offer two ways to deal with this problem. The first is to handle isolated sets of pixels of a non-contiguous bin separately, violating the minimum S/N criterion as the bin is being split up. The alternative is to redistribute the pixels to an adjacent neighbor bin. In the latter case, the S/N of the neighboring bin will be elevated, which can lead to an increased scatter in S/N. At the same time, 63 one sacrifices resolution, as the effective number of bins is decreased. Throughout the remainder of this discussion, we do not enforce contiguous bins in the quad-tree algorithm for simplicity. We simply note that this problem is absent in the WVT algorithm, which can easily be made to enforce contiguous bins.

The main problem with the quadtree algorithm lies in its small set of discrete bin sizes. Except in small transition regions, where the bin shapes are not square, the bin area is restricted to values of 4n pixels. This discontinuous distribution of bin sizes is visible in the binned image, and illustrated in the upper panels of Figure

3.3, which show the radial dependence of the bin areas for quadtree (left) and WVT

(right) binning. The solid line indicates the optimal, theoretical bin size needed to produce the target S/N. The discrete steps in the quadtree bin area translate into an inhomogeneous S/N distribution, shown in the lower left panel of Figure 3.3. Each sharp increase in S/N corresponds to a sudden jump in bin size, which decreases the local resolution beyond the requirements of the target S/N. These jumps in S/N are easily visible as circular rings in the fractional diﬀerence image in the bottom left of Figure 3.2, showing that the binning algorithm can create spurious structure.

In contrast, WVT binning allows bins to adjust their size smoothly in single pixel steps, which results in a reduced scatter around the target S/N and the removal of misleading spurious features (bottom right panels of Figures 3.2 and 3.3).

The spatially correlated fractional error distribution resulting from quadtree binning can be particularly misleading when the the bin value is decoupled from the 64

actual S/N distribution. An good example is a hardness ratio map. Here, the signal

is given by a ﬂux ratio of two independent bandpasses, whereas the S/N is determined

by the total ﬂux of both bands. Figure 3.4 show quadtree and WVT binned hard-

ness ratio maps of the Perseus cluster. The eye identiﬁes two concentric rings in the

quadtree binned map (left) at around 50 and 150 arcsec. These features are imprints

of the discontinuous jumps in bin size, and are completely absent in the WVT binned

map (right). WVT binned hardness ratio maps are described in more detail in §3.5.2.

3.4.2 Comparison with VT

As the WVT algorithm generalizes the method of CC03, which was designed for

optical integral ﬁeld spectroscopic data, it is natural to test the code on the same

type of data. We apply our WVT binning algorithm to the test data provided by

Cappellari & Copin, in their on-line code release. The test data consist of a list

of coordinates and signal and noise values of the wavelength-integrated spectra of a

SAURON (Bacon et al. 2001) observation of NGC 2273.

Figure 3.5 compares the results of both algorithms for a target S/N of 50. Both yield consistent results with a comparable scatter around the target S/N of only ∼ 6%.

The only noticable diﬀerence lies in the compactness of the individual bins, especially close to the border and in regions of strong gradients. While CC03’s code tends to generate strongly elongated shapes in these cases, the WVT bins stay consistently rounder. To quantitatively measure roundness, we introduce the average bin radius 65

Figure 3.2: Comparison between Quadtree (left column) and WVT binning (right column); Middle Panels: Logarithmically scaled, binned intensity images. The square indicates the region of the zoom-in shown in the upper panels. Each bin has been outlined to emphasize the diﬀerence in the binning structure. Note the darker “stranded” bins on the left; Lower panels: Absolute fractional diﬀerence between the model surface brightness and the binned simulated data. 66

Figure 3.3: Upper panels: area per bin vs. radius for quadtree (left) and WVT (right), the solid line indicates the theoretical prediction to produce a constant S/N of 20 per bin for our test model. Lower panels: corresponding S/N per bin; note the jumps in S/N due to the discrete bin sizes for the quadtree binning, which is completely absent in WVT; the solid line shows the target S/N, the dashed lines indicate the natural scatter of ∼ 2 in quadtree and the 3σ rms scatter in WVT.

Rav and the eﬀective bin radius Reﬀ :

av 1 X Ri = Rj, (3.6) Ai j∈Vi r A Reﬀ = i . (3.7) i π

The more compact the bin, the smaller is the ratio Rav/Reff . Its minimum at a value of 2/3 represents a perfectly circular bin. Figure 3.6 shows Rav/Reff as a function of the distance from the galaxy center and confirms that the WVT algorithm (filled 67

Figure 3.4: Comparison of quadtree (left) and WVT binning (right); Both panels show adaptively binned hardness ratio maps of the core of the Perseus cluster, with dark colors indicating regions of higher temperature and/or lower photoelectric absorption. Note how quadtree binning leads the eye into identifying two ring structures, due to the strong jumps in the S/N where the bin area suddenly quadruples.

circles) produces more compact bins without edge eﬀects. At a distance of 20 arcsec,

CC03’s Voronoi bins (open circles) get more elongated, as shown by the jump in

Rav/Reff . This is mainly due to CC03’s use of a weighted bin centroid, which pushes the generators toward the bright end of the bin, elongating the bins in the opposite direction. 68

Figure 3.5: Final result after application of the CC03’s Voronoi binning code (left) and the WVT algorithm (right) to the SAURON data of NGC 2273. After completion of the binning process, the bins have been projected onto a ﬁner grid to make it easier to identify diﬀerences in the shape of the bins.

3.5 Applications to X-ray data

3.5.1 Intensity Maps

The most common application for adaptive binning in X-ray astronomy is intensity binning. As discussed above, CC03’s Voronoi binning algorithm is valid only for purely Poissonian data. This would correspond to raw counts for a perfectly ﬂat detector response without any background. However, real X-ray data are not as simple. Many X-ray faint targets have surface brightness values comparable to the background, which itself may be spatially dependent. In addition, real observations exhibit strong variations in eﬀective area per pixel, due to chip gaps, node boundaries, 69

or partly overlapping multiple exposures. An observation’s eﬀective area Ek per pixel k is saved in an “exposure map,” which together with the eﬀective exposure time τ,

3 can be used to convert raw counts Ck per pixel into a ﬂux Fk with physical units of

photons sec−1 cm−2 arcsec−2:

Ck Fk = − Bk. (3.8) Ek τ

Here, Bk is the background ﬂux per pixel. The variance in the same pixel can be expressed as C σ2 = k + σ2 , (3.9) Fk 2 2 Bk Ek τ

where σBk denotes the uncertainty that is attached to the background value. The

prescription for combining these quantities to produce a S/N per bin is given by

equation (3.1). For the hypothetical case where τ = 1, Ek = 1 and FBgk = 0, the

signal Fk reduces to pure counts and the binning scheme will converge to a solution

with a constant number of counts per bin.

We use the well-known 50 ks Chandra observation of Cassiopeia A (Hwang et al.

2000) to demonstrate the power of adaptive binning for X-ray images. The lower

left panel of Figure 3.7 shows the unbinned, exposure map corrected counts image for the full exposure. In the panel directly above, we restrict the data to only 1 ks of exposure time. We bin this image with the WVT algorithm to a target S/N of 5

(upper right). A comparison with the full 50 ks exposure shows that WVT binning

3Alternatively, one can multiply the photon counts with their detected energy to get units of ergs sec−1 cm−2 arcsec−2; see http://cxc.harvard.edu/ciao/download/doc/expmap intro.ps for more details on exposure maps. 70 successfully reduces the noise, bringing out the large-scale features in the outer parts of the image, while keeping the appropriate resolution in the better exposed ﬁlamentary features. Even in this short exposure, one is able to pick out the central neutron star in the WVT binned image. The image in the lower right of Figure 3.7 shows the full

50 ks image, adaptively binned to a S/N of 20, to demonstrate the applicability of

WVT binning to a diﬀerent S/N regime.

3.5.2 Hardness Ratio Maps

Another useful tool in X-ray astronomy is the hardness ratio (or “color”) map.

The hardness ratio HAB can generally be deﬁned as the quotient between the ﬂuxes

FA and FB in two diﬀerent bands A and B, summed over all pixels of the bin Vi:

P FA,k HAB = k∈Vi . (3.10) i P F k∈Vi B,k

The associated error can be expressed in terms of the noise in the individual bands:

s (P σ2 ) (P σ2 ) k∈Vi A,k k∈Vi B,k σHAB = Hi + (3.11) i (P F )2 (P F )2 k∈Vi A,k k∈Vi B,k

Depending on the choice of energy bands, a hardness ratio map can be used as a diagnostic for any spectrally identiﬁable properties, such as temperature gradients or photoelectric absorption features (e.g. SF01). A general discussion about the physical interpretation of these maps, an appropriate choice of bands, and a generalization to n diﬀerent bands can be found in SF01 or Fabian et al. (2000). 71

We use the well-known 25 ks Chandra observation of the Perseus cluster (Fabian

et al. 2000) to demonstrate a WVT binned hardness ratio map. The right panel of

Figure 3.4 shows a color map for the Perseus cluster, in which bright colors indicate regions of lower temperature and/or lower photoelectric absorption. Our choice of bands (A: 0.3 − 1.2keV, B:1.2 − 5keV) shows both eﬀects for illustrative purposes; in principle, a diﬀerent choice is able to separate these two properties. The sharp dark feature close to the center is due to the photoelectric absorption “shadow” of an infalling dwarf galaxy in the line of sight (Fabian et al. 2000). To the north-east

of the center, one can pick out a giant radio cavity, with cooler rims surrounding it.

The smooth color gradient toward the center also supports a cooling ﬂow model (see

e.g. Sarazin 1988) and the “swirl” of the bright emission has been interpreted as a

sign for angular momentum of the infalling gas (Fabian et al. 2000). Note that the

WVT color map does not contain the spurious circular features present in its quadtree

counterpart.

3.5.3 Maps of Temperature (or other Spectral Parameters)

Hardness ratio maps are often insuﬃcient to disentangle the spectral components

of extended sources. This requires a detailed spectral analysis of multiple regions

within the ﬁeld of view. Current state-of-the-art techniques to generate maps of

temperature or other spectral parameters usually specify a regular grid of points,

within which circular or square regions are “grown” until they reach a minimum 72

number of counts for the spectral analysis (e.g. Nulsen et al. 2002; O’Sullivan et al.

2005). One can extract a spectrum and create response ﬁles for each region and

feed them into an X-ray spectral ﬁtting package such as Xspec4, ISIS5 or Sherpa6.

Just as in adaptive smoothing (see also §3.6), the measurements in this “adaptively accreted” temperature map are not independent of each other. The user is burdened with the task of deciding which features are actually resolved and thus believable, i.e. which features are larger than the extraction regions. WVT binning, on the other hand, has the power to automatically divide the ﬁeld into unbiased, independent bins with constant source counts per bin, while keeping the individual bins as compact as possible. In addition, this reduces automatically the number of time-consuming spectral ﬁts from the total number of pixels to the number of independent bins.

To demonstrate this capability, we adaptively bin the 46 ks Chandra observation of

NGC 4636 (Jones et al. 2002b) to 900 counts per bin. We then extract a spectrum for

each bin and ﬁt it with an absorbed, single temperature APEC7 model. The left panel

of Figure 3.8 shows the resulting temperature map, with the corresponding relative

error distribution on the right. This ﬁgure is directly comparable to Figure 2a of

O’Sullivan et al. (2005). They interpret the asymmetric temperature distribution as

the result of hotter gas surrounding the cool core of NGC 4636, which is penetrated by

a “plume” of gas extending to the southwest. Inside of this plume sits a concave, rising

4http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/ 5Interactive Spectral Interpretation System, http://space.mit.edu/ASC/ISIS/ 6http://cxc.harvard.edu/sherpa/ 7Astrophysical Plasma Emission Code, http://cxc.harvard.edu/atomdb/sources apec.html 73 radio bubble, surrounded by cool rims. The higher temperature inside this cavity is interpreted as a projection eﬀect, as the bubble pushes the cooler gas away and thus increases the relative contribution of the hotter surrounding gas along the line of sight. The WVT binned temperature map shows the same large-scale features as the

O’Sullivan et al. (2005) map, with no ambiguity as to their statistical signiﬁcance. 74

Figure 3.6: Comparison of bin compactness between Voronoi binning (open circles) and WVT binning (ﬁlled circles). The dashed line indicates the theoretical limit for a perfect circle. 75

Figure 3.7: Top: Flux-calibrated Chandra image of Cassiopeia A with an exposure time of 1 ks (left) and the same data adaptively binned with WVT to a target S/N of 5 (right); Bottom: Cassiopeia A with the full exposure of 50 ks (left) and the same image binned to a S/N of 20 (right). 76 0keV, as indicated by the . 55 to 1 . uncertainties, in percent, of the fitted values are shown in right panel. The error distribution σ color bar. The relativeis 1 not completely uniform inof this the case owing instrument to response a for combination of large different off-axis levels angles, in background and contribution, differences degradation in the spectral shape for varying temperatures. Figure 3.8: Temperature map of NGC 4636. Temperatures are scaled linearly from 0 77

3.5.4 Isolation of Diﬀerent Components

In many astronomical sources, the observed emission comes from multiple over-

lapping components. A good example are normal elliptical galaxies, where the diﬀuse

X-ray emission is made up of contributions from interstellar gas and low mass X-

ray binaries (LMXBs). Because of their spectral diﬀerences, hot gas and LMXBs

contribute diﬀerently to the soft-band and the hard-band images. Diehl and Statler

(2005, 2006b) show how this fact can be exploited to recover the gas emission alone.

Let FS,k and FH,k represent the background-subtracted soft and hard images in each pixel k. We can express both as linear combinations of the unresolved point source emission Pk, the gas emission Gk, and their respective softness ratios γ and δ:

FS,k = γPk + δGk, (3.12)

FH,k = (1 − γ)Pk + (1 − δ)Gk. (3.13)

Thus, the uncontaminated gas image and its associated noise can be expressed as

1 − γ γ G = F − F ; (3.14) k δ − γ S,k 1 − γ H,k s 1 − γ γ 2 σ = σ2 + σ2 . (3.15) G,k δ − γ S,k 1 − γ H,k

Diehl and Statler (2005) discuss the determination of the constants γ and δ with spectral models.

Figure 3.9 demonstrates the isolation of the gas emission using WVT binning, in a simulated observation. We assume gas and LMXB sources with very different spatial 78 distributions for purposes of illustration. We adopt an elliptical de Vaucouleurs profile for the LMXBs (top left), and a β model, with a nearly orthogonal major axis, for the gas (top right) and simulate hard and soft band images. The bottom left panel of Figure 3.9 shows the full band emission, which is nearly round. Applying WVT adaptive binning (lower right) to the gas image (equation [3.14]), we are able to reconstruct the true shape of the diffuse gas emission very accurately.

3.6 Adaptive Binning vs. Adaptive Smoothing

3.6.1 Adaptive Smoothing in X-ray astronomy

Two adaptive smoothing algorithms are in widespread use due to their inclusion in the main data analysis systems of Chandra and XMM-Newton. Confusingly, both algorithms are named asmooth. The most widely known asmooth algorithm was invented by (Ebeling et al. 2006) and originally implemented in IDL. An early C++ version of this method is distributed as part of the Chandra Interactive Analysis of Observations (CIAO) under the name of csmooth. For clarity, we will refer to this method as csmooth and specify the implementation where appropriate. The second existing asmooth algorithm is the adaptive smoothing tool of the XMM Science

Analysis System (XMMSAS), which we call XMM-asmooth. Although the output of either algorithm is generally not used for quantitative analyses, they have become the primary tools to create “pretty pictures” for papers, talks and press releases. 79

Figure 3.9: Upper left: Model surface brightness distribution for unresolved point sources; Upper right: Model surface brightness distribution for the hot, isothermal gas; Lower left: Simulated Poisson image for the full band, including contributions of both point sources and gas; Lower right: Reconstruction of the gas surface brightness distribution with the help of WVT binning. 80

Adaptive smoothing algorithms are thus instrumental in forming and inﬂuencing the

perceptions of the broader astronomical community and the public.

In adaptive smoothing, the size of the smoothing kernel changes over the ﬁeld of

view to create a constant S/N per pixel in the output image. It is worth emphasizing

that the number of independent measurements is equally decreased in adaptively

smoothed and adaptively binned images of the same target S/N. Thus one does not

gain any additional spatial information by smoothing rather than binning.8

In this section, we give some cautionary advice on the interpretation of adaptively

smoothed images. To illustrate, we take a β–model surface brightness distribution

−1 (equation [3.5]) with I0 = 10 cts pix , β = 0.67, and rc = 64 pix, with a background

of 2 cts pix−1, shown in the upper left of Figure 3.10. We simulate a counts image,

which we adaptively smooth or bin to a target S/N of 5.

3.6.2 Comparison with XMM-asmooth

The XMM-asmooth algorithm is thoroughly described in the XMMSAS 6.0.0 user

manual. 9 The basic idea is to increase the size of the smoothing kernel for each pixel

until the pixel can “accrete” enough signal to meet the S/N requirement. Thus, each

pixel has a scale associated with it, which determines the size of the convolution kernel

that contributes to the smoothed ﬂux value at this point. In WVT binning, each bin

8An exception to this statement is when there is ﬁlamentary structure narrower than the local bin size, just above the detection threshold. 9http://xmm.vilspa.esa.es/sas/current/doc/asmooth/index.html 81

Figure 3.10: A comparison of WVT binning with adaptive smoothing. Upper left: Model surface brightness distribution; The other three panels show the simulated counts image, adaptively binned image with WVT binning (upper right), adaptively smoothed with CIAO’s csmooth (lower left) and XMM-asmooth (lower right). In the csmoothed image, note the radial “fingers”, the annulus of deficient emission (deep purple) and the boundary effects in the corners. 82

has a scale associated with it. In both cases, the scale is determined from the local S/N

distribution. We choose XMM-asmooth’s default Gaussian kernel, as it is the most

commonly used. Figure 3.10 shows the results of applying WVT binning (upper right)

and XMM-asmooth (lower right) to the same test model. Both algorithms are able

to reproduce the underlying surface brightness distribution. Figure 3.11 compares

the distributions of relative errors for XMM-asmooth (long dashed line) and WVT

binning (solid line). Both distributions are consistent with the constant targeted S/N

value of 5, but XMM-asmooth’s error distribution is not as regular as WVT’s and is

skewed slightly toward higher ﬂuxes.

The skewed error distribution is a result of XMM-asmooth’s tendency to preferen-

tially misidentify high flux pixels over low flux pixels as real features. We find that the

XMM-asmooth algorithm tends to build “bridges”, connecting nearby, independent

noise peaks, and making them appear as linear ﬁlamentary structures. Examples can

be seen in the outer parts of Figure 3.10. A cleaner illustration is shown in Figure

3.12. Here we have simulated a ﬂat-ﬁeld image, with a vertical gradient in S/N. The

figure compares the results of XMM-asmooth (left) and WVT binning (right). The smoothed image shows a wealth of spurious linear features that strongly lead the eye, suggesting filaments and cavities. The binned image, on the other hand, looks to the eye like a featureless but noisy flat field. One can easily see that all of the apparent structure in the smoothed image happens at scales slightly smaller than the WVT 83 bin sizes, and is therefore not statistically significant despite the identical target S/N of 5 given as input.

In conclusion, if an adaptively smoothed image is necessary, we urge that it be published only in conjunction with its smoothing scale map or an equivalent WVT binned image.

3.6.3 A Cautionary Note on CIAO’s csmooth

More than half of all Chandra press release images of the diﬀuse emission from galaxies and clusters of galaxies are generated with the CIAO tool csmooth. We demonstrate here that this algorithm creates very serious artifacts for images of diﬀuse emission and should be used only with extreme caution. Similar concerns were also previously raised by SF01.

The csmooth algorithm (Ebeling, White & Rangarajan, private communication)

ﬁrst calculates a set of smoothing kernel sizes, ranging from the size of a single pixel to that of the entire image. Starting with the smallest kernel, all pixels with a suﬃcient

S/N within the kernel to match the target S/N requirements are convolved and added to the output image. These pixels are then removed from the input image, so they make no contribution at larger scales. The algorithm then picks the next larger kernel and starts over with the remaining pixels. This continues until no more pixels are left in the image, or the kernel size reaches its maximum. The ﬁnal csmoothed image 84

Figure 3.11: Histogram of relative errors, compared to the model surface brightness, for the example of Figure 3.10. The WVT binning (solid line) and XMM-asmooth (dashed line) histograms are consistent with the target S/N value of 5 (i.e. they approximate a Gaussian with a width of 20%). Note that the adaptively smoothed image is not a statistically better representation of the true surface brightness. The histogram of csmooth results (dotted line) is very irregular with a wide range of positive and especially negative errors, demonstrating the failure of this algorithm. 85

Figure 3.12: Comparison between XMM-asmooth (left) and WVT binning (right): the simulated counts data was derived from a ﬂat Poisson distribution with a count rate of 1 cts pix−1, with a spatially variable background “ramp” increasing linearly from 0 cts pix−1 at the bottom to 5 cts pix−1 at the top of the image.

is the sum of all these individually convolved slices, and the ﬂux from each pixel is

spread over a diﬀerent area, according to its smoothing scale.

Because a diﬀerent smoothing kernel is assigned to each pixel in the input image,

each pixel in the output image is the sum of many convolutions of diﬀerent parts of the

input image with diﬀerent kernels. This is fundamentally distinct from the XMM-

asmooth algorithm, where the kernel is assigned to the pixel in the output image,

whose ﬂux is then a result of a single convolution using a single kernel. In other

words, XMM-asmooth collects flux, while csmooth distributes flux. These procedures are identical only for pure convolution with a fixed kernel. When the kernel is variable, the csmooth algorithm has the effect of moving flux from low surface brightness regions 86

into high surface brightness regions. This has previously been noted by SF01 in the

adaptively smoothed image of the Perseus cluster, where they ﬁnd the ﬂux per pixel in

the X-ray cavities dropping to half the value derived from raw data. This behavior is

also particularly destructive in regions of relatively ﬂat emission, where csmooth will

move ﬂux into the high-ﬂux tail of the noise distribution, creating spurious emission

features in the smoothed image. A good example is given in the lower left panel of

Figure 3.10, where csmooth obviously produces spurious radial features.10

An additional problem affecting csmooth is its definition of S/N. In this paper, we define the signal-to-noise ratio as the quotient of the background corrected signal divided by the total noise in each bin. Unfortunately, up to CIAO 3.1, csmooth’s

option to supply an external background map to calculate the S/N distribution in

the equivalent way does not function correctly. Instead, the only available option is to

compute the background from a local annulus surrounding the smoothing kernel. This

local signiﬁcance approach is valid for point sources on top of diﬀuse emission, but not

for the diﬀuse emission itself. For extended sources, the local “background” region

includes signiﬁcant amounts of the diﬀuse emission, resulting in strong S/N variations

across the ﬁeld and a overestimate of required smoothing scales. Figure 3.13 shows

the spatial error distribution (left panel), as well as the scale map, indicating the

distribution of smoothing kernel sizes. Due to computing the S/N locally, csmooth

will always employ the largest available smoothing kernel in the outer parts of an

10This image looks very similar to the claimed radial “ﬁnger” structures, seen in the csmoothed image of NGC 4649 (Randall et al. 2004). 87

image, no matter what target S/N is chosen, or how high the ﬂux at the boundaries

is. In our example, the kernel reaches its maximum size at a radius of about 150

pixels, and starts to disperse the ﬂux over a large area. This results in an annulus of

depressed emission at larger radii (deep purple colors in Figure 3.10 and dark regions

in Figure 3.13). The missing ﬂux from this annulus accumulates in adjacent regions with smaller smoothing scales, producing a relatively sharp surface brightness edge at the transition point. The relative errors in these two regions range from +100% to

-200% (see Figures 3.11 and 3.13), indicating the magnitude of this eﬀect.

The noticeable strength of smoothing artifacts actually increases with an increase

in target S/N in csmooth. This may be caused by the asymmetric Poissonian error distribution, which will be taken into account in a future csmooth release (Harald

Ebeling, private communication).

3.7 Availability of the Code

WVT binning is implemented in IDL 5.611, and publicly available under

http://www.phy.ohiou.edu/ diehl/WVT. It has also been submitted to the Chan-

dra contributed software website12. An extensive manual and download instructions

are provided on the website, along with multiple examples for its usage.

11http://www.rsinc.com 12http://cxc.harvard.edu/cont-soft/soft-exchange.html 88

Figure 3.13: Left panel: Relative error distribution for the csmoothed image in the lower right panel of Fig. 3.10; note the large-scale spatially dependent error distribution which leads to the identiﬁcation of spurious features. Right panel: The csmooth scale map, indicating the spatial distribution of the smoothing kernel size. Note how smaller kernel sizes translate into stronger positive deviations in the error distribution; in particular, note the correspondence between the transition to the largest smoothing kernel and the sharp edge in the error distribution that leads to the annulus of deﬁcient emission.

The published version is fully functional and applicable to 2-dimensional images as well as 1-dimensional pixel lists to generate intensity maps and color maps. We also provide csh and Sherpa s-lang scripts to generate temperature maps from adaptively binned images.

The code is not limited to use with X-ray data or integral ﬁeld spectroscopy. To adapt the code to handle completely diﬀerent types of problems, it is only necessary to adjust two external functions which calculate the S/N per bin, without any modi-

ﬁcations to the main program. Our manual includes detailed instructions on how to achieve this. 89 3.8 Conclusions

We have presented a generalization of the Voronoi adaptive binning technique by Cappellari and Copin (2003), broadly applicable to X-ray and other data. The generalized algorithm exploits the properties of weighted Voronoi tesselations, rather than the overly restrictive Gersho conjecture. WVT binning is applicable to any type of data as long as there is a way to robustly calculate the S/N, and the S/N distribution changes smoothly over the size of a bin. We have demonstrated the capabilities of WVT binning on exposure- and background-corrected X-ray intensity images, color and temperature maps, and in isolating the diﬀuse gas emission in elliptical galaxies.

WVT binning overcomes the shortcomings of both Voronoi and quadtree binning, the latter of which is in growing use in X-ray astronomy. Sanders et al. (2005) have recently published results using a “contour binning” algorithm. In this new adaptive binning algorithm, the bin boundaries follow the isophotes of an adaptively smoothed image. We are unable to make a rigorous quantitative comparison with this technique, as the details are still unpublished. However, the maps that are published suggest that this new binning algorithms creates very irregular and elongated bins, which lead the eye and introduce a shell-like appearance in their binned X-ray cluster images of

Perseus. In anticipation of their paper, we would like to reemphasize that our WVT binning produces an unbiased distribution of compact bins, and does not lead the eye. 90

We have also demonstrated the pitfalls of adaptive smoothing, and regretfully advise against the use of the CIAO tool csmooth for images of extended diﬀuse emission, as it creates very serious artifacts. If an adaptive smoothing technique has to be used, we recommend the XMMSAS tool XMM-asmooth instead. However we urge that adaptively smoothed images be published only in conjunction with the smoothing scale map or an equivalent WVT binned image to facilitate the identiﬁcation of real structures. 91 Chapter 4

A Chandra Gas Gallery and

Comparison of X-ray and Optical

Morphology

4.1 Introduction

The launch of Chandra and XMM-Newton opened a new era in our understanding of the hydrodynamic histories of galaxies and clusters. Early spectral evidence by

ROSAT and ASCA (e.g. Fabbiano et al. 1994; Buote and Canizares 1997) already

suggested soft diﬀuse gas and harder stellar point sources as the two dominant com-

ponents of the X-ray emission of normal elliptical galaxies. But Chandra made it possible for the ﬁrst time to spatially resolve a signiﬁcant fraction of the point source component into individual sources, which are now believed to consist mainly of low- mass X-ray binaries (LMXBs, e.g. Sarazin et al. 2003, and references therein). This

has signiﬁcantly contributed to the understanding of the correlation between X-ray

2 and blue luminosity. The LX–LB diagram shows a steep LX ∝ LB relation at the gas- dominated group and cluster scale, and gets shallower toward low X-ray luminosities for normal elliptical galaxies due to the increasing importance of the point source 92

component (O’Sullivan et al. 2001). For these galaxies, the LMXB emission severely contaminates the diﬀuse hot gas emission and complicates eﬀorts to reveal its spatial structure.

It has long been assumed that the hot interstellar medium (ISM) in elliptical galaxies is in hydrostatic equilibrium with the underlying gravitational potential (e.g.

Forman et al. 1985). The desire to make this assumption is natural since it then

gives us a powerful tool to probe the host galaxy’s mass distribution. As such, radial

mass proﬁles derived from observed X-ray pressure proﬁles are among the strongest

providers of evidence for the existence of massive dark matter halos surrounding

normal elliptical galaxies (e.g. Forman et al. 1985; Killeen and Bicknell 1988; Paolillo et al. 2003; Humphrey et al. 2006; Fukazawa et al. 2006) and have been found to be consistent with those derived from gas kinematics in spiral galaxies (Sofue and Rubin

2001, and references therein) and stellar kinematics in ellipticals (e.g. Statler et al.

1999), implying dark halos with mass proﬁles similar to those of isothermal spheres.

Unfortunately, stellar kinematics can only probe the dark matter content out to a

few optical radii. Farther out, one has to rely on X-ray mass proﬁles, gravitational

lensing (Keeton 2001) or kinematical planetary nebula (PN) data (Napolitano et al.

2004). A recent study by Romanowsky et al. (2003) using PN data advocates the

lack of dark matter halos around some elliptical galaxies, at odds with standard Λ-

CDM simulations (e.g. Springel et al. 2005). This discrepancy may be reconciled by 93 appealing to radial orbits of the halo stars (Dekel et al. 2005), which underlines the diﬃculty of interpreting PN kinematics.

The assumption of hydrostatic equilibrium in elliptical galaxies has always been considered well founded and understood. If this assumption holds, one consequence is that the isophotes of the hot gas emission should exactly trace the projected potential isophotes. Thus, Buote and Canizares (1994) propose to use the shape of the gas isophotes to determine the shape of the dark matter halo, and subsequently use this method to claim a highly ﬂattened triaxial dark matter halo for the elliptical galaxy

NGC 720 (Buote and Canizares 1994; Buote et al. 2002). However it has not been shown that there is a test to verify that hydrostatic equilibrium holds precisely enough all the way through a galaxy to make this kind of inference valid.

Statler and McNamara (2002) argue that the extreme X-ray flattening of NGC 1700 provides a counterexample of an object that cannot be in hydrostatic equilibrium, and suggest that it is rotationally flattened. Rotational flattening might be expected for a variety of reasons (Mathews and Brighenti 2003a). A large fraction of the hot gas in elliptical galaxies is thought to come from stellar mass loss, and should carry the stellar angular momentum. A fraction of the hot gas may also be acquired externally during mergers, stripped off during close encounters, or fall in from a circumgalactic gas reservoir (Brighenti and Mathews 1998). In each case, the gas should contain a significant amount of angular momentum. In the standard cooling flow scenario the gas should slowly flow inward, conserving angular momentum and settling into 94

a rotationally supported cooling disk (Brighenti and Mathews 1997, 1996; Kley and

Mathews 1995). However, Hanlan and Bregman (2000) demonstrate, with ROSAT

and Einstein data for 6 elliptical galaxies, a lack of gas disk signatures. They ﬁnd

ellipticities that generally do not exceed values of ∼ 0.2, whereas disk models predict

ellipticities larger than ∼ 0.5.

Detailed Chandra and XMM studies of over two dozen individual early-type galax-

ies are now published in the literature. Many of these observations reveal systems that

are morphologically disturbed, with a large variety of suggested causes. For example,

Jones et al. (2002a) argue for the presence of shocks in NGC 4636; Finoguenov and

Jones (2001) ﬁnd evidence for interactions with the central radio source in NGC 4374;

and Machacek et al. (2004) suggest that NGC 1404 is moving relative to the Fornax

intracluster gas. Only a few objects appear round and quiescent, such as NGC 4555

(O’Sullivan and Ponman 2004) or NGC 6482 (Khosroshahi et al. 2004). Interest-

ingly, both Ciotti and Pellegrini (2004) and Mathews and Brighenti (2003b) combine

stellar kinematics information with Chandra X-ray observations of NGC 4472 and

independently argue for a lack of hydrostatic equilibrium in this particular galaxy.

Nonetheless, the presumption persists that hydrostatic equilibrium holds in the ma-

jority of early-type galaxies (e.g. Humphrey et al. 2006; Fukazawa et al. 2006)

The main obstacle to understanding the true physical state of the hot ISM in elliptical galaxies is the separation of the gas and unresolved LMXB contributions to the diffuse emission, which is particularly important for X-ray faint galaxies. So far, 95 two main approaches have been employed. (1) Resolved point sources are removed, and the residual diffuse image is adaptively smoothed. It is then argued or hoped that the contribution of unresolved point sources can be neglected while interpreting the diffuse emission and that what is shown is close to the gas morphology (e.g. Buote et al. 2002). (2) The observation is separated into broad radial bins with sufficient signal to extract and fit a spectrum with a two component model, thus spectrally separating gas and LMXBs in the radial profile (e.g. Humphrey et al. 2006). Method

(1) has the obvious disadvantage that one does not know what one is looking at. One gains no information on gas morphology in X-ray faint systems which are known to be

LMXB dominated. Method (2) allows some insight into the radial distribution and extent of the gas but reveals nothing about the true elliptical shape or asymmetric features.

This is the ﬁrst paper in a series that analyzes data on 54 elliptical galaxies in the

Chandra public archive. We homogeneously reanalyze the observations and introduce a new technique to isolate the gas from LMXBs. A new adaptive binning technique

(Diehl and Statler 2006a) is then used to reveal for the ﬁrst time the morphology of the gas alone. We present a gas gallery and quantitative morphological analysis.

To address the question of whether hydrostatic equilibrium generally holds in normal ellipticals, we compare gas and stellar morphologies and examine the evidence for rotational support. Subsequent papers in this series will take up the questions of the origin of observed asymmetries in the hot gas (Diehl and Statler 2006c, hereafter Paper 96

II) and address the importance of central active galactic nuclei (AGN) in reheating

the hot gas (Diehl and Statler 2006d, hereafter Paper III).

The remainder of this paper is organized as follows. In §4.2 we describe the

details of the data reduction pipeline, the new isolation technique and the method

used to derive ellipticity proﬁles. In §4.3 we present our comparison between optical and X-ray properties and address the question of rotational support. We discuss the implications of our ﬁndings in §4.4, before we summarize in §4.5.

4.2 Data

4.2.1 Sample Selection and Pipeline Reduction

We select all E and E/S0 galaxies having non-grating ACIS-S observations with

eﬀective exposure times longer than 10 ks in the Chandra public archive of cycle 1-4 by

cross-correlating their galaxy types with the Lyon–Meudon Extragalactic Database

(LEDA; Paturel et al. 1997). We remove brightest cluster galaxies and objects with

purely AGN-dominated emission. This sample is almost identical to that used in a

previous paper (Diehl and Statler 2005), except for the removal of two galaxies. We

exclude the NGC 4782/NGC 4783 galaxy pair due to its ongoing merger and the

dwarf elliptical NGC1705 whose luminosity is two orders of magnitude smaller than

that of the next largest object. Our ﬁnal sample consists of 54 early-type galaxies,

thirty-four of which are listed as members of a group in the Lyon Group of Galaxies 97

(LGG, Garcia 1993) catalog, with 19 identiﬁed as the brightest group member. Eight are also identiﬁed as members of X-ray-bright groups in the GEMS survey (Osmond and Ponman 2004), together with 5 additional galaxies that are not listed in the LGG catalog.

We apply a homogeneous data reduction pipeline to all observations from their event 1 files using CIAO version 3.1 with calibration data base 2.28. The basic data reduction steps follow the recommendations according to Chandra’s ACIS data analysis guide1. The newest gain file is applied and adjusted for time-dependent gain variations to account for the drift of the effective detector gains with time caused by changes in the charge transfer inefficiency. Observation-specific bad columns and pixels are removed and each observation is restricted to its good time intervals. We additionally filter each light curve by iteratively applying a 2.5σ threshold to remove background flares. The remaining light curve is then clipped at 20% above the average count rate, to match the standard of the Markevitch blank sky background files2.

Each light curve is inspected and verified to be clean. If the entire observation is affected by a very long flare that manifests itself as an underlying “ramp” in the light curve, we flag the object and use a local background spectrum in our spectral analysis instead of blank sky fields. The background correction for the subsequent spatial analysis is not taken from the blank sky background files, but rather derived from surface brightness profile fits (see also §4.2.2) which will automatically correct for

1http://cxc.harvard.edu/ciao/guides/acis data.html 2http://cxc.harvard.edu/cal/Acis/Cal prods/bkgrnd/acisbg/COOKBOOK 98

flux offsets from residual flares. The remaining event list is filtered to retain standard

ASCA grades 0, 2, 3, 4, and 6 to optimize the signal-to-background ratio. Cosmic ray afterglows, as ﬂagged by the CIAO tool acis detect afterglow, are only removed for the purpose of source detection to minimize the number of spurious detections.

These photons are retained for the rest of the analysis, since a signiﬁcant portion of the ﬂux of even moderatively bright point sources has been found to be accidently rejected by this procedure3.

Our analysis is restricted to photon energies between 0.3–5 keV, maximizing the relative contribution of soft hot gas emission, while avoiding the rise of the particle background at higher energies. All quoted X-ray luminosities are restricted to this band. We split this energy range further into a soft (0.3–1.2 keV) and a hard (1.2–

5.0 keV) band. To create ﬂux-calibrated images that take the spatially dependent spectral changes into account, we create mono-energetic exposure maps in steps of

7 in PI (∼ 100 eV). The observation is split into 14.6 eV-wide (the width of one PI channel) individual images. A photon-flux-calibrated “slice” is created by dividing this counts image by the energetically closest exposure map. The sum of all individual slices represents the final photon flux image. These flux-calibrated images allow an accurate flux determination even in cases where a spectral analysis is impossible due to the lack of sufficient signal.

3http://cxc.harvard.edu/ciao/threads/acisdetectafterglow/ 99

4.2.2 Isolating the X-ray Gas Emission

To isolate the hot gas emission we follow the procedure outlined by Diehl and

Statler (2005). A summary is repeated here with some additional details, which are

essential for the morphological analysis in this paper.

We use the CIAO tool wavdetect to identify point sources, remove regions enclosing

95% of the source flux and refill the holes with simulated Poisson counts to obtain an image of diffuse emission. We determine uniform background values for the soft and hard bands by extracting radial surface brightness profiles for the diffuse emission from the calibrated photon-flux images and fitting them with β, double-β and Sérsic models plus an additive constant background. The sole purpose of these fits is to determine the background value; all other fitting parameters are discarded for the subsequent analysis. If there is insufficient signal to produce an accurate fit, we compute the average surface brightness level outside a 2.5 arcmin radius and use it as the background value. We then subtract the spatially uniform backgrounds from the photon-flux calibrated images to obtain the background corrected images of diffuse emission for the soft and hard bands.

Unresolved point sources are modeled and removed from the diffuse emission to isolate the hot gas emission alone. To do this, we split the background corrected, photon-flux calibrated images into the soft band S and hard band H. Gas and point source components contribute at different levels to each band, determined by their respective softness ratios γ and δ. By expressing both bands as linear combinations 100 of the hot gas component G and the unresolved point source component P , we can solve this system of equations to isolate the gas emission itself:

S = γP + δG, (4.1)

H = (1 − γ)P + (1 − δ)G; (4.2) 1 − γ γ thus,G = S − H . (4.3) δ − γ 1 − γ

This decomposition depends on the softness ratios γ and δ. To determine the softness of the unresolved point sources, we first analyze the hardness ratios of resolved point sources. We find no evidence for any spatial dependence or luminosity dependence of their spectral properties. This is in agreement with studies by Irwin et al. (2003), which suggest a universal nature of LMXBs, and allows us to use the known spectral properties of resolved LMXBs as a template for their unresolved counterparts. For each galaxy, we select resolved point sources between 500 and 5 optical radii from the center to avoid the influence of the central AGN, and to minimize contributions from serendipitous background sources. We exclude high luminosity sources (> 200 counts) to ensure that the spectral fits are driven by low-luminosity sources. If more than 10 sources fulfill these selection criteria, we fit an absorbed power law model to the combined LMXB spectrum. To get an equivalent point source spectral model for galaxies without sufficient resolved point sources, we simultaneously fit a power-law

37 −1 to all low-luminosity (LX ≤ 5×10 erg s ) LMXBs available in our complete galaxy sample. This combined ﬁt yields a photon index of 1.603, which we adopt as the 101

representative spectral model for source-poor galaxies. By integrating the adopted

unabsorbed spectral model over the soft and hard band, we derive the point source

softness ratio γ.

To find the softness ratio of the hot gas component, δ, we extract a spectrum from the diffuse emission within the inner 3 optical radii of each galaxy. We use an absorbed single temperature APEC thermal plasma model for the hot gas and add the adopted power-law model to represent unresolved point sources. We fix the redshift parameter to the LEDA value, while temperature, metallicity and normalizations are generally allowed to vary freely. For low signal-to-noise spectra, we fix the metallicity to the solar value. All described spectral fits are computed with the CIAO tool Sherpa and corrected for Galactic absorption, with the hydrogen column density fixed at the

Galactic value for the line of sight, as determined by the CIAO tool Colden4.

To reliably interpret the sparse gas images and to reveal any spatial features,

we bin the gas images with an adaptive binning method using weighted Voronoi

tesselations (Diehl and Statler 2006a)5 to achieve an approximately constant signal-

to-noise ratio per bin of 4. In background dominated, very-low signal-to-noise regions,

the required bin size can get very large and the bins occasionally “eat” into the inner

emission to accrete suﬃcient signal. To avoid this eﬀect, we restrict the maximum

bin size for these objects, resulting in a drop of signal-to-noise per bin in the outer

regions.

4http://cxc.harvard.edu/toolkit/colden.jsp 5http://www.phy.ohiou.edu/∼diehl/WVT 102

A few things should be kept in mind regarding our new isolation technique for the hot gas. First, we assume isothermal gas throughout the galaxy, resulting in a spatially constant δ parameter. We test the validity of this assumption by creating two-dimensional temperature maps for systems with the highest signal-to-noise data and correct the gas image for a spatially dependent δ value. Although most galaxies exhibit temperature gradients, the corrections are generally < 10% and do not affect the gas morphology. Spatial temperature gradients and inhomogeneities will be examined in more detail in Paper III. However, one should be aware that strong localized temperature diﬀerences can potentially result in an over-subtraction of hotter features and under-subtraction of colder features.

Second, the region influenced by the central PSF of an AGN may be subtracted incorrectly, as the AGN softness ratio is most likely different from that of the unresolved point source component. Thus, we exclude the central regions from our analysis, and one should refrain from interpreting the gas maps at the very center. A detailed analysis of the central AGN and its effects on the overall morphology will be presented separately in Paper II. One should also keep in mind that possible direct

X-ray jet signatures could be masked out in our analysis, as jet knots would most likely be identiﬁed as point sources and thus removed.

A drawback of our approach is the inevitable loss of signal. Since we are subtracting a scaled version of the hard band from the soft band to isolate the gas emission, we effectively subtract a part of the gas flux. Even though our technique corrects for this 103 missing flux, one still loses a certain amount of signal, reducing the spatial resolution in the adaptively binned gas image. The softness of the gas comes close to that of the unresolved point sources for temperatures exceeding ∼ 1.5 keV. From that point on, both components become increasingly indistinguishable and the signal-to-noise ratio of the gas image can be very low, even if there is substantial gas present. Fortunately, few objects in our sample have temperatures exceeding 1 keV.

The definite advantage of our algorithm is that we can properly isolate the hot gas emission, without assumptions about the spatial distribution of unresolved point sources, or their total flux. Even the effect of a spatially variable point source detection limit (due to variations in background levels and the changes in size and shape of the point spread function) is compensated for by our algorithm.

To give the reader a better understanding of the relative contributions of the hot gas and the resolved and unresolved point source components, we list the relative fractions in Table 4.1 for a radial range between 2.500 and 3 J-band eﬀective radii

(RJ). This shows that for a large subset of galaxies, a significant percentage of point sources is still unresolved and contaminates the diffuse emission, disguising the true gas morphology. In some cases (e.g. NGC 3115) the diffuse emission is even consistent with being almost entirely due to unresolved point sources. 104 9 4 9 12 32 15 12 17 21 18 31 25 33 25 20 21 35 19 10 d ± ± ± X ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 5 PA 19 35 12 43 − − − − − 06 06 88 2114 116 90 0803 52 05 06 20 153 04 11 0808 29 77 14 166 05 09 42 0642 49 37 09 42 09 68 ...... ······ ······ ······ ······ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 d X ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 24 20 24 57 29 17 15 14 23 10 46 06 22 23 21 28 33 17 43 ...... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 40 42 41 40 40 42 40 41 41 41 42 41 40 41 40 42 38 41 40 41 41 40 43 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 c × × × × × × × × × × × × × × × × × × × × × × × Gas 0 2 2 6 0 1 4 3 1 9 1 3 3 5 7 7 1 5 4 4 8 2 7 , ...... X 2 1 3 2 2 2 0 0 1 7 9 3 1 3 2 5 2 7 3 0 0 3 1 L ± ± ± ± ± ± ± ± ± ± ± ± ± > > > < > > < > < < 6 8 7 7 0 2 6 3 4 1 5 3 0 ...... b 1% 2 1% 1% 1% 2 1% 5 1% 1 1% 1 2% 5% 1% 1% 1% 3 1% 9 1% 9 1% 2% 1% 1% 9 1% 1 1% 2 1% 4 1% 2 54% resol ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± X-ray properties f b 6% 21 9% 31 8% 47 9% 12 9% 18 9% 5 12%14% 4 9 13% 15 13% 18 16%10% 5 12 23% 8 87% 78 16% 1 11% 22 18% 2 13% 1 42% 6 10% 16 10% 10 10% 31 15% 1 Chandra unres ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± f b 9% 9 8% 38 13% 17 14% 7 13% 24 13% 5 16%10% 1 18 10% 18 23% 7 23%16% 5 16 11% 21 19%10% 9 15 13% 30 43% 0 10% 35 10% 32 10%13% 7 10 10% 12 15% 41 Table 4.1. Gas ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± f a τ 4371 49 79 / Name ObsId NGC2434 2923 25 69 NGC1553NGC1600 4283 NGC1700 783 19 2069 61 39 85 NGC1404NGC1407NGC1549 2942 29 791 94 2077 43 20 70 52 NGC1316 2022 26 78 NGC1265NGC1399 3237 82 15 319 24 85 NGC0821 4006 13 17 NGC1132 801 12 83 NGC0741 2223 29 58 NGC0533NGC0720 2880 35 492 89 34 74 NGC0507 317 26 69 NGC0404 870 24 94 NGC0383 2147 43 49 NGC0315 4156 52 58 IC4296NGC0193 3394 4053 24 29 74 85 IC1459 2196 52 58 IC1262 2018 31 58 105 5 5 6 25 36 26 15 29 35 10 34 11 14 d ± ± ± X ± ± ± ± ± ± ± ± ± ± PA 22 − 2226 105 14 89 39 0203 109 2 04 11 128 03 106 07 91 06 100 07 118 06 73 06 35 ...... ······ ······ ······ ······ ······ ······ ······ ······ ······ ······ 0 0 0 0 0 0 0 0 0 0 0 0 0 d X ± ± ± ± ± ± ± ± ± ± ± ± ± 39 23 18 32 09 05 15 18 09 39 18 38 20 ...... 0 0 0 0 0 0 0 0 0 0 0 0 0 40 41 42 41 41 40 39 41 40 39 40 41 42 40 40 40 40 40 39 39 39 39 40 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 c × × × × × × × × × × × × × × × × × × × × × × × Gas 8 5 9 3 0 9 0 3 2 5 1 5 0 3 8 1 7 3 2 3 1 7 9 , ...... X 0 3 1 0 2 0 2 2 1 7 2 8 1 1 3 1 2 1 4 6 6 8 9 L ± ± ± ± ± ± ± ± ± ± > < > > < > > > > < < < < 6 3 7 1 1 8 9 8 2 3 ...... b 2% 1% 2 1% 1% 1 1% 2 4% 1 2% 2% 1% 2 2% 8 5% 1% 1% 1% 5 1% 1% 4 1% 7 1% 4 3% 2% 5% 2% 10% resol ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± f b 9% 18 5% 38 9% 50 8% 15 5% 48 4% 75 8% 41 8% 63 18% 0 11% 9 17% 3 15% 11 18% 9 10% 16 10% 37 10% 57 16% 5 12% 2 18% 9 10% 19 13% 19 15% 85 19% 6 Table 4.1 unres ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± f 6% 6 2% 43 8% 14 9% 11 7% 19 4% 11 9% 35 b 11% 21 18% 0 11% 11 17% 3 11% 7 23% 17 20% 19 10% 4 12% 8 16% 12 12% 10 18% 5 11% 18 13% 1 22% 0 21% 60 Gas ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± f a τ 4728 112 57 / 4727 / Name ObsId NGC5018NGC5044 2070 25 798 61 20 100 NGC4697 784 NGC4649 785 31 80 NGC4636 323 46 95 NGC4621 2068 24 42 NGC4564 4008 17 72 NGC4555 2884 27 73 NGC4552 2072 53 80 NGC4526 3925 38 55 NGC4494 2079 19 0 NGC4472 321 35 83 NGC4406 318 14 89 NGC4374 803 28 86 NGC4365 2015 40 44 NGC4261 834 31 63 NGC4125 2071 63 80 NGC3923 1563 16 74 NGC3585 2078 35 32 NGC3379 1587 30 14 NGC3377 2934 39 15 NGC3115 2040 14 2 NGC2865 2020 25 34 106 8 16 26 27 d ± X ± ± ± PA 14 279 041517 2 17 47 . . . . ······ ············ ······ 0 0 0 0 d X ± ± ± ± 38 21 22 20 . . . . 0 0 0 0 . J 42 41 42 41 40 41 42 39 R 2 10 10 10 10 10 10 10 10 . c × × × × × × × × Gas 9 9 3 1 2 7 7 6 , ...... X 0 0 1 1 8 5 2 1 L 8 and 1 ± ± ± > < < > < . 3 9 7 . . . b 1% 1% 2 1% 3 1% 1 2% 3% 1% 7% 5 keV band. − resol ± ± ± ± ± ± ± ± f 3 . Table 4.1 b 5% 48 10%11% 4 1 16%13% 2 1 19% 2 20% 4 13% 46 for the 0 unres ± ± ± ± ± ± ± ± 1 f − b 6% 24 14%11% 6 14 16%13% 4 9 30% 41 25% 13 22% 4 Gas ± ± ± ± ± ± ± ± f . J R a exposure time in ks. τ and 3 00 Chandra Percentages of observed photon fluxes for the hot gas, unresolved and resolved point sources, inte- X-ray gas ellipticity and position angle, evaluated between 0 Effective Total X-ray gas luminosity in ergs s b c a d Name ObsId NGC7052NGC7618 2931 9 802 90 11 85 NGC5846NGC6482 788 3218 24 19 95 90 NGC5532NGC5845 3968 48 4009 28 30 57 NGC5171 3216 34 83 NGC5102 2949 34 50 grated between 5 107

4.2.3 X-ray Gas Luminosity

To calculate the total X-ray gas luminosity, we adaptively bin the calibrated gas images into circular annuli and produce radial surface brightness profiles, as described in Diehl and Statler (2005). X-ray surface brightness profiles of galaxy clusters and groups are generally well described by β or double-β profiles with β values between

∼ 0.6 − 1.0. Our β model fits indicate that the gas profiles of normal ellipticals are generally shallower. For 28 out of 45 galaxies with sufficient signal to constrain the

ﬁt, the best ﬁt β values are < 0.5, consistent with the known relation between gas temperature and β for groups and clusters (e.g. Voit et al. 2002).

However, a β value below 0.5 yields infinite total flux when extrapolated to large radii. As this renders the β models unusable for determining total luminosities, we adopt the well-known Sérsicmodels instead. The Sérsicmodel has the advantage of yielding finite fluxes and produces equivalently good fits. The values for our best

Sérsicmodel fits are published in an earlier paper (Diehl and Statler 2005). We derive X-ray gas luminosities by summing the calibrated gas images over the field of view, and use the model fits to correct for missing flux outside the field of view. The luminosities listed in Table 4.1 are also corrected for absorption effects by multiplying a correction factor, derived from the best spectral fit, which we integrate with and without absorption by the Galactic neutral hydrogen. The error bars for luminosities can get quite large for objects with very wide gas emission, where a significant fraction of flux is derived from the uncertain extrapolation to large radii. The quoted 108 uncertainties in Table 4.1 also include systematic errors associated with uncertainties in the δ and γ parameters from section 4.2.2, as well as the uncertainty in our adopted distances (for more details, see Diehl and Statler 2005). In cases where the uncertainties are larger than the actual values due to uncertainties in the extrapolation or where we have insufficient signal for a surface brightness model fit, we determine the luminosity by summing the flux in the field of view. If the summed flux represents a detection at a > 3σ level, we report the 3σ lower bound as a low limit in Table 4.1.

If this is not the case, we report the 3σ upper bound as an upper limit.

4.2.4 X-ray Ellipticity and Position Angle Proﬁles

The extremely sparse nature of X-ray data generally prohibits the use of isophote

fitting techniques commonly employed with optical data. Moreover, because our gas-only images are obtained from scaled differences of the hard and soft bands, they contain many individual pixels with large negative counts, which can render standard algorithms numerically unstable. To avoid this problem, we fit isophotes to the adaptively binned gas images, adapting techniques used in N-body simulations.

We populate each bin randomly with a number of pseudo counts (particles) such √ that the expected N Poisson fluctuations match the signal-to-noise ratio in the bin. The pseudo count fluxes (masses) are chosen to give the correct flux in each bin. Isophotes are then fitted to the pseudo count distribution using an iterative algorithm that diagonalizes the second-moment tensor in a thin elliptical ring and 109 manipulates the axis ratio until the eigenvalues match those for a constant density ring of the same shape (Statler and McNamara 2002). Twenty random realizations are run, and the distribution of complex ellipticities is used to find the mean isophotal ellipticity, major axis position angle, and errors at each radius. Straightforward tests show that this technique is able to robustly recover simulated isophotal profiles of the sorts found in the data.

4.2.5 Optical Data

Optical data for the sample galaxies are given in Table 4.2. We adopt the eﬀective

J-band ellipticity J, position angle PAJ and half-light radius RJ (Table 4.2), as well as the absolute K magnitude from the 2MASS extended source catalog (Jarrett et al.

2000). These ellipticities and position angles are extracted at a constant magnitude level, approximately 3σ above background noise level, generally translating to an extraction radius between 20–40 arcsec.

In addition, we extract R-band images from the second epoch of the Digitized

Sky Survey (DSS-2R) and make use of publicly available optical surface photometry from the literature. In particular, we adopt B (20 galaxies), V (20), and I (19) photometry from Goudfrooij et al. (1994)6, V (21), R (25), and I (23) from Bender et al. (1988), U (13), B (15), and R (14) from Peletier et al. (1990) and F 814W

(9) photometry from Falc´on-Barroso et al. (2006). Refer to Table 4.2 for details.

6PA profiles from Goudfrooij et al. (1994) have been corrected for mirror-image flips by matching the profiles to other published photometry and DSS-2R images. 110

We use the optical photometry to extract eﬀective optical position angles PAopt and ellipticities opt between 0.8–1.2 RJ.

We also query the Hyperleda (Prugniel et al. 1998) data base to derive average rotational velocities between 0.8–1.2 RJ. In cases where Hyperleda does not provide the data in electronic form, we read off approximate values from published kinematic profile plots. The list of references that are used to derive the adopted rotational velocity is given in Table 4.2. This rotational velocity is closely related to the maximal rotational velocity but is generally a better defined quantity, as it is independent of the observational cutoff of the available kinematic data. 111 e e Ref. opt PA Photometry 10 105 T 38 31 T,W 4216 141 T,V 89 V 26 43 U,V 10 63 U 26 39 T ...... opt ········· ········· ········· 0 0 0 d Ref. 31 F 0 99 D 0 20 B 75 A rot 134 E 133 C 0 111 A 0 ······························ ······ ··············· ··············· ··············· ······ ······ ··············· v Hyperleda 10 10 10 11 10 10 11 11 11 8 10 11 11 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 c × × × × × × × × × × × × × × × × B 6 2 2 9 9 4 5 5 5 0 0 4 5 4 3 7 ...... L 1 9 4 0 0 1 0 0 0 1 1 0 0 0 2 1 LEDA ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 9 8 4 5 6 6 0 1 0 4 0 1 0 3 7 4 ...... 2 7 J PA 04 150 4 30 52 9 30 140 8 24 25 2 38 95 1 41 145 3 20 60 1 12 75 1 2216 50 15 1 1 20 55 3 06 70 1 19 42 4 34 85 5 J ...... b 9 0 8 0 8 0 9 0 9 0 4 0 2 0 1 0 9 0 8 0 5 0 5 0 1 0 4 0 ...... J R Table 4.2. Optical properties 16 36 17 49 33 19 17 23 33 25 17 27 33 25 33 26 33 22 33 17 33 14 33 25 28 29 33 14 2MASS ...... ············ ············ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± ± ± ± ± ± K M 70 19 19 07 01 94 01 98 33 84 71 06 53 43 ...... 25 26 25 24 26 24 26 25 26 25 24 26 25 25 − − − − − − − − − − − − − − 5 7 4 7 9 8 2 6 2 8 0 1 8 7 8 6 ...... 1 1 1 2 0 9 7 3 14 11 16 11 10 10 11 21 a ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± D 2 0 0 5 5 1 7 6 7 3 9 2 8 6 2 8 ...... Name NGC1132 98 NGC0741 79 NGC1399 20 NGC1265 109 NGC1316 21 NGC0821 24 NGC0720 27 NGC0533 77 NGC0507 71 NGC0404 3 NGC0315 71 NGC0383 73 NGC0193 60 IC4296 51 IC1459 29 IC1262 143 112 e e ··· Ref. opt PA Photometry 10 123 T,U,V,W 25 40 T,U 18 157 T,U 46 81 T,U 36 47 13 67 T,U,V,W 50 40 T,U,V,W 27 89 T 32 7 U,V 13 124 T 04 56 T,U 12 162 T ...... opt ········· ········· ········· ········· ········· d Ref. 7 N 0 30 M 0 25 M 0 90 K 80 D 0 89 D 0 85 J 10 I 93 D 0 10 D 0 60 G 0 20 G 0 89 F 0 185 D 0 100 L 0 254 K 188 H rot < < v Hyperleda < 10 10 10 10 10 10 10 9 10 10 10 10 11 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 c × × × × × × × × × × × × × × × × × B 0 2 2 4 6 9 3 5 9 0 6 2 5 1 7 6 7 ...... L 1 1 1 1 1 0 0 1 0 1 0 3 0 1 0 3 0 LEDA ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 7 3 1 5 8 8 6 0 6 4 2 2 3 4 4 6 2 ...... J Table 4.2 PA 06 148 5 24 37 4 16 158 5 37 80 5 28 47 5 33 107 3 09 70 1 40 42 8 57 42 1 22 155 3 08 145 2 30 90 8 28 5 1 34 158 4 10 143 3 07 20 7 12 163 3 J ...... b 8 0 7 0 5 0 0 0 8 0 3 0 9 0 7 0 4 0 8 0 3 0 9 0 8 0 9 0 0 0 4 0 3 0 ...... J R 11 34 17 40 19 25 25 33 28 43 18 32 11 29 09 27 09 36 20 14 29 19 33 15 33 24 17 33 18 29 26 36 19 19 2MASS ...... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± K M 10 91 24 03 30 81 85 81 05 43 78 59 06 06 69 60 79 ...... 25 24 25 25 25 24 23 22 24 24 23 25 26 25 24 25 24 − − − − − − − − − − − − − − − − − 9 6 8 7 0 7 5 5 4 5 9 2 9 5 6 5 8 ...... 0 1 2 2 3 1 0 0 0 3 2 8 9 1 1 3 1 a ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± D 4 4 6 9 9 0 6 2 7 8 6 4 0 5 7 8 0 ...... Name NGC4374 18 NGC4365 20 NGC4261 31 NGC4125 23 NGC3923 22 NGC3585 20 NGC3379 10 NGC3377 11 NGC3115 9 NGC2865 37 NGC2434 21 NGC1700 54 NGC1600 66 NGC1553 18 NGC1549 19 NGC1407 28 NGC1404 21 113 e e Ref. opt PA Photometry 06 53 U,W 27 143 U,V,W 05 17 T 31 94 T,U 44 66 T,U,V 20 103 U,V 23 145 U,V 37 163 T,U,W 56 48 T,U,W 08 126 U,W 16 177 T,U 18 157 U,V 25 123 U,V ...... opt ········· d Ref. 10 R 0 70 R 0 65 Q 0 30 M 0 40 O 0 73 D 0 110 S 0 110 P 0 110 D 0 140 D 0 155 D 0 205 L 117 D 0 100 D 0 ··············· ··············· ··············· ··············· rot < v Hyperleda < 10 9 11 9 10 10 10 10 10 10 10 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 c × × × × × × × × × × × × × × × × × × B 0 4 5 4 0 8 4 9 0 6 0 5 7 4 7 4 7 3 ...... L 1 1 0 2 0 1 3 0 1 0 1 1 1 0 0 0 1 1 LEDA ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 4 3 2 4 2 0 3 7 9 7 9 8 1 3 8 7 8 9 ...... J Table 4.2 PA 06 30 4 32 140 5 24 155 1 50 50 2 22 175 6 04 20 4 28 95 6 33 65 1 19 110 5 22 148 2 37 165 2 54 50 6 16 125 5 08 150 2 63 111 2 13 170 2 15 153 8 25 120 5 J ...... b 5 0 9 0 8 0 0 0 3 0 3 0 6 0 4 0 2 0 3 0 9 0 9 0 4 0 9 0 8 0 8 0 2 0 7 0 ...... J R 20 34 21 4 33 16 14 79 33 10 28 25 33 15 14 42 15 45 13 59 20 32 17 19 33 10 14 25 20 43 11 30 10 59 14 59 2MASS ...... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± K M 04 96 95 33 09 76 27 98 39 41 56 94 78 20 67 16 66 07 ...... 25 22 26 24 21 24 25 23 25 24 24 22 25 24 24 24 25 25 − − − − − − − − − − − − − − − − − − 3 5 9 7 2 0 0 8 2 9 7 2 0 6 6 9 8 1 ...... 2 2 0 4 6 0 1 0 1 1 1 1 0 0 1 14 15 14 a ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± D 9 9 3 5 0 2 9 7 8 7 3 0 4 3 9 1 3 1 ...... Name NGC5846 24 NGC5845 25 NGC5171 99 NGC5532 104 NGC5102 4 NGC5044 31 NGC5018 39 NGC4697 11 NGC4649 16 NGC4636 14 NGC4621 18 NGC4564 15 NGC4555 97 NGC4552 15 NGC4526 16 NGC4494 17 NGC4472 16 NGC4406 17 114 ) ), ). ), e e ), D: 1998 1997 2006 1997 Ref. ). ( ( Binney -band), K 1995 Longhetti ( opt 2002 ( ), P: PA ), H: Photometry 27 65 T,U 49 63 U . . 1997b opt ( 0 0 1994 Prugniel et al. Paturel et al. ( d Pellegrini et al. Bonfanti et al. Ref. ), L: aco-ars et al. Falcón-Barroso rot ······ ······ ··············· ), C: v 1997 Hyperleda Longo et al. ): absolute magnitude ( Simien and Prugniel ( ), W: ) and LEDA ( 1994 11 10 10 ( 2000 ), G: ), S: 1990 2001 10 10 10 Simien and Prugniel ( ( Fisher c × × × 1998 1993 -band). from published optical surface photometry. ( B 4 2 2 ( . . . J , taken from Hyperleda ( 1 J ), O: L 0 1 2 J ), K: − R LEDA R ± ± ± 2 2 . . 1 0 6 1998 1 . . . 1992 ( erg s 1 Jarrett et al. ( − − 32 Tonry et al. Peletier et al. 8 8 . . 10 J × Carollo et al. Graham et al. ), V: Table 4.2 2 PA Prugniel and Simien Bettoni . 28 65 1 50 60 4 20 5 4 J ), R: ), F: . . . = 5 1988 ), J: ( ), B:

b 6 0 8 0 6 0 B, . . . J 1995 ( L 1994a R ( 1994b 1997a ( Simien and Prugniel ( 33 12 33 21 33 11 2MASS . . . evaluated between 0 0 0 0 1 ), N: ± ± ± − K Bender et al. M 66 40 48 . . . 1988 ( 25 25 25 ), U: − − − D’Onofrio et al. 1994 , eﬀective ellipticity and position angle (all ( 8 5 6 00 . . . ), E: 8 10 11 Carollo and Danziger a Carollo and Danziger Simien and Prugniel ± ± ± 1994 D ( 2 2 9 . . . ), Q: ), I: 1990 1998 ( ( Davies and Birkinshaw Data taken from the 2MASS extended source catalog ( Rotational velocities in km s Distances and associated errors in Mpc, taken from Ellipticity and position angle, evaluated between 0 Absolute blue luminosity in units of Goudfrooij et al. a e b c d Name et al. Bender et al. references. A: et al. half-light radius in T: M: LEDA errors are assumed to be 15%. NGC7052 70 NGC7618 77 NGC6482 58 115 4.3 Results

4.3.1 X-ray vs. Optical Luminosity

For the ﬁrst time, we have spatially isolated the hot gas emission in normal ellipti-

cal galaxies to allow an unbiased morphological analysis of a large sample of objects.

Figure 4.1 shows the X-ray gas gallery, along with the optical DSS-2 R-band images

for each object. We rescale all images to show the same physical size of 50 kpc, except

for the two closest galaxies, where we indicate the size by a separate scale bar. We

have ordered Figure 4.1 with decreasing absolute K luminosity, a good indicator of the total stellar mass of the host galaxies. There is a surprisingly large spread in

X-ray properties for galaxies that have similar stellar contents, i.e. that are close to each other in the figure. Galaxies with similar optical properties can have gas luminosities differing by orders of magnitude (e.g. NGC 5044 and NGC 1549, NGC 4555 and NGC 0533). At the same time, galaxies with comparable gas contents can have extremely different optical appearances (e.g. NGC 1404 and NGC 4649).

These qualitative observations are consistent with the scatter in the well-known

2 LX ∝ LB relation (O’Sullivan et al. 2001, and references therein), one of the elemen- tary empirical correlations connecting X-ray and optical parameters. O’Sullivan et al.

(2001) also observe a ﬂattening of the relation toward lower blue luminosities. They

attribute this trend to the increasing relative importance of point source emission,

which is unresolved in their ROSAT and Einstein data. Our LX,Gas–LB relation, with 116

Figure 4.1: Adaptively binned Chandra X-ray gas surface brightness maps (right) and optical DSS R-band images (left). The objects are ordered by 2MASS K band luminosity, starting with the most luminous galaxy on the top left of the page, and decreasing to the right and then to the next row. The physical scale of each image is 50 kpc × 50 kpc, except where indicated by an individually attached scale bar. The color range of the X-ray gas distribution is scaled logarithmically between 5 × 10−11 and 3 × 10−7 photons sec−1cm−2 arcsec−2. The x and y-axes are labelled according to right ascension and declination (2000), respectively. 117

Figure 4.1: Continued 118

Figure 4.1: Continued 119

Figure 4.1: Continued 120

Figure 4.1: Continued 121

Figure 4.1: Continued 122 the stellar source contribution removed, (Figure 4.2) is consistent with a single slope, and agrees well with O’Sullivan et al. (2001)’s best ﬁt (dashed line). Nonetheless, we still see a large scatter in this relation, covering almost two orders of magnitude in X-ray luminosity for a given absolute B magnitude. A recent study by Ellis and

O’Sullivan (2006) shows a similar relation between X-ray and K-band luminosities, with an almost identical scatter, suggesting a large scatter in X-ray luminosities as the dominant cause.

4.3.2 X-ray vs. Optical Morphology

Not only do the luminosities of the hot gas and stellar components differ vastly, there are also significant differences between the X-ray and optical morphology. In fact, Figure 4.1 shows that it is impossible to predict the gas morphology from looking at the stellar distribution, or vice versa. There are some optically flat galaxies with round X-ray isophotes (e.g. NGC 0720), and others with very flat X-ray emission

(e.g. NGC 1700). Optically round galaxies show a similar range in X-ray ellipticities, ranging from round (e.g. NGC 1404) to ﬂat (e.g. NGC 0533).

Many galaxies, in fact, appear asymmetrically disturbed. We discuss this asymmetry and its origin in Paper II. For now, it is important to ﬁrst quantify the overall shape of the gas emission. If the gas is in true hydrostatic equilibrium, the hot gas isophotes should trace the potential isophotes (e.g. Binney and Tremaine 1987; Buote and Canizares 1994). Thus, we construct X-ray gas ellipticity and position angle pro- 123

Figure 4.2: Total X-ray gas luminosity in erg s−1 as a function of absolute blue 32 −1 luminosity in units of blue solar luminosity (LB, = 5.2 × 10 erg s ) taken from LEDA. The dashed line shows the best ﬁt by O’Sullivan et al. (2001), which they statistically correct for the expected contribution from unresolved point sources. Our data is consistent with their relation. 124

files, shown in Figure 4.3 (solid circles), with published optical profiles overlaid. The optical profiles are generally “well-behaved” and reveal only modest radial trends in their ellipticities and position angles. Optical isophotal twists, if present at all, rarely exceed a few degrees.

The X-ray proﬁles tell a completely diﬀerent story. Often, the gas ellipticities change rapidly as a function of radius (e.g. NGC 1399, NGC 4374). These features are often accompanied by sudden changes in position angle (e.g. NGC 4636, NGC 5044).

Isophotal twists in the gas emission are common, and only very few objects show proﬁles that are consistent with a single major axis orientation (e.g. NGC 3923,

NGC 1700). In many cases isophotal twists or sudden changes in ellipticity also coincide with asymmetries in the gas images (e.g. NGC 5044).

It is generally agreed that the potentials of early-type galaxies are stellar-mass dominated inside 1 or 2 optical eﬀective radii (e.g. Mamon andLokas 2005). To test whether the X-ray gas ﬂattening is consistent with hydrostatic equilibrium, we extract mean ellipticities for the hot gas emission and the star light between 0.8 and

1.2 RJ. Figure 4.4 shows that there is absolutely no correlation between optical and gas ellipticities. This lack of correlation is independent of our choice of extraction radius. An equivalent result is also obtained if we replace the optical ellipticities with the 2MASS J-band eﬀective ellipticities.

This is very surprising if the standard assumption of hydrostatic equilibrium is truly valid for the hot interstellar medium. If one assumes an oblate logarithmic 125

Figure 4.3: Radial isophotal ellipticity and position angle profiles for the subset of 36 elliptical galaxies containing sufficient signal. Large filled circles with error bars denote X-ray gas profiles; other symbols denote optical profiles as indicated in the figure. The 2MASS ellipticity and position angle are marked with arrows at the right border. The vertical dashed lines mark the 2MASS J-band effective radius. 126

Figure 4.3: Continued.

potential, the equipotential surfaces should be about one third as ﬂattened as the underlying density distribution (Binney and Tremaine 1987). However, Figure 4.4 shows no correlation between the observed X-ray gas ellipticity and stellar ellipticity.

In particular, we find that the X-ray isophotes are often much flatter than the stellar isophotes, an observation difficult to explain with hydrostatic gas sitting quietly in a potential well.

We do observe a tendency for galaxies to have their X-ray gas major axis aligned with the stellar distribution. Figure 4.5 shows a histogram of the absolute diﬀerences 127

Figure 4.4: X-ray gas ellipticity vs. optical ellipticity, both evaluated between 0.8 − 1.2 RJ. There is no correlation, contrary to what what would be expected if the gas were in hydrostatic equilibrium in a stellar-mass-dominated potential. 128

between the 2MASS J-band major axis position angles (PAJ) and gas position angles

(PAX). A Kolmogorov-Smirnov test rules out a random distribution at the 97% con-

ﬁdence level. Given the fact that isophotal twists often correlate with the orientation of asymmetries in the gas, it is not clear whether this alignment is a consequence of the underlying potential. An alternative is that it is a consequence of a misalignment between radio sources optical major axes (Palimaka et al. 1979), which is present in our sample and which we fully discuss in Paper II.

4.3.3 Rotational Support

A significant fraction of the hot gas in elliptical galaxies is believed to be due to stellar mass-loss (e.g. Brighenti and Mathews 2000). Thus, the gas should contain a significant amount of specific angular momentum, causing it to settle into a flattened rotating disk (Brighenti and Mathews 1997). This scenario predicts a relationship between the stellar rotational velocity and the X-ray gas ellipticity, with faster rotating systems exhibiting flatter gas isophotes. Figure 4.6 shows the observed X-ray ellipticity between 0.8 and 1.2RJ as a function of mean stellar rotational velocity in the same radial range. In agreement with previous ROSAT and Einstein observations of elliptical galaxies (Hanlan and Bregman 2000), we find no evidence for any correlation between these parameters. A Spearman rank analysis yields a probability of

54% for the null hypothesis of no correlation. 129

Figure 4.5: Histogram of absolute diﬀerences between the 2MASS J-band position angle PAJ and the X-ray gas position angle (PAX) between 0.8−1.2RJ. The error bars indicate the 1σ uncertainties per bin. Gas and stellar major axes have a tendency to be aligned, at the 97% conﬁdence level.

Such a lack of correlation could still be consistent with an alternative scenario,

where the majority of the hot gas is not due to stellar mass loss, but instead is

acquired externally through mergers, infalling gas clouds or through tidal stripping

during close encounters. The hot gas would then slowly ﬂow toward the center and

settle into a cooling disk (e.g. Brighenti and Mathews 1997). Thus, if angular mo-

mentum is conserved during the inﬂow, one should be able to observe a trend for 130

Figure 4.6: X-ray ellipticity as a function of rotational stellar velocity between 0.8 − 1.2 RJ. No correlation is present, contrary to what is expected if the hot gas would be due to stellar mass-loss and subsequently settle into a cooling disk. 131

the X-ray ellipticities to rise inward (Hanlan and Bregman 2000), as the angular mo-

mentum becomes more important. The detailed ellipticity proﬁles in Figure 4.3 do not support this prediction observationally, ellipticities do not systematically increase inward. Moreover, signiﬁcant rotational support would not account for the prevalence of strong isophotal twists.

4.4 Discussion

4.4.1 Implications for Hydrostatic Equilibrium

Within one stellar eﬀective radius, the gravitational potentials of normal elliptical galaxies are dominated by its stellar component, with a rather negligible contribution of the dark matter halo (e.g. Mamon andLokas 2005). Thus, if the assumption of hydrostatic equilibrium were valid, one would expect the hot gas to trace the isophotes of the underlying stellar gravitational potential (Buote and Canizares 1994). Since projected isopotentials are rounder than the projected isopleths of the underlying density, we would also expect the gas emission to be rounder than the starlight. Sur- prisingly, we do not observe any correlation between the optical and X-ray ellipticities at any radius. The gas emission is not even systematically rounder than the stellar light, as one would expect. Thus, the hot gas is not in hydrostatic equilibrium, at least to the extent that the information about the shape of the potential is lost. We therefore conclude that it is impossible to use the hot gas in elliptical galaxies to re- 132 liably infer the shape of the total mass distribution. Buote and collaborators (Buote et al. 2002; Buote and Canizares 1996, 1994) have used this technique to argue for a

flattened dark matter halo in NGC 720. While it is possible that hydrostatic equilibrium could hold in some individual systems, our results show that this would be the exception rather than the rule, and there is no independent test to reveal where hydrostatic equilibrium does hold. In the case of NGC 720, we find that, after resolved and unresolved LMXB emission are removed, the gas ellipticity is considerably reduced; thus even if hydrostatic equilibrium were in effect in NGC 720, there would still be no evidence for a flat halo.

If we were instead to assume that the morphology of the gas emission really were a result of the underlying potential, our data would require extremely ﬂat, complex dark matter halos with signiﬁcant substructure to explain the large ellipticities and isophotal twists. This is highly unlikely and inconsistent with stellar kinematics (e.g.

Cappellari et al. 2006) or simulations of large-scale structure formation (e.g. Springel et al. 2005). Even though triaxial dark matter halos are able to produce simple twists in X-ray isophotes (Romanowsky and Kochanek 1998), these eﬀects would be insuﬃcient to explain the complexity and magnitude of the observed features.

The assumption of hydrostatic equilibrium is also the theoretical basis for a widely used technique to derive radial mass proﬁles, based on circularly averaged, deprojected

X-ray pressure proﬁles (e.g. Forman et al. 1985; Killeen and Bicknell 1988; Paolillo et al. 2003; Humphrey et al. 2006; Fukazawa et al. 2006). If we are correct and the 133

gas is not hydrostatic, what are the consequences for radial mass proﬁles? Imagine

a region that was locally overpressured by a factor q. Assuming adiabatic expansion

this region would expand by a factor q1/5 in linear size over a sound crossing time

scale of ∼ 108 years, to regain pressure equilibrium. To redistribute gas a signiﬁcant

distance along an equipotential would thus imply an overpressure q ∼ 10. If the

galaxy were globally overpressured by this factor, one would infer a mass a factor

of q too large. However, normal ellipticals are probably only locally overpressured,

and so averaging azimuthally over N over- and underpressured regions in a radial

analysis would tend to reduce this eﬀect by a factor of order N 1/2, resulting in a mass estimate in error by a factor of a few. Such overpressures would not drive a wind, since adiabatic expansion requires only modest readjustments in linear size to smooth out even an order of magnitude diﬀerence in pressure.

4.4.2 Implications for Rotational Support

The hot gas in elliptical galaxies is believed to come from some combination of stellar mass loss, infall or mergers. In each case, the gas should carry signiﬁcant amounts of angular momentum. In a standard cooling ﬂow model that conserves angular momentum, the gas will settle into rotationally supported cooling disks (Brighenti and

Mathews 1997, 1996; Kley and Mathews 1995). These rotating cooling ﬂow models predict ellipticity proﬁles that rise inward, with minimal isophotal twist. 134

Figures 4.3 and 4.1 show that these predictions are inconsistent with observations.

Although we do find rather large X-ray ellipticities, they do not systematically increase toward smaller radii. Our profiles also reveal dramatic isophotal twists and asymmetries that would not arise naturally in a scenario where the ellipticities are caused by rotation alone. In addition, we find no relation between stellar rotational velocity and the gas flattening, as one would expect if the gas is mainly due to stellar mass loss. Thus, we conclude that the X-ray gas morphology is not dictated by rotation, in agreement with previous ROSAT observations (Hanlan and Bregman

2000).

The question now is whether the failure to observe rotationally flattened X-ray disks is a serious blow to cooling flow models. One way to save the cooling flow picture would be to efficiently transfer angular momentum through turbulence in the gas (Shadmehri and Ghanbari 2002; Brighenti and Mathews 2000), but it is unclear how effective this process is for elliptical galaxies. Another alternative is that spatially distributed multi-temperature mass dropout can circularize the X-ray isophotes (Hanlan and Bregman 2000). However, recent XMM-Newton spectroscopy of normal elliptical galaxies (e.g Xu et al. 2002; Buote et al. 2003) rules out the existence of sufficient intermediate temperature gas. In addition, Bregman et al.

(2006) are able to directly trace the amount of this intermediate gas by measuring its

O VI emission (∼ 105.5K) with the Far Ultraviolet Spectral Explorer (FUSE). Bregman et al. (2005) examine the spatial distribution of this warm gas for NGC 4636 and 135

NGC 5846 and constrain the size of the cooling region to be smaller than 0.8 kpc and

0.5 kpc, respectively. Their measurements are consistent with moderate cooling ﬂows with centrally concentrated mass dropout and rule out spatially distributed dropout for these galaxies.

Another explanation for the lack of disk signatures is that the hot gas is actually

flowing outward instead of inward, eliminating the need for the gas to settle into a cooling disk. An idea by Brighenti and Mathews (2006) seems to be successful in stopping inward cooling flows by AGN-induced massive jet outflows, which are stable for several gigayears.

Alternatively, morphological asymmetries, which are clearly signiﬁcant, may be masking possible disk signatures. Whatever the cause of these asymmetries (see Paper

II), this effect could be effective in disrupting the flattest X-ray isophotes at small radii close to the center. Detailed simulations are needed to confirm this possibility.

Thus, our results do not imply that rotational support of the hot gas in elliptical galaxies has no importance at all. We can merely state that it is not the dominant factor that causes the large observed ellipticities.

There is other evidence that gas rotation might be present. For example, Statler and McNamara (2002) find extremely flat X-ray emission in NGC 1700, which they interpret as a large-scale cooling disk. Their model yields a specific angular momentum and cooling time for the hot gas that is consistent with the gas having been acquired during the last major merger. We find that removal of unresolved point 136

sources somewhat reduces the X-ray ellipticity of this object; but the data are still

consistent with their claimed 15 kpc rotating disk. Additional support for rotation

has recently been reported by Bregman et al. (2005), who ﬁnd that the O VI line

structure of NGC 4636 exhibits signs consistent with rotation. Also, an analysis of

ASCA data for the hot gas in the Centaurus cluster shows signatures of bulk rotation

(Dupke and Bregman 2001).

4.5 Conclusions

We have analyzed the X-ray emission of 54 normal elliptical galaxies in the Chan-

dra archive and isolated their diﬀuse hot interstellar gas emission from the emission

of discrete stellar point sources for the ﬁrst time. We qualitatively and quantitatively

compare the morphology of the hot gas to the shape of the stellar distribution and

find that they have very little in common, despite the known LX–LB relation. We compute ellipticity and position angle profiles for the X-ray gas and compare them to published optical profiles. In particular, we do not find a correlation between optical and X-ray ellipticities, suggesting that the gas is at least far enough out of hydrostatic equilibrium that the information about the shape of the underlying potential is lost.

We also argue that X-ray derived radial mass proﬁles may be in error by factors of as much as a few, without the necessity for the galaxy to drive a global wind. 137

Although we find very large X-ray gas ellipticities to be common, the gas morphology is generally inconsistent with rotationally flattened disks, and a comparison with stellar rotational velocities yields no evidence for significant rotational support.

The fact that neither the shape of the underlying potential nor rotational support determine the overall distribution of the X-ray emitting gas, combined with its general disturbed appearance, suggests the involvement of another major component: the central AGN. We assess the importance of the AGN in Paper II, where we draw a connection between gas morphology and AGN luminosity. These new ﬁndings are consistent with the AGN constantly stirring up the interstellar medium by inﬂating buoyant bubbles, which may also play a role in redistributing the angular momentum of the hot gas through entrainment. These intermittent AGN outbursts could also be responsible for disrupting or masking the signatures of cooling disks in the central regions of elliptical galaxies. 138 Chapter 5

Morphological Evidence for AGN feedback

5.1 Introduction

In the ﬁrst paper of this series (Diehl and Statler 2006b, hereafter Paper I) we conducted an initial morphological analysis of the hot interstellar medium (ISM) of normal elliptical galaxies, derived from archived Chandra observations of 54 objects.

This paper introduced a new technique to isolate the diffuse hot gas emission from the contaminating effects of unresolved point sources, and presented a gallery of adaptively binned gas-only images. By fitting elliptical isophotes to these images, we demonstrated that the apparent flattening of the X-ray gas is completely uncorrelated with, and often significantly larger than, that of the starlight. Since these ellipticities were extracted around one optical effective radius, where gravitational potentials are expected to be stellar-mass dominated (e.g. Mamon andLokas 2005), the absence of any correlation implies that the hot gas cannot be in hydrostatic equilibrium.

Consequently, eﬀorts to measure the shapes of dark matter halos using X-ray gas isophotes cannot succeed (e.g. Buote and Canizares 1994; Buote et al. 2002) and 139

radial mass proﬁles derived from X-ray data (Humphrey et al. 2006; Fukazawa et al.

2006) could be in error by factors of several.

This paper takes up the question left unaddressed by Paper I: what is the origin

of the gas ﬂattening, if not gravitational? In Paper I, we already excluded rotational

ﬂattening as the dominant cause. A qualitative analysis of gas morphologies also

revealed that they are often asymmetric and disturbed. In this paper we will now

quantify this asymmetry, show that it and the isophotal ellipticity are evidently caused

by the same underlying disturbance, and show strong evidence that the root cause

of this disturbance is the activity of the central active nucleus, even in those systems

with very weak active galactic nuclei (AGN).

Asymmetries are well-known in X-ray studies of galaxies, groups and clusters.

Chandra and XMM-Newton observations of clusters of galaxies reveal strong devia-

tions from smooth surface brightness distributions. Many of these features are be-

lieved to be due to cold fronts, caused by infalling substructure into the cluster center

(e.g. Chatzikos et al. 2006), or gas sloshing in the gravitational potential (e.g. As- casibar and Markevitch 2006). In other cases, depressions in the surface brightness

distribution are found to be coincident with extended radio emission (e.g. Nulsen

et al. 2005). These depressions, or “bubbles”, are generally believed to be pockets of

low-density extremely hot plasma, inﬂated by jets powered by the central AGN (Mc-

Namara et al. 2000). However, there are many cases where the depressions have no

obvious radio counterparts, which has brought them the nickname “ghost cavities” 140

(McNamara et al. 2001). These cavities are now understood as relic bubbles that

have detached from the radio source and are buoyantly rising radially outward in the

cluster gas.

Unexpectedly, Chandra and XMM observations of normal elliptical galaxies have

also revealed a wealth of highly disturbed gas morphologies with qualitatively similar

properties to clusters. Many individual observations have been analyzed in detail

and a variety of diﬀerent explanations have been proposed. Sharp, one-sided drops

in surface brightness are usually interpreted as signs of ram-pressure, distorting the

gas in elliptical galaxies as they move through the ambient intracluster or intragroup

medium, as in NGC 4472 (Irwin and Sarazin 1996; Biller et al. 2004) and NGC 1404

(Machacek et al. 2004). To explain the very asymmetric emission in NGC 7618,

Kraft et al. (2006) even argue for a major group-group merger. Other observations

are not interpreted as results of environmental eﬀects, but rather as signatures of

the central AGN. For a few cases, such as NGC 4374 (Finoguenov and Jones 2001)

or NGC 4472 (Biller et al. 2004), the association with the AGN is indicated clearly by the correspondence between the radio source and depressions in the X-ray gas distribution. In other objects, one can directly detect the X-ray counterpart of the radio jet (Sambruna et al. 2004). However, most cases are less clear-cut. For example, the origin of the shock-like features seen in NGC 1553 (Blanton et al. 2001) or

NGC 4636 (Jones et al. 2002b) is still a mystery. The morphologies in other galaxies 141

qualitatively resemble ghost cavities very close to the core (e.g. NGC5044, Buote

et al. 2003), without evidence for an active radio source.

These individual cases come with their own individual interpretations and analysis techniques, making general statements about elliptical galaxies problematic. More- over, detailed analyses are generally limited to the X-ray brightest elliptical galaxies with clearly identiﬁable features. Thus, they are often dismissed as special cases, and the common perception of elliptical galaxies as round, hydrostatic objects has not evolved signiﬁcantly since the days of Einstein and ROSAT. However, our comprehensive morphological Chandra survey of normal elliptical galaxies in Paper I shows that disturbances and asymmetries in the gas are actually the norm rather than the exception, even for relatively X-ray faint galaxies. Most galaxies in the archive lack the signal, and therefore the contrast, to reliably identify these features and their origins individually. In this paper, we introduce a statistical measure of asymmetry

(the asymmetry index, η) that allows us to treat all objects on an equal footing. We will show that the asymmetry index is strongly correlated with measures of nuclear activity, and not with environment.

The analysis in this paper begins with the elliptical isophotal ﬁts of Paper I, and is organized as follows. In §5.2 we review the techniques of Paper I and describe the

sample. We then calculate smooth functional ﬁts to the isophotal proﬁles, use these

ﬁts to generate symmetric surface brightness models, and use the residuals from these

models to deﬁne the asymmetry index η for each galaxy. We show by simulations 142 that η is a monotonic measure of the sort of asymmetry expected from multiple cavities, and that it is independent of non-morphological parameters. We describe our techniques to extract the central AGN X-ray luminosity and to determine radio power and environment. In §5.3 we show that the asymmetry and isophotal ellipticity are correlated, and thus measure the same underlying disturbance. We show that neither of these quantities depends on environment, but that they are correlated with measures of AGN power instead. The consequences for AGN feedback in galaxies are discussed in §5.4, before we conclude with a reiteration of our major results in §5.5.

5.2 Data Analysis

5.2.1 Summary of Paper I and Preliminary Analysis

Our full sample, as described in Paper I of this series, consists of 54 early-type galaxies observed with the the ACIS-S instrument on the Chandra satellite during cycles 1-4. The data have been homogeneously reprocessed to avoid problems due to changes in the standard calibration pipeline over time. We will brieﬂy summarize the generation of those data products essential for the understanding of this paper and refer the interested reader back to Paper I for more details.

In Paper I, we presented a new method to isolate the hot gas emission in elliptical galaxies from the contamination of unresolved point sources. This method is based on the fact that point sources and hot gas contribute differently to soft (0.3−1.2 keV) 143 and hard (1.2 − 5 keV) bands, due to their intrinsically different spectra. Thus, by subtracting a properly scaled version of the hard band image from the soft band, we are able to remove the contribution of the harder unresolved point sources and isolate the soft gas emission self-consistently, correcting for the amount of gas flux subtracted from the hard band as well. All images are photon-flux calibrated, corrected for exposure map effects and background. We adaptively binned the gas maps with an adaptive binning technique using weighted Voronoi tesselations (Diehl and Statler

2006a)1. Paper I presented the resulting Chandra gas gallery for elliptical galaxies.

For a subset of 36 galaxies with sufficient signal, we were able to characterize the overall shape of the gas by deriving ellipticity and position angle profiles. A qualitative comparison with optical DSS-2 R-band images and a quantitative comparison with published optical surface photometry reveal little correlation between optical and X- ray properties. In particular, we find no correlations between the optical and X-ray ellipticities at any radius. Even within one effective radius, where stars dominate the gravitational potential (e.g. Mamon andLokas 2005; Humphrey et al. 2006), the two are completely uncorrelated. These findings contradict the assumption that the gas in elliptical galaxies simply rests in hydrostatic equilibrium, and precludes using the gas isophotes to constrain the shape of dark matter halos (Buote and Canizares

1994; Buote et al. 2002). Instead of being hydrostatically calm, the gas morphology is always highly disturbed, even for rather X-ray faint galaxies.

1http://www.phy.ohiou.edu/∼diehl/WVT 144

In this paper, we restrict our analysis to the subset of 36 galaxies (Table 5.1)

for which we derived ellipticity proﬁles in Paper I. In addition to the data prod-

ucts described in Paper I, we also produce calibrated energy-ﬂux images, which are

necessary to determine the central X-ray AGN luminosity (§5.2.3). Similar to the

technique used in Paper I to derive photon-ﬂux calibrated images, we create mono-

energetic exposure maps in steps of 7 in PI (∼ 100 eV) and generate counts images in each individual PI channel (14.6 eV-wide). We then divide each counts image by

the energetically closest exposure map to create a photon-ﬂux-calibrated “slice,” and

multiply each slice by the appropriate energy of the PI channel. Finally, we sum all

energy-weighted slices to produce a calibrated energy-ﬂux image that automatically

adjusts the eﬀective exposure map to spatial changes in the spectral composition

of the galaxies, due to radial temperature gradients and/or point source or AGN

contributions. This energy-ﬂux calibrated image can be used to derive ﬂux values,

upper limits and ﬂux-calibrated surface brightness proﬁles even in situations with

insufficient signal to perform spectral fits. 145 e 25 13 12 11 14 22 18 19 25 25 22 19 22 31 25 31 43 13 ...... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2MASS ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ρ 07 13 28 27 10 74 96 09 95 57 17 47 41 77 66 43 52 03 10 ...... 3 3 3 3 3 2 2 3 2 2 3 3 3 2 2 2 2 3 log 31 32 ··· ··············· ··· ··· ··· ··· ··· ··· ··· ······ ··· ··· ··· ··· ··· 10 10 d × × 2 8 . . 1 0 FIRST L ± ± 8 4 . . 3 2 30 32 34 33 32 32 30 31 32 30 32 32 28 33 33 33 33 33 34 ············ 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 d × × × × × × × × × × × × × × × × × × × 7 3 0 3 4 5 3 1 9 3 6 8 5 6 3 8 7 9 4 ...... NVSS 1 0 1 0 0 0 2 1 1 2 0 1 0 0 0 1 1 2 0 L ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < < 1 3 6 0 1 7 6 4 1 1 8 3 3 0 6 8 3 ...... 1 3 1 3 2 9 3 6 2 6 1 4 1 6 5 9 1 38 39 40 38 38 38 39 38 39 39 39 38 39 38 39 37 40 40 40 41 40 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 c × × × × × × × × × × × × × × × × × × × × × 5 3 0 0 3 9 5 0 1 8 6 8 8 7 9 0 3 1 4 2 6 AGN ...... , 2 1 1 1 0 0 2 1 0 1 5 2 0 6 1 4 3 1 0 4 0 X L ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < < < < < < 0 3 5 5 0 4 2 1 2 0 4 4 2 8 9 ...... ) Radio (20cm) Environment 3 3 4 047 041 2 095 1 013 1 023 2 091 5 074 1 038 032 1 042 055 042 040 6 032 3 074 1 059 4 065 1 ··· ...... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Chandra b ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± η < 050 242 028 174 174 114 167 131 106 334 110 130 133 244 138 394 ...... X-ray ( Table 5.1. Gas morphology, AGN properties and environment 20 0 08 0 03 05 0 06 0 21 14 0 06 0 04 0 08 0 08 0 14 0 09 0 09 0 06 0 42 0 09 0 05 0 ...... ············ ······ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a X ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± 23 29 17 15 14 24 57 24 10 46 06 22 43 17 28 33 21 23 ...... Name NGC0821 NGC1132NGC1265 0 NGC1316NGC1399 0 NGC1404 0 NGC1407 0 NGC1549 0 NGC1553 0 NGC1600 0 0 NGC0741 0 NGC0533NGC0720 0 0 NGC0507 0 IC1262IC1459IC4296 0 NGC0193 0 NGC0315 0 0 NGC0383 0 NGC0404 0 146 e 13 14 13 12 31 09 22 25 12 13 14 16 31 10 43 25 ...... ··· ··· ··· ··· 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2MASS ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ρ 16 18 31 41 54 62 19 66 47 09 13 89 43 31 56 82 10 ...... 3 3 3 3 2 3 3 2 3 3 3 2 2 3 2 2 log 29 32 30 31 29 30 31 31 29 29 31 32 29 29 29 ··· ··· ··· ··· ······ 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 d × × × × × × × × × × × × × × × 7 5 6 5 4 9 5 7 4 6 2 3 5 2 8 ...... 9 0 2 0 6 0 0 0 5 7 0 0 2 2 2 FIRST L ± ± ± ± ± ± ± < < < < < < < < 4 9 1 2 2 5 7 ...... 3 3 4 3 2 1 1 29 31 31 29 29 33 30 31 30 31 30 31 34 30 30 30 29 29 29 30 ······ 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 d × × × × × × × × × × × × × × × × × × × × 7 4 8 7 0 3 2 8 2 3 2 2 4 6 2 8 8 8 7 3 ...... NVSS 8 0 2 6 0 0 0 1 0 1 0 0 1 1 2 3 0 4 8 10 L ± ± ± ± ± ± ± ± ± < < < < < < < < < < < 9 5 1 1 6 7 0 7 2 ...... 2 2 1 8 6 2 1 1 3 39 38 40 38 38 38 38 37 38 37 38 40 38 37 38 37 38 38 38 39 39 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 c Table 5.1 × × × × × × × × × × × × × × × × × × × × × 9 2 2 4 6 6 4 1 6 4 4 9 2 5 1 5 2 0 7 6 9 AGN ...... , 1 7 4 4 3 2 1 4 4 1 1 0 0 2 1 8 2 5 0 2 1 X L ± ± ± ± ± ± ± ± ± ± < < < < < < < < < < < 2 2 6 6 9 2 1 2 6 2 ...... ) Radio (20cm) Environment 6 1 1 177 7 050 8 021 8 012 9 028 009 6 054 1 027 2 033 069 ...... 0 0 0 0 0 0 0 0 0 0 Chandra b ± ± ± ± ± ± ± ± ± ± η 478 130 077 149 086 258 142 056 044 154 ...... X-ray ( 06 0 07 0 03 0 11 0 04 0 02 0 07 0 06 0 06 0 06 0 ...... ························ ······ ······ ·················· ············ 0 0 0 0 0 0 0 0 0 0 a X ± ± ± ± ± ± ± ± ± ± 39 09 18 15 05 32 18 38 20 20 ...... Name NGC4374NGC4406 0 NGC4472 0 NGC4494 0 NGC4526NGC4552 0 NGC4555 0 NGC4564 NGC4621 NGC4636 0 NGC4261NGC4365 0 NGC4125 0 NGC3923 0 NGC3585 NGC3115 NGC3377 NGC3379 NGC2434 NGC2865 NGC1700 0 147 ). e 31 31 31 15 25 12 11 31 13 ...... ··· ··· 0 0 0 0 0 0 0 0 0 2000 2MASS ± ± ± ± ± ± ± ± ± ρ 72 76 64 97 11 39 65 50 17 10 ...... 2 2 2 2 3 3 3 2 3 log . 00 Jarrett et al. 30 31 31 33 30 29 ··· ··· ··· ··· ······ ··· 10 10 10 10 10 10 d × × × × × × 5 2 8 6 1 4 ...... 1 0 0 1 1 3 FIRST L ± ± ± ± < < 0 1 4 7 . . . . 1 2 5 6 31 30 29 30 32 33 31 31 34 28 31 30 , and FIRST within 30 J 10 10 10 10 10 10 10 10 10 10 10 10 and model Sérsic plus point source fits to R d × × × × × × × × × × × × β 0 0 1 8 8 4 3 7 9 0 5 4 ...... NVSS 0 0 1 0 1 2 2 4 1 1 1 4 L ± ± ± ± ± ± ± < < < < < 7 2 6 8 0 1 8 ...... 2 1 1 5 4 6 9 39 40 39 38 40 38 38 39 38 36 37 38 -band effective radius from 2MASS extended source catalog, 10 10 10 10 10 10 10 10 10 10 10 10 J c ( ) from NVSS within 3 Table 5.1 5 keV, derived from × × × × × × × × × × × × 1 J 7 5 5 8 3 5 3 6 6 1 7 3 − AGN ...... − R , 1 0 2 0 3 3 1 2 3 2 3 6 X 2 3 . . Hz L 1 ± ± ± ± ± ± ± < < < < < 1 − 1 4 8 9 6 0 0 ...... − ) Radio (20cm) Environment 6 6 ), derived from the 2MASS extended source catalog ( 8 2 . − 067 1 018 2 022 8 060 3 032 035 3 080 ··· ...... ) between 0 0 0 0 0 0 0 0 Chandra 1 b − ± ± ± ± ± η < < between 0 X 225 118 141 049 213 . . . . . X-ray ( 14 0 17 0 04 0 15 14 0 03 0 22 26 ...... ·················· ······ 0 0 0 0 0 0 0 0 . a η X ± ± ± ± ± ± ± ± 20 18 38 21 22 09 39 23 )...... 2000 Asymmetry index 20 cm continuum radio luminosity (in ergs s Mean X-ray gas ellipticity X-ray AGN luminosity (in ergs s Projected local galaxy density (in Mpc Name b c a d e NGC7618 0 NGC7052 0 NGC5846NGC6482 0 0 NGC5171 NGC5532 NGC5845 NGC4649NGC4697 0 NGC5018 0 NGC5044 0 NGC5102 0 Reported errors only include statistical errors, no systematic errors are included. Jarrett et al. radial surface brightness profiles. 148

5.2.2 Quantifying Asymmetry

Deﬁnition of the Asymmetry Index η

Since many of our galaxy observations lack the required signal and resolution to reliably identify individual asymmetric features in the gas surface brightness maps, we are forced to measure asymmetry statistically. We first construct a smooth, symmetric surface brightness model to subtract from the gas map. We base this model on the isophotal profiles computed in Paper I. These profiles give surface brightness (IX), ellipticity (X),and major axis position angle (PAX) as a function of mean radius r.

We fit this surface brightness profile in log r−log IX space with a quadratic Chebychev polynomial. For two galaxies with more complex surface brightness profiles, we use a third order polynomial and for one other object, we resort to fourth order. To accommodate moderate changes in ellipticity and isophotal twists, we fit the ellipticity and position angle profiles in log r − X and log r − PAX space with a straight line.

From the fits, we compute a smooth, symmetric model for the gas distribution. The left panel of Figure 5.1 shows all three profile fits for NGC 4649. The adaptively binned gas map in the right panel has the elliptical isophotes of the adopted fits overlaid. Finally, we bin the surface brightness model to match the binning structure of the adaptively binned gas map and subtract the smooth model to reveal small scale asymmetries in the gas distribution. 149

To quantify the degree of asymmetry in this residual map, we deﬁne the asymme-

try index η in the following way:

N " 2 2# 1 X Gi − Mi σG,i η = − . (5.1) N M M i=1 i i

The asymmetry index is the sum over all pixels i of the squared relative deviations of the binned gas image Gi from the smooth model Mi, over and above the expected

2 statistical deviations due to Poisson noise σG,i . We ﬁnd that η is an unbiased measure

of asymmetry, independent of exposure time, radial ﬁtting range, background level

or signal-to-noise ratio. The errors on the η values are estimated from a bootstrap

analysis of 20 Monte-Carlo simulations.

Figure 5.2 show representative examples spanning the range of η values present in

our sample. NGC 6482 (η < 0.032, left) shows no apparent signs of disturbance and is statistically consistent with a smooth, purely elliptical model (Khosroshahi et al.

2004). In NGC 4472 (η = 0.077, center), one can detect low-level surface brightness

depressions at several radii (Biller et al. 2004). NGC 4374 (right; Finoguenov and

Jones 2001) has the highest η value (η = 0.48) in our sample. This sequence can

serve as a guide for meaning of η. However, one should keep in mind that the ex-

amples in Figure 5.2 have been chosen to have high signal-to-noise ratios for display purposes.Most galaxies have signiﬁcantly less signal and the asymmetric structures cannot be picked out by eye as easily.

2Equation (5.1) is equivalent to an area-weighted average over bins. We ﬁnd empirically that an unweighted average gives too much emphasis to bright regions and small-scale structure. 150

Figure 5.1: Left panel: Gas X-ray surface brightness (in photons s−1 cm−2 arcsec−2), ellipticity and position angle profile for NGC 4649. Solid lines indicate the Chebychev polynomial fits. Right panel: Adaptively binned gas map of NGC 4649 with the fitted elliptical isophotes overlaid. 151 ; Left: η . The x and y-axes are 2 − arcsec 478). Colors depict gas surface . 2 − = 0 cm 1 η − photons s 6 − to 10 10 − 10 × 077); Right: NGC 4374 ( . = 0 η 032); Center: NGC 4472 ( . 0 η < NGC 6482 ( labelled according to right ascension and declination (2000), respectively. brightness levels with the color scale ranging from 5 Figure 5.2: Gas surface brightness maps for three elliptical galaxies, showing the range in asymmetry index 152

Simulations and Tests

To test the behavior of the asymmetry index η, we simulate images that qualita-

tively reproduce the variety of gas morphologies seen in the data. We start with a

256 × 256 pixel realization of a S´ersic model with index n = 4 and a half-light radius of 50 pixels. We then add disturbances as relative surface brightness depressions surrounded by enhanced rim emission, mimicking the appearance of AGN-induced

“bubbles”, often observed in clusters of galaxies (e.g. McNamara et al. 2000). Figure

5.3 shows a one-dimensional cut through our adopted circular bubble template pro-

ﬁle, which is obtained by subtracting two e−(r/σ)4 functions with slightly diﬀerent σ

values, and adjusting their normalizations such that integrating the 2-d proﬁle yields

a total deviation of zero. We deﬁne the “depression strength” as the maximum rel-

ative deviation at the bubble center, indicated by the −100% mark in our template,

while the dashed vertical lines in Figure 5.3 mark the “bubble size”. We then control the level of asymmetry in our simulations by varying the depression strength, bubble size, and the total number of bubbles.

We simulate the disturbed gas images by randomly distributing the bubbles over the entire Sérsicmodel image. Then, following our real data analysis, we construct a smooth model to subtract. For simplicity, we extract a radial surface brightness profile from circular annuli, and fit it with a Sérsic model, instead of constructing a fully general elliptical model. We adaptively bin the image to a signal-to-noise per bin of 4, and apply the same binning structure to the smooth model. After 153 subtracting the binned model, we derive the asymmetry index from the residuals according to equation (5.1). We produce a suite of test simulations, keeping two parameters fixed while varying the third. For small numbers of simulated bubbles, the disturbed surface brightness models resemble galaxies in which one is able to reliably identify the location of individual bubbles. Although very large numbers of simulated bubbles are unrealistic for real galaxies, we increase the number of bubbles beyond the physically motivated level to achieve more complex asymmetries in the morphology.

We ﬁnd that η is largely independent of the bubble size, but correlates positively with the number of simulated bubbles and their relative depression strength, as shown in the left and middle panel of Figure 5.4. We compute the expected trends by simulating 20 random spatial conﬁgurations for each parameter set without adding

Poisson noise, and computing the average of all η values of these “perfect” data sets.

We ﬁnd that our asymmetry index values are fair representations of the expected values.

The asymmetry index is constructed to account for the statistical scatter in the data and to be insensitive to differences in data quality. To verify this, we repeat our tests, keeping the bubble parameters fixed while varying the total galaxy luminosity, background level, cutoff radius, and the exposure time of the observation. We find no correlations with any of these parameters. As an example, in the right panel of

Figure 5.4 we show one test in which we vary the exposure time. One can see that η 154

Figure 5.3: One-dimensional cut through our adopted two-dimensional simulated “bubble depressions“, demonstrating the fractional depression strength of the bubble with respect to its radial extent. The bubble has negative surface brightness deviations within the bubble radius RBubble , and slightly enhanced rims around it. The proﬁle shape is chosen such that the integrated deviations integrate to 0 over all radii.

is not aﬀected by the increasing resolution that is a result of the rising total number

of counts. We conclude that η is an unbiased measure of the asymmetry present in the gas maps, and unaﬀected by non-morphological data properties.

5.2.3 X-ray AGN Luminosities

We identify the location of the central AGN in the X-ray image by overlaying the high-accuracy center from the 2MASS extended source catalogue (Jarrett et al. 2000).

The 2MASS position is derived from the luminosity weighted center of the co-added

K, J and H band images and has a typical 1σ-uncertainty of only 0.300. We combine 155

Figure 5.4: Results of testing the asymmetry index against models with simulated bubble-like depressions (see Fig. 5.3). The asymmetry index η is sensitive to the number of simulated bubbles (left), the relative strength of the depression (middle) and the eﬀective exposure time, characterized by the total number of counts (right). The dashed lines mark the expected behavior for perfect data.

this uncertainty with Chandra’s pointing accuracy3, and manually assign the AGN to the brightest X-ray point source in the 0.3 − 5.0 keV counts image within a ∼ 3 pixel radius of the 2MASS center. If multiple source candidates are within this field, we take the point source closest to the peak of the diffuse emission. In cases where soft gas emission completely dominates the central region, we revert to the 2−5 keV band for identification instead. This technique allows a rather reliable AGN identification, with only few ambiguous cases.

Unfortunately, the location of the AGN coincides with the peaks of both the diﬀuse gas emission and the stellar point source component. While this helps in pinpointing the location of the AGN, it makes it diﬃcult to determine the AGN

3http://cxc.harvard.edu/mta/ASPECT/abs point.html 156

flux. The standard technique is to extract a spectrum from the central region and to attempt to spectrally disentangle the AGN component from the contaminating diffuse gas and LMXBs (e.g. Kim and Fabbiano 2003). However, the weak AGN in normal elliptical galaxies often yield insufficient counts to constrain all parameters in this complex spectral fit. This fit is additionally complicated by the fact that the AGN and unresolved LMXB components are both well-described by featureless power-laws, and can sometimes become virtually indistinguishable. For many observations in our sample, the AGN contributes no more than a few counts, making a reliable spectral

ﬁt practically impossible.

Instead, we decide to spatially disentangle the X-ray AGN emission from its complex background using the energy-flux calibrated images of diffuse emission. The energy weighting makes it easier to distinguish the hard AGN component. We bin the energy-flux image into circular annuli centered on the AGN position and adaptively change the annular bin sizes to enforce a minimum signal-to-noise requirement of 2. As this would result in very large numbers of bins at larger radii, we also require the annular width to be larger than 10% of the mean bin radius to ensure proper azimuthal averaging within a bin.

We fit the inner 32 arcsec of the radial surface brightness profile with a two- component model, one representing the point source and one the diffuse emission.

The point source profile is obtained from a normalized mono-energetic point-spread function (PSF) centered on the position of the central AGN and computed at its 157 mean photon energy. We bin the PSF image to the same circular binning, to give a point source model with only the normalization flux as a free parameter. To represent the diffuse emission we use a Sérsicor a β model, on top of a uniform background.

Figure 5.5 shows the inner 10 arcsec of two galaxies with a statistically signiﬁcant

AGN detection (NGC 4261, left) and a non-detection (NGC 6482, right). The dashed lines indicate the diffuse component from the Sérsic (grey) and β model fit (black), while the solid lines show the same fits with the additional AGN component. All

fits are inspected by eye and obviously unconverged fits are repeated over a different radial extent until a satisfactory fit is obtained.

Even though both models generally produce equally good fits, the β model fits systematically yield higher fluxes for the AGN, as the β-profile is flatter at small radii.

We adopt the average of the AGN fluxes yielded by the β and Sérsicmodel fits as the best value. The difference between the two individual fits and the average value is assumed to represent a 3σ systematic error and is combined with the statistical errors yielded by each profile fitting procedure. Finally, we correct the AGN fluxes for Galactic absorption with the same correction factor that is used to correct the total gas flux, computed from integrating the best spectral fit for the gas emission with and without the Galactic absorption factor. This correction may be a slight overestimate, since the AGN emission is generally harder and less strongly affected by absorption; on the other hand the column density is also likely to be higher due to intrinsic absorption inside the galaxy. The correction is generally rather small, well 158

below our statistical and systematical errors, and does not aﬀect the computed X-ray

AGN luminosity signiﬁcantly.

The ﬁnal AGN luminosities LX,AGN are reported in Table 5.1, together with the

combined statistical and systematic errors. Flux values that are detected below the

1σ conﬁdence limit are reported as upper limits. For objects with insuﬃcient signal

to produce a surface brightness proﬁle, we sum up the energy-ﬂux calibrated image

within the region containing 99% of the PSF ﬂux and correct for a ﬂat background

extracted from an adjacent annulus extending out to 10 arcsec. Since we have no way

to distinguish between a central peak in gas emission, LMXBs, or an actual AGN for

these galaxies, we quote the 3σ upper bound of the summed ﬂux as an upper limit

on the AGN luminosity.

5.2.4 Radio AGN Luminosities

We use the NRAO VLA Sky Survey (NVSS Condon et al. 1998) to derive homo-

geneous 20 cm radio continuum luminosities for our sample. We inspect all NVSS

images and remove obviously non-associated background sources from the source list.

As we are interested in the AGN’s impact on the ISM, we sum up all associated

radio sources within 3 optical radii to derive the NVSS radio luminosity LNVSS, thus including contributions from radio lobes as well. For the majority of our sample, the limited spatial resolution of the NVSS survey precludes reliably distinguishing between extended and point-like radio sources. Only where unambiguously possible, 159

Figure 5.5: Radial X-ray surface brightness profiles for the inner 600 of NGC 4261 (left) and NGC 6482 (right). Solid grey lines indicate Sèrsicmodel fits, solid black lines show β model fits, including a PSF model for the central AGN. Dashed lines show the same model fits without the AGN component. NGC 4261’s AGN is detected on a 7σ level, NGC 6482 profile reveals no AGN signature. For NGC 6482, the AGN flux yielded by the Sérsicmodel fit is so small that the black dashed line is invisible, as it is covered by the black solid line.

we determine the NVSS position angle by manually measuring the orientation of the major axis.

Twenty-three galaxies in our sample have been observed in the Faint Images of the

Radio Sky at Twenty-Centimeters (FIRST) VLA survey (Becker et al. 1995), which has a much higher spatial resolution than NVSS, with a similar detection limit. We extract FIRST radio luminosities from the inner 3 optical effective radii to match the NVSS extraction region. A comparison between the two radio surveys ensures that both are yielding consistent values. However, the higher spatial resolution of the FIRST survey gives us the opportunity to extract fluxes from the central point 160 source alone, largely excluding contributions from the radio jets. Thus, instead of using a large extraction radius, we sum the flux within a smaller 30 arcsec radius to determine the FIRST AGN luminosity LFIRST, listed in Table 5.1. These values are systematically smaller than the NVSS fluxes due to the smaller extraction region, but still very well correlated. This indicates that our larger NVSS sample is not heavily contaminated by background objects, but that the extra flux is most likely associated with extended radio jets.

5.2.5 The Galaxy Environment

To quantify the environment, we measure the projected galaxy density in the vicin- ity of our sample galaxies by counting the number of neighbors listed in the 2MASS extended source catalog (Jarrett et al. 2000). We identify all galaxies within a projected radius of 100 kpc at the distance of the target as “neighbors.” For relatively nearby objects, we restrict this distance to a maximum angular size of 15 arcmin, to minimize contamination by random foreground or background objects. Despite the smaller physical extraction radius, the number of neighbors for the nearby objects is still sufficient to derive a galaxy density, as the incompleteness limit drops significantly, and lower-luminosity neighbors can be identified. But because the 2MASS catalog is flux-limited, we have to cope with a distance-dependent completeness limit.

We use the K-band Schechter luminosity function from Kochanek et al. (2001) to correct for incompleteness. We integrate the luminosity function down to the com- 161 pleteness limit at the object’s distance and divide by the integral of the luminosity function down to a reference luminosity, which we arbitrarily chose as MK = −11.5.

Thus, we can calculate the fraction of all galaxies above the reference luminosity that we are able to detect. After correcting for incompleteness in this way, our galaxy densities ρ2MASS are independent of distance. We list the values for ρ2MASS in Table

5.1 in units of galaxies per Mpc2. The errors include only statistical errors due to the galaxy counting statistics; deriving systematic errors due to background objects or uncertainties in the galaxy luminosity function are beyond the scope of this paper.

Ideally, one would also like to restrict the list of neighbors in velocity space, to remove galaxies that are simply aligned along the line of sight. Such a three-dimensional restriction requires an additional unbiased source of radial velocities. However, available radial velocities are heavily biased toward “more interesting” regions of the sky and better studied objects. Thus, we refrain from using these velocities and use the projected galaxy density ρ2MASS instead, a measure similar to the Tully density parameter (Tully 1988), but well-deﬁned for our entire sample. All conclusions based on our ρ2MASS are reproducible with the Tully parameter instead. 162

Figure 5.6: The X-ray asymmetry index η as a function of X-ray ellipticity X. The observed positive correlation suggests a common underlying cause for both the large measured X-ray ellipticities and the asymmetries.

5.3 Results

5.3.1 X-ray Ellipticity and Asymmetry

Figure 5.6 shows a comparison between the mean X-ray ellipticities between

0.8 − 1.2 optical radii and the asymmetry index η. There is a clear trend for ﬂat- 163

ter galaxies to be also more asymmetric, suggesting a common underlying cause for

both morphological properties. That is, whatever causes the disturbances on small

scales is also responsible for shaping the overall gas morphology at larger scales. This

partly explains our results from Paper I, where we ﬁnd that the gas ellipticities are

uncorrelated with the ellipticities of the starlight, and thus are not simply dominated

by the shape of the smooth underlying gravitational potential.

5.3.2 Environmental Inﬂuence on Morphology

The probability of interactions with neighboring galaxies through mergers, tidal

stripping or close encounters naturally increases with the local number density of

galaxies. The same is true for the eﬀects of ram-pressure induced by movement

relative to the ambient medium, which scale with density of the intracluster gas, a

quantity that also depends on galaxy density. Thus, if interactions are important in

inﬂuencing the gas morphology of elliptical galaxies, we would expect a correlation

between morphological parameters and the projected galaxy density ρ2MASS.

Figure 5.7 shows that neither the gas ellipticity (upper panel), nor the asymmetry index (lower panel) shows any trend with this measure of environment. A Spearman rank analysis yields a probability of 74.2% for the null hypothesis for the dependence of X-ray ellipticity and 33.5% for the asymmetry dependence on ρ2MASS. Thus, the

X-ray gas morphology is not mainly driven by interactions, although they may be important for some individual objects. However, our morphological analysis is re- 164

Figure 5.7: X-ray ellipticity X (top) and asymmetry index η (bottom) as a function of projected galaxy density ρ2MASS. Both plots indicate that environment is not the driving factor causing the high ellipticities and asymmetries. 165

stricted to an inner region, where we have enough signal to compute an isophotal

model. The environment may play a more important role at larger radii, which can

be probed with XMM-Newton or archive ROSAT observations.

To ensure that these conclusions are independent of our deﬁnition of galaxy den-

sity, we repeat our analysis with other environmental measures: the Tully density

parameter (Tully 1988), the distance to the 10th closest neighbor in the 2MASS extended source catalog (Jarrett et al. 2000), and the number of galaxies associated

with a galaxy group, as listed in the Lyon Group of Galaxies (LGG Garcia 1993)

catalog. All of these measures of environment yield the same result: the environment

is not causing the observed asymmetries or large ellipticities of the hot gas.

5.3.3 Gas Morphology and the Central AGN

Correlation between Radio and X-ray AGN Luminosities

Figure 5.8 compares the AGN X-ray luminosity with both the NVSS (left) and

FIRST (right) 20 cm continuum radio powers. Both plots show a clear correlation

between radio and X-ray luminosities, spanning almost six orders of magnitude. The

slope is consistent with a purely linear relation between both luminosities, as indicated

by the solid lines. A Spearman rank analysis for the LNVSS–LX,AGN relation rejects

the null hypothesis of no correlation at the 99.99% conﬁdence level. The correlation

is not simply a consequence of plotting distance vs. distance, it is equally signiﬁcant

if the distance dependencies of both parameters are removed. 166

Figure 5.8: X-ray AGN luminosity vs. 20 cm continuum radio luminosity with data taken from NVSS within 3 optical radii (left) and from FIRST (right) within a 3000 radius. Arrows indicate 3σ upper limits. The slope of the relationship between radio and X-ray luminosity is close to be linear, as indicated by the solid lines. Thus, X-ray and radio luminosities are likely caused by the same underlying phenomenon, and are independent measures of AGN activity.

A survey of radio emission from normal elliptical galaxies by Wrobel and Heeschen

(1991) suggests that the majority of their radio ﬂux is due to AGN activity rather than star formation. The fact that X-ray and radio luminosities show a tight relationship supports this conclusion for our galaxy sample, as well as indicating that we have properly identiﬁed and isolated the central AGN in the X-ray images. We conclude that both the radio and the X-ray AGN luminosities are reliable tracers of the central

AGN activity, most likely powered by gas accreting onto a supermassive black hole. 167

AGN dominates Gas Morphology

Figure 5.9 shows the dependence of the asymmetry index η on the two independent

measures of AGN activity: the X-ray luminosity LX,AGN of the central point source

(left panel) and the NVSS radio power LNVSS, integrated over three optical radii (right panel). Both AGN properties correlate well with η, such that more disturbed galaxies also exhibit stronger signs of AGN activity. A Spearman rank analysis between

LNVSS and η rejects the null hypothesis of no correlation at the 95.3% confidence level, which is elevated to 99.3% when upper limits are included. The same analysis between the LX,AGN and η yields slightly lower confidence values: 91.7% confidence for the data values only, and 96.6% when upper limits are also included. Since we established in §5.3.3 that both luminosities are independent measures of the same phenomenon, we can combine the two probabilities to compute the null hypothesis of no correlation between general AGN activity and asymmetry. For the data values only, the probability for the existence of a correlation is 99.8%, or 99.998% if upper limits are included as well. This AGN–asymmetry connection is the first strong evidence that the central AGN is generally responsible for disturbing the hot gas morphology even in normal elliptical galaxies and provides further support for the importance of AGN feedback in general.

A comparison with our simulations in §5.2.2 suggests two possible interpretations

for the increase of asymmetry with AGN luminosity: the number of inﬂated bubbles,

or the strength of the created depressions. The asymmetry index is equally sensitive 168

to both and cannot distinguish between them. However, a qualitative investigation

of the gas morphologies (see Paper I) suggests that the depression strengths are the

more likely explanation. The examples in Figure 5.2 already shows the trend that

galaxies with larger η values tend to have stronger surface brightness depressions,

most likely caused by the stronger interaction of more powerful radio sources with

the ISM.

Figure 5.6 (§5.3.1) shows that the large-scale gas morphology is evidently also

aﬀected by the AGN-induced disturbances. Thus, the AGN is responsible for the

lack of correlation between optical and X-ray ellipticities which we describe in Paper

I. We also report in the earlier paper a tendency for the hot gas major axes to be

aligned with those of the starlight. Taking a subsample of 22 galaxies that have

X-ray and stellar ellipticities > 0.1, in order to have well-deﬁned position angles

(PA), we conduct a Kolmogorov-Smirnov (KS) test, which puts the probability for a

chance correlation at only 3.1%. The PA diﬀerences between the gas and the stellar

component, in 15◦-wide bins, are shown as the grey-shaded histogram in Figure 5.10.

A tempting explanation for this alignment is that it reﬂects the orientation of the underlying gravitational potential, which is dominated by the stellar component at these radii. However, our sample exhibits an anti-correlation between radio and optical major axes, which is shown as the solid histogram in Figure 5.10. This con-

troversial phenomenon has been observed early-on by Palimaka et al. (1979), but has

not been conﬁrmed in subsequent studies (Sansom et al. 1987). Nevertheless, a KS- 169 test yields only a 6.2% probability for the null hypothesis in our small sample of 19 galaxies with identiﬁable radio major axes.

In case of a relatively stable radio jet axis, one would expect the jet to preferen- tially evacuate gas along the axis, creating a misalignment between radio and X-ray gas emission. We do observe this anti-correlation, shown in the dashed histogram in Figure 5.10. But only 12 galaxies have both reliable X-ray and radio position angles, leading to an inconclusive 11.7% probability for the null hypothesis. Thus, the detection of this misalignment is marginal and awaits conﬁrmation with a larger sample.

A two-sided KS test yields an 80.6% probability that the radio–optical anticorre- lation and the X-ray–optical alignment are drawn from the same distribution. Thus, we cannot conclude that the gravitational potential is responsible for the observed alignment. The data are consistent with the alignment being caused by the eﬀects of the radio source on the hot ISM.

5.4 Discussion

5.4.1 Causes and Consequences of Disturbances in the Gas

Morphology

Our initial morphological analysis in Paper I revealed a prevalence of rather large

X-ray ellipticities together with a surprising amount of disturbance in the hot ISM of 170

Figure 5.9: Asymmetry index η as a function of X-ray AGN luminosity LX,AGN (left) and 20 cm radio continuum power LNVSS taken from NVSS (right). Both plots indicate that the central AGN luminosity is positively correlated with the observed asymmetry in the gas, with the correlation extending all the way down to the weakest AGN.

normal elliptical galaxies. Now we have found clear evidence for the central AGN to

be the dominant cause of these asymmetries. Most surprisingly, our analysis shows

that this phenomenon is not restricted to powerful radio sources, but rather forms

a continuous correlation down to the weakest AGN. This is in sharp contrast to the

common perception of elliptical galaxies as being quiet, hydrostatic objects.

From the very beginning of X-ray studies of normal elliptical galaxies, it has been

believed that the hot gas sits quietly in the gravitational potential well (e.g. Forman

et al. 1985). But few direct tests have been conducted to test this hypothesis, of-

ten with negative outcome (e.g. Ciotti and Pellegrini 2004; Mathews and Brighenti 171

Figure 5.10: Histogram of absolute diﬀerences between optical (2MASS J-band, PAJ), radio (NVSS 20cm continuum, PANVSS), and X-ray gas (PAX) position angles. The grey shaded histogram with dotted contours shows that there is a clear tendency for galaxies to have X-ray and optical isophotes aligned (reproduced from Diehl and Statler 2006b). The solid line shows an anti-correlation between optical and radio position angles, and the dashed line an anti-correlation between radio and X-ray position angles, providing support for the idea that the radio source is responsible for producing the X-ray–optical alignment.

2003b). Most of these tests were restricted to the detailed analysis of individual

objects and thus widely disregarded as general statements. But our comparison of

optical and X-ray morphologies in Paper I revealed that even within one eﬀective

radius, where the gravitational potential is dominated by the stellar component (Ma- mon andLokas 2005), there is no correlation between stellar and gas ellipticities, very

much at odds with predictions from hydrostatic equilibrium. In fact, many X-ray el- 172

lipticities even exceed those of the starlight, quite the opposite of what is expected

from purely gravitational eﬀects. We also noted the prevalence of asymmetries in

the hot gas in Paper I, which we have now statistically quantiﬁed in this paper with

the asymmetry index η. We ﬁnd that the large observed ellipticities and the amount of asymmetry in the gas are intimately correlated, pointing toward a common cause that dictates the X-ray appearance at small and large scales.

We ﬁnd strong evidence that the central AGN is responsible for disturbing the hot gas over a large range of radii. Intermittent AGN activity stirs the hot gas, pushing it far enough out of equilibrium that any information about the shape of the underlying potential is irreversibly lost. This renders the “geometrical test for dark matter” (e.g.

Buote and Canizares 1994; Buote et al. 2002) untenable for normal elliptical galaxies

(Paper I).

X-ray derived radial mass proﬁles also heavily rely on the assumption of hydrostatic equilibrium. We argued in Paper I that systems temporarily overpressured or underpressured by a factor of a few could yields mass proﬁles in error by the same factor, without dramatic changes to the X-ray gas content. The missing ingredient in Paper I was the link to a viable source to generate these pressure disturbances, which is now found to be the central AGN. That we observe morphological disturbances in the hot ISM in nearly all elliptical galaxies and that some objects even reveal signatures of multiple outbursts (e.g. O’Sullivan et al. 2005) provide evidence

that the duty cycle of the AGN is shorter than or comparable to the sound crossing 173 time. Thus, the hot gas is continually disturbed, without having time to resettle into equilibrium.

To properly address how badly mass profiles are affected by AGN driven winds will require detailed simulations including realistic AGN-feedback, as well as the comparison with mass profiles computed with independent techniques. A study by Fukazawa et al. (2006) uses the same Chandra data from this work to generate mass profiles based on hydrostatic equilibrium. To confirm the validity of this assumption, they compare their X-ray derived mass profile with optically derived profiles for the very well-studied elliptical galaxy NGC 3379, but find a systematic difference of a factor of ∼ 7. Pellegrini and Ciotti (2006) reconcile this discrepancy by fitting NGC 3379’s

X-ray proﬁles with a wind model instead, bringing optical and X-ray masses back into agreement. This result emphasizes our point that hydrostatic equilibrium should not be assumed blindly. For now, X-ray derived dark matter proﬁles for elliptical galaxies should be generally taken with a grain of salt, and one should add a systematic error associated with the uncertainty in the assumption of hydrostatic equilibrium.

5.4.2 Implications for Interactions with the Intergalactic Medium

Our analysis shows that the observed asymmetries in the hot gas and its large ellipticities are not mainly a consequence of interactions with the surrounding intracluster or intragroup medium or interactions with neighboring galaxies. However, we want to emphasize that interactions with the ambient medium can still have a 174

signiﬁcant impact on larger scales. Our morphological analysis is conﬁned to a region

within Chandra’s limited field of view, restricted further by our need for sufficient signal to fit isophotes. Thus, our asymmetry index is not sensitive to anything outside a certain radius which depends on the average surface brightness of the object and the exposure time of the observation.

The majority of X-ray halos associated with elliptical galaxies extend well beyond this radius, as was already demonstrated with observations with the Einstein and

ROSAT satellites (e.g. Forman et al. 1985; O’Sullivan et al. 2003). Interactions with the ambient medium may very well have a major inﬂuence on the gas structure at the outermost radii. We can only conclude that these interactions are not the dominant cause for the asymmetries within the radial range that we are probing.

5.5 Conclusions

We have extended our earlier work from Paper I on normal elliptical galaxies, which show no correlation between optical and X-ray gas ellipticities, contrary to what is expected from gas in hydrostatic equilibrium. Instead we ﬁnd that the hot gas is generally very disturbed. To elucidate the nature of the observed asymmetries in the hot gas, we introduce the asymmetry index η, which measures the statistical deviation from a symmetric surface brightness model. This allows a systematic study of asymmetry even in relatively low-luminosity objects, in which asymmetric features are barely resolved. 175

We ﬁnd no indications that the galaxy environment is mainly responsible for disturbing the hot gas through interactions with neighbor galaxies or the ambient medium. Instead, we ﬁnd a strong correlation between the asymmetry index and two independent measures of AGN activity: the radio continuum power at 20cm from

NVSS (Condon et al. 1998) and the X-ray AGN luminosity extracted from Chandra data. The observed AGN–asymmetry correlation persists all the way down to the weakest AGN, where the NVSS survey reaches its detection limit. This is quite surprising, since these objects generally lack extended jet signatures in their radio images and are mostly detected as weak central point sources, if at all.

Thus, except for a few individual cases, the observed asymmetries rarely have direct radio counterparts. The emerging picture is consistent with the AGN persistently stirring up the interstellar medium through intermittent outbursts, and strengthens the case for the AGN to be responsible for oﬀsetting cooling in normal elliptical galaxies. We will address the impact of the central AGN on temperature and entropy proﬁles in detail in Paper III of this series (Diehl and Statler 2006d). 176 Chapter 6

The Thermodynamic Structure of the Gas

6.1 Introduction

In the first two papers of this series, we conducted the first comprehensive morphological analysis of the hot gas in normal elliptical galaxies. We employed a new technique to separate the gas emission from the contaminating unresolved point source contribution and produced a gallery of adaptively binned gas-only images, which reveal generally disturbed morphologies. A comparison between optical and X-ray ellipticity profiles show no correlation, calling the assumption of hydrostatic equilibrium into question for these objects. We showed that a quantitative measure of asymmetry is strongly correlated to the activity of the central active galactic nucleus (AGN).

Surprisingly, this AGN–morphology correlation forms a continuous trend down to the lowest detectable AGN luminosities, indicating the importance of AGN feedback, even in rather X-ray faint elliptical galaxies.

In this paper, we address the question of whether the central AGN is merely redistributing the gas, or heating it as well. We produce radial temperature proﬁles and

find that they show a variety of distinct types. In particular, we confirm the presence 177 and commonness of negative (outwardly falling) temperature gradients (Humphrey et al. 2006; Fukazawa et al. 2006; Randall et al. 2006; Khosroshahi et al. 2004). We show evidence that the temperature gradients in the inner 2 optical effective radii are dominated either by AGN feedback or compressive heating, and that supernova feedback is unlikely to play a dominant role. In contrast, we find that the temperature gradients at larger radii are influenced by the presence of ambient intragroup or intracluster medium.

Outwardly rising (positive-gradient) temperature proﬁles are usually understood as being the result of eﬃcient radiative cooling in the dense central regions. In addition, at large radii, any accreting gas can shock-heat itself, and may amplify the temperature gradient. This interpretation is supported by the short central cooling times observed for galaxies, groups, or clusters, which may drop well below 100 Myr in the central regions of galaxies. However, cooling times are equally short in galaxies with negative temperature gradients, i.e. with a warm center. Several solutions have been proposed to explain these counter-intuitive objects.

Fukazawa et al. (2006) suggest that the gradients are a function of environment, with outwardly rising (positive) gradients caused by the hotter ambient intracluster or intragroup gas surrounding the galaxy. Galaxies with negative gradients should instead be isolated.

Humphrey et al. (2006), on the other hand, propose a bimodal distribution of temperature gradients, and suggest that the total mass of the system is the decisive 178

factor for the sign of the gradient. The division between their two groups happens

13 at a virial mass of ∼ 10 M , implying a distinction between normal galaxies and

groups. They hypothesize further that the temperature gradients could be related to

a signiﬁcant diﬀerence in the galaxies’ evolutionary histories.

Humphrey et al. (2006) also discuss the possibility of explaining negative gradients

by compressive heating. They note that during a slow inﬂow of relatively cool gas

(< 1−2 keV) the energy gain through gravitational heating would exceed the radiative

losses. For the inﬂow of hotter baryons, radiative cooling would dominate and one

would observe a positive temperature gradient instead. However, they ﬁnd no reason

13 for hot baryons to be speciﬁc to systems above their break mass ∼ 10 M , and

suspect the environment as a fuel source instead.

Khosroshahi et al. (2004) observe a negative temperature gradient for the fossil

group candidate NGC 6482 and argue along the same lines. They model NGC 6482’s

temperature proﬁle successfully with a steady-state cooling ﬂow with a reasonable

˙ −1 cooling rate of M = 2M yr , and adopt it as their preferred solution. They also

estimate that type Ia supernovae (SN) may be responsible for balancing about 1/3 of the radiative losses in this galaxy. They ﬁnd the contribution from type II SN to be insigniﬁcant and argue against AGN feedback on grounds of the very relaxed appearance of NGC 6482. 179

In this paper, we show that the distribution of temperature gradients is not bimodal, and that the gradients in the inner 2 optical eﬀective radii are not inﬂuenced by the environment. We propose instead that the AGN is responsible.

In §6.2, we will summarize our analyses and results from Papers I and II, and describe the methodology to derive radial temperature profiles, two-dimensional temperature maps, and deprojected electron density profiles. We then go on to discuss the various types of temperature profiles seen in our sample in §6.3. For a quantitative analysis, we split the radial range into two regions: the inner region extending out to 2 effective radii and an outer region between 2 − 4 effective radii. We fit and analyze the two gradients separately, and demonstrate that the inner gradient is determined by galaxy properties, while the outer gradient is caused by the presence of hot ambient medium. We also present temperature maps for a subsample of 12 galaxies and show that they appear very disturbed. We find that these disturbances are spatially correlated with asymmetric features in the gas images, which we argued in Paper II are induced by the central AGN. In §??, we concentrate on the overall shape of density, cooling time and entropy profiles, and the consequences for the X- ray luminosity–temperature relation. In §6.6, we will discuss the implications of our

findings for cooling flows, SN heating and AGN feedback, before we briefly summarize in §6.7. 180 6.2 Data Analysis

6.2.1 Summary of Papers I+II and Preliminary Analysis

In Paper I of this series, we introduced a technique to separate the hot gas emission

in elliptical galaxies from the contamination of unresolved point sources. We applied

this technique to a Chandra archive sample of 54 elliptical galaxies and presented a

gallery of adaptively binned gas-only images, which were photon-ﬂux calibrated and

background corrected. We used these gas maps to derive isophotal ellipticity proﬁles

and conducted a systematic morphological analysis. The gas morphologies almost

always look disturbed, and a comparison with optical ellipticity proﬁles argues for a

general lack of hydrostatic equilibrium in elliptical galaxies. In Paper II, we traced

the origin of these disturbances to the inﬂuence of the central AGN by showing that a

quantitative measure of asymmetry is tightly correlated with radio continuum power

and nuclear X-ray luminosity, down to the weakest detectable AGN. In this third

paper, we examine whether the AGN may also play a role in heating the gas and

maintaining it in the X-ray gas phase.

We make use of several parameters from Papers I and II. We list those essential

to our analysis in Tables 6.1 and 6.2 for completeness, along with some additional

quantities. We extract absolute K magnitudes MK and J-band eﬀective radii RJ from the 2MASS extended source catalog (Jarrett et al. 2000). We adopt 20 cm radio

continuum radio luminosities LNVSS from the NRAO VLA Sky Survey (NVSS, Condon 181

et al. 1998) within 3RJ (see Paper II). In addition, we extract 6 cm radio continuum luminosities L6cm from the GB6 catalog of radio sources (Gregory et al. 1996), the

Parkes-MIT-NRAO 4.85GHz Surveys (Wright et al. 1996), and a 6 cm radio catalog by Becker et al. (1991) in the same region. Central velocity dispersion values are taken from the Lyon–Meudon Extragalactic Database (LEDA; Paturel et al. 1997).

We also adopt the projected galaxy density parameter ρ2MASS from Paper II, which is based on the number of neighbors in the 2MASS extended source catalog, and corrected for incompleteness. As it is one of the few accessible parameters to describe the galaxy environment, we also list the Tully (1988) galaxy density ρTully. 182

Table 6.1. Chandra X-ray luminosity and temperature proﬁle parameters.

a b c c Name LX,Gas TX α02 α24

IC1262 2.0 ± 1.7 × 1043 1.30 ± 0.01 0.29 ± 0.02 0.21 ± 0.07 IC1459 4.3 ± 3.2 × 1040 0.48 ± 0.02 −0.00 ± 0.03 −0.27 ± 0.04 IC4296 1.1 ± 0.4 × 1041 0.88 ± 0.02 0.23 ± 0.04 0.08 ± 0.07 NGC0193 2.5 ± 0.8 × 1041 0.77 ± 0.01 ······ NGC0315 9.4 ± 3.4 × 1040 0.64 ± 0.01 0.02 ± 0.02 ··· NGC0383 < 7.5 × 1041 0.98 ± 0.04 0.42 ± 0.06 0.50 ± 0.16 NGC0404 < 2.1 × 1038 0.28 ± 0.07 ······ NGC0507 > 5.7 × 1042 1.03 ± 0.01 0.01 ± 0.01 0.16 ± 0.10 NGC0533 9.6 ± 3.5 × 1041 0.98 ± 0.01 0.18 ± 0.04 ··· NGC0720 9.3 ± 2.7 × 1040 0.57 ± 0.01 −0.05 ± 0.03 −0.04 ± 0.15 NGC0741 3.2 ± 1.3 × 1041 0.96 ± 0.02 0.31 ± 0.04 −0.10 ± 0.12 NGC0821 < 3.3 × 1040 ········· NGC1132 > 9.1 × 1042 1.02 ± 0.01 0.24 ± 0.07 −0.22 ± 0.11 NGC1265 < 1.1 × 1042 0.86 ± 0.08 ······ NGC1316 5.7 ± 2.1 × 1040 0.62 ± 0.01 −0.04 ± 0.04 0.12 ± 0.26 NGC1399 > 7.9 × 1041 1.13 ± 0.01 0.17 ± 0.02 0.10 ± 0.03 NGC1404 1.7 ± 0.4 × 1041 0.58 ± 0.01 −0.10 ± 0.01 0.15 ± 0.05 NGC1407 1.0 ± 0.3 × 1041 0.87 ± 0.01 0.11 ± 0.04 0.46 ± 0.23 NGC1549 > 2.0 × 1040 0.34 ± 0.03 ······ NGC1553 2.8 ± 2.6 × 1040 0.41 ± 0.01 −0.21 ± 0.13 −0.28 ± 0.12 NGC1600 > 1.2 × 1042 1.18 ± 0.04 ······ NGC1700 > 3.2 × 1041 0.43 ± 0.01 −0.06 ± 0.14 ··· NGC2434 2.6 ± 2.0 × 1040 0.53 ± 0.03 ······ NGC2865 < 9.9 × 1040 0.66 ± 0.09 ······ NGC3115 < 8.7 × 1039 0.50 ± 0.04 ······ NGC3377 < 6.1 × 1039 ········· NGC3379 < 6.3 × 1039 0.33 ± 0.03 −0.27 ± 0.06 ··· NGC3585 > 4.2 × 1039 0.33 ± 0.01 ······ NGC3923 4.3 ± 1.3 × 1040 0.48 ± 0.02 −0.07 ± 0.01 −0.37 ± 0.11 NGC4125 7.2 ± 2.7 × 1040 0.44 ± 0.01 −0.06 ± 0.02 −0.15 ± 0.16 NGC4261 4.8 ± 1.1 × 1040 0.78 ± 0.01 0.25 ± 0.05 ··· NGC4365 > 3.8 × 1040 0.64 ± 0.02 0.14 ± 0.04 ··· NGC4374 5.9 ± 1.3 × 1040 0.71 ± 0.01 0.16 ± 0.02 0.44 ± 0.08 NGC4406 > 1.0 × 1042 0.78 ± 0.01 0.06 ± 0.01 −0.05 ± 0.04 183

Table 6.1

a b c c Name LX,Gas TX α02 α24

NGC4472 > 8.5 × 1041 0.97 ± 0.01 0.14 ± 0.01 ··· NGC4494 < 2.1 × 1040 ········· NGC4526 8.8 ± 7.5 × 1039 0.35 ± 0.03 ······ NGC4552 2.1 ± 1.2 × 1040 0.57 ± 0.01 −0.21 ± 0.04 0.42 ± 0.16 NGC4555 > 2.3 × 1041 0.97 ± 0.03 · · · −0.02 ± 0.03 NGC4564 > 2.0 × 1039 ········· NGC4621 1.1 ± 0.9 × 1040 0.23 ± 0.03 ······ NGC4636 2.7 ± 2.0 × 1041 0.69 ± 0.01 0.11 ± 0.01 0.04 ± 0.02 NGC4649 1.3 ± 0.3 × 1041 0.80 ± 0.01 0.02 ± 0.01 −0.01 ± 0.01 . NGC4697 > 3.5 × 1040 0.32 ± 0.01 ······ NGC5018 < 1.9 × 1041 0.45 ± 0.09 ······ NGC5044 2.6 ± 0.8 × 1042 0.91 ± 0.01 0.09 ± 0.01 0.12 ± 0.02 NGC5102 < 1.6 × 1039 0.38 ± 0.08 ······ NGC5171 > 2.7 × 1042 0.80 ± 0.05 ······ NGC5532 < 8.7 × 1041 0.61 ± 0.02 · · · −0.38 ± 0.07 NGC5845 < 5.2 × 1040 0.32 ± 0.05 ······ NGC5846 3.9 ± 0.9 × 1041 0.71 ± 0.01 0.02 ± 0.02 0.03 ± 0.17 NGC6482 1.7 ± 1.3 × 1042 0.74 ± 0.01 −0.09 ± 0.01 −0.34 ± 0.02 NGC7052 > 1.1 × 1041 0.53 ± 0.03 ······ NGC7618 2.3 ± 0.9 × 1042 0.80 ± 0.01 −0.14 ± 0.06 −0.12 ± 0.08

aTotal X-ray gas luminosity in ergs s−1 for the 0.3 − 5 keV band, see Paper I for more details bLuminosity weighted temperature within 3 optical radii. c Temperature gradients, measured in log r/RJ − log T/ keV space, between 0 − 2RJ (α02) and 2 − 4RJ (α24). 184 97 97 42 59 59 15 05 08 25 20 28 ...... d ··· ··· ··· ··· ··· ··· ··· ··· ··· 0 0 Tully ρ 19 18 0 22 0 14 0 11 1 12 1 13 1 25 25 0 22 19 25 0 43 13 25 31 22 31 0 ...... ······ ··· ··· 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2MASS ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ρ Environment 09 96 74 10 27 28 13 07 95 03 17 57 43 52 77 66 41 47 ...... log 3 2 2 3 3 3 3 3 2 3 3 2 2 3 2 2 3 2 32 31 31 31 31 31 31 32 31 33 32 32 31 33 33 33 33 33 32 29 32 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 × × × × × × × × × × × × × × × × × × × × × 1 6 9 2 8 4 2 6 2 2 1 3 8 6 5 5 3 1 6 3 5 ...... GB6 0 2 1 1 4 3 3 2 2 4 1 0 2 1 1 3 0 0 0 4 0 L ± ± ± ± ± ± < < < < < < < < < < < < < < < 0 8 7 0 8 2 c ...... 2 6 5 6 3 1 32 31 30 32 34 32 32 30 33 28 32 32 30 34 33 33 33 33 33 Radio ··· ··· 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 × × × × × × × × × × × × × × × × × × × 1 3 5 4 0 3 3 7 6 9 8 6 3 4 9 8 7 5 3 ...... NVSS 1 2 0 0 0 0 1 1 1 0 2 0 2 1 1 0 1 0 0 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± < < 6 6 7 1 0 3 6 1 4 3 1 1 3 8 0 8 3 ...... 3 5 6 3 4 3 5 9 3 2 5 3 4 1 2 8 6 96 6 5 2 6 1 6 6 6 1 3 4 b 13 1 21 9 36 1 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ··· ± ± ± σ L 38 LEDA 8 335 9 177 0 203 4 272 3 233 9 337 8 227 98 199 247 9 290 124 315 275 242 8 277 55 9 333 296 1 308 4 266 ...... J R a Table 6.2. Optical, radio, and environmental parameters 33 24 17 33 18 29 26 36 19 19 16 36 17 49 17 23 33 19 33 25 33 26 33 25 17 27 33 17 33 25 33 14 33 22 28 29 33 14 ...... ········· ······ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± K 2MASS M 06 06 69 60 79 19 07 01 70 19 98 01 94 84 06 71 33 53 43 ...... 26 25 24 25 24 25 26 24 25 26 25 26 24 25 26 24 26 25 25 − − − − − − − − − − − − − − − − − − − Name NGC1600 NGC1553 NGC1549 NGC1407 NGC1404 NGC1399 NGC1316 NGC1265 NGC0821 NGC1132 NGC0741 NGC0507 NGC0533 NGC0720 NGC0383 NGC0404 IC4296 NGC0193 NGC0315 IC1459 IC1262 185 33 60 09 97 45 04 31 41 99 93 84 34 40 12 52 08 49 11 19 ...... d ··· ··· 4 1 0 0 0 Tully ρ 12 1 22 25 2 09 2 31 2 12 3 13 1 14 3 13 2 14 0 13 0 16 0 31 0 10 0 43 25 0 ...... ··· ··· ··· ··· ··· 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2MASS ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ρ Environment 47 19 62 66 54 41 31 18 16 09 13 89 43 82 56 31 ...... log 3 3 2 3 2 3 3 3 3 3 3 2 2 3 2 2 31 32 31 30 30 30 30 31 30 33 30 33 31 31 31 30 30 30 31 31 32 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 × × × × × × × × × × × × × × × × × × × × × 0 0 0 8 2 1 3 0 3 0 0 1 2 6 0 4 7 5 2 2 4 ...... GB6 0 2 0 4 7 6 6 0 6 0 9 0 1 2 2 2 2 4 7 1 2 L ± ± ± ± ± < < < < < < < < < < < < < < < < 8 9 7 3 8 c . . . . . 1 1 2 1 4 31 29 31 31 30 29 29 31 30 33 30 34 31 30 30 29 29 29 30 30 Radio ··· 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 × × × × × × × × × × × × × × × × × × × × 3 7 8 4 2 0 7 8 2 3 2 2 4 6 2 7 8 8 3 8 ...... NVSS 0 2 0 6 1 8 0 0 0 1 0 0 1 1 0 3 2 4 8 10 ± ± ± ± ± ± ± ± ± < < < < < < < < < < < 7 9 6 1 1 5 0 7 2 ...... Table 6.2 3 2 2 2 2 3 3 2 8 2 1 2 2 2 8 1 6 1 6 4 2 2 3 5 2 3 5 b 18 6 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ··· ± σ L LEDA 3 202 9 4 253 99 158 225 8 263 8 149 2 288 7 235 8 280 7 255 5 320 0 226 8 247 3 207 79 139 205 4 257 8 170 9 235 3 188 ...... J R a 13 59 33 10 14 25 17 19 20 32 20 43 11 30 10 59 14 59 11 34 17 40 19 25 25 33 28 43 18 32 09 27 11 29 09 36 20 14 33 15 29 19 ...... 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± K 2MASS M 41 94 56 78 20 67 16 66 07 10 91 24 03 30 81 81 85 05 43 78 59 ...... 24 25 24 22 24 24 24 25 25 25 24 25 25 25 24 22 23 24 24 25 23 − − − − − − − − − − − − − − − − − − − − − Name NGC4636 NGC4564 NGC4621 NGC4555 NGC4552 NGC4526 NGC4494 NGC4472 NGC4406 NGC4374 NGC4365 NGC4261 NGC4125 NGC3923 NGC3585 NGC3377 NGC3379 NGC3115 NGC2865 NGC2434 NGC1700 186 is 84 84 17 38 29 60 49 ...... d -band ··· ··· ··· ··· Tully 0 0 Tully J ρ ): Com- ρ 1 − and 31 31 31 15 0 25 13 0 31 0 11 0 12 3 Becker et al...... K ··· ······ ··· 0 0 0 0 0 0 0 0 0 M 2MASS ± ± ± ± ± ± ± ± ± ρ Environment (in erg s 64 72 76 97 11 17 50 65 39 ), and ...... log 2 2 2 2 3 3 2 3 3 6cm L 1996 ( ); 31 32 32 31 34 31 30 32 31 31 30 31 , Tully galaxy density 10 10 10 10 10 10 10 10 10 10 10 10 1998 2 − × × × × × × × × × × × × 5 6 3 3 4 1 1 4 9 0 6 0 ...... GB6 7 0 1 1 1 0 2 1 4 8 6 0 L ± ± ± < < < < < < < < < Wright et al. 7 6 3 c . . . ), -band absolute magnitude 6 1 1 K Condon et al. 1996 33 31 31 30 34 32 31 28 31 30 29 30 Radio ). ( ). 10 10 10 10 10 10 10 10 10 10 10 10 × × × × × × × × × × × × 2000 4 0 3 0 7 8 9 5 0 8 1 4 1997 ...... NVSS 1 0 0 0 2 2 1 1 1 4 4 1 ± ± ± ± ± ± ± < < < < < 7 2 6 8 1 0 8 ...... 2 Table 6.2 Gregory et al. Jarrett et al. Paturel et al. 9 9 1 8 3 1 4 6 8 4 8 2 3 9 b 18 5 ± ± ± ± ± ± ± ± ± ··· ··· ± σ L LEDA . is scaled logarithmically and in units of Mpc 3 − 6 303 6 8 271 95 234 239 8 0 293 3 66 3 238 6 214 4 173 2 334 ...... J ) from LEDA ( 1 R − 2MASS ρ a 33 12 33 11 33 21 2120 4 34 33 10 33 16 14 79 28 25 33 15 14 42 15 45 ...... 0 0 0 0 0 0 0 0 0 0 0 0 ± ± ± ± ± ± ± ± ± ± ± ± K 2MASS M ): 20 cm radio continuum luminosity from NVSS ( 40 66 48 96 04 33 95 09 76 27 98 39 ...... in kpc. 1 − J 25 25 25 22 25 24 26 21 24 25 23 25 R − − − − − − − − − − − − (in erg s ). NVSS Velocity dispersion (in km s Projected galaxy density 2MASS data from the extended source catalog ( L b d a c Name 1991 NGC7618 NGC7052 NGC6482 NGC5845 NGC5846 NGC5532 NGC5171 NGC5102 NGC5044 NGC5018 NGC4697 NGC4649 eﬀective radius bination of 6 cm radio continuum luminosities from ( scaled linearly and in units of Mpc 187

6.2.2 Projected Radial Temperature Proﬁles

To produce radial temperature proﬁles, we divide the X-ray counts image of each galaxy into elliptical annuli, according to the X-ray ellipticity proﬁles computed in

Paper I. For those galaxies with insufficient signal to fit ellipses, we revert to circular annuli. We find no evidence that this choice affects our results in any way. We adapt the width of our annuli to contain a minimum of 900 counts above the background level, which we determine by the appropriately rescaled Markevitch blank-sky background files1.

We then extract a source and background spectrum for each annulus and fit them with a two-component model in the CIAO analysis package Sherpa. The first component consists of an APEC 2 plasma model to represent the hot gas emission. A quantitative comparison with its better-know predecessor, the Mekal model, shows nearly identical fitting results. We fix the gas metallicity at the solar abundance value.

Unresolved point sources are represented by a power-law model with the power law index ﬁxed at 1.6. This “universal” spectral model is an adequate representation for the emission of low-luminosity low-mass X-ray binaries, as demonstrated in Paper I and determined independently by Irwin et al. (2003). We also add a multiplicative absorption component, for which we ﬁx the hydrogen column density to the Galactic value, evaluated at the target position with the CIAO tool Colden3.

1http://cxc.harvard.edu/cal/Acis/Cal prods/bkgrnd/acisbg/COOKBOOK 2Astrophysical Plasma Emission Code 3http://cxc.harvard.edu/toolkit/colden.jsp 188

We repeat our spectral analysis for a few objects with the gas abundance as a

free parameter, and find that our choice to fix them to the solar value does not affect

the ﬁtted temperature. Since the metallicity is poorly constrained by the ﬁts in low

signal-to-noise systems, we ﬁx the metallicity for all of our galaxies, in order not to

introduce systematic diﬀerences in the analysis.

6.2.3 Two-Dimensional Temperature Maps

We use the publicly available adaptive binning technique “WVT binning”4 (Diehl and Statler 2006a) to adaptively bin the photon-count images to a target signal-to-

noise ratio of ∼ 30 per bin, resulting in approximately 302 = 900 counts per bin. We

also restrict the maximum bin size to be 1/16 of the ﬁeld of view to prevent bins

in background dominated regions from growing excessively. We then extract source

and background spectra for each bin and use the CIAO tool Sherpa to ﬁt them with

the same two-component model that we use in the radial temperature ﬁts. However,

here we find that keeping the metallicity fixed results in some non-convergent fits

at large radii. We believe that this is caused mainly by the lower non-background

corrected count threshold, and partly by a true decrease in metallicity, as one starts to

probe the intragroup or intracluster medium. Thus, we decide to free the abundance

parameter for deriving temperature maps. A comparison with temperature maps

that are computed with a ﬁxed abundance parameter shows that this choice does

4http://www.phy.ohiou.edu/∼diehl/WVT 189 not affect the fitted temperatures, but allows us to fit temperatures at larger radii.

We note that while freeing the abundance parameter in our ﬁts improves the overall convergence, the abundances are still poorly constrained.

6.2.4 Deprojected Density Proﬁles

We use the gas-only images from Paper I to derive radial gas surface brightness profiles. We start by binning the image into circular annuli whose widths are determined by two criteria: i) the signal-to-noise ratio in each bin has to be > 5; ii) the width of the bin has to be larger than 5% of the mean bin radius r, to ensure proper azimuthal averaging and to avoid effects of asymmetric features. During deprojection, we have to assume spherical symmetry, which is not always justified by the morphology of the X-ray emitting gas. Thus, deprojected density values at a certain radius should be understood as an approximate azimuthal average.

To deproject the gas surface brightness into the radial volume emissivity ν(r), we use an algorithm similar to the standard “onion peeling” technique (e.g. Sun et al.

2003). First, we estimate the contributions from radii outside the field of view by extrapolating the best fitting circular Sérsicmodel to large radii. We then project the model contributions to all inner annuli and subtract them. The algorithm then starts with the largest annulus in the field of view and deprojects it, assuming a constant density in a spherical shell. Subsequently, the code moves to the next smaller annulus, 190 removing all projected contributions from outer shells until the algorithm reaches the innermost shell.

For noisy surface brightness profiles, this technique is prone to numerical instabil- ity, producing “waves” in the emissivity profiles due to over- or under-subtraction of larger annuli caused by noise in the surface brightness profile. To reduce this effect requires a much higher signal-to-noise ratio than is typically reached in these data.

We therefore apply a smoothing spline to the surface brightness profile and then deproject using the technique described above. Empirical tests show the most stable results without affecting the overall shape of the profile are achieved around a spline smoothing factor of 0.1, which we adopt for all objects. Errors on the deprojected volume emissivity are obtained by bootstrapping with 100 simulated profiles. The smoothing step allows an unbiased deprojection of even low signal-to-noise profiles, without choosing a particular parametric model. We test our procedure by simulating Sérsic profiles and comparing the deprojected profile with the exact result (Ciotti

1991), ﬁnding excellent agreement.

To convert the volume emissivity to an electron density proﬁle, we need to evaluate the radiative cooling function over the bandpass of our gas images (0.3 − 5 keV).

We use the CIAO package Sherpa to compute the effective cooling function Λ(T ) by integrating the photon-flux of the hot gas spectrum for different temperatures.

The assumed spectral model is an APEC plasma model of temperature T , with the metallicity ﬁxed at 30% of the solar value, since we are unable to constrain metal- 191

licity gradients sufficiently by our spectral fits alone. Published metallicity profiles

(e.g. Sun et al. 2003) of other ellipticals or groups show little variation in the ra-

dial metallicity distribution, justifying this necessary assumption; however, we note

that regions with intrinsically higher metallicity would result in an overestimate of

the electron density. We ﬁnally convert the deprojected volume emissivity into an

2 electron density proﬁle ne(r) using the relation ν(r) = ne(r) Λ[T (r)], evaluating the cooling function according to the projected radial temperature proﬁle.

6.3 The Temperature Structure of Elliptical Galax-

ies

6.3.1 Radial Temperature Proﬁles

A Chandra study of 7 elliptical galaxies by Humphrey et al. (2006) reveals rather

unexpected X-ray temperature profiles. In particular, they find profiles with negative

temperature gradients, in contrast to what is observed in clusters, which usually

have cool centers with an outward rise in temperature. Based on their small sample,

Humphrey et al. (2006) propose a bimodal distribution of temperature gradients, with

13 objects below a virial mass of 10 M having negative gradients and galaxies above having positive gradients.

Figure 6.1 shows the compilation of our Chandra temperature proﬁles. All proﬁles

are overlaid in one plot, with the radial axes scaled by their J-band eﬀective radius 192

RJ. This plot already clearly indicates the absence of any real bimodality in the tem-

perature profiles. Instead, we find a continuous distribution of temperature profiles,

ranging from purely positive to isothermal to purely negative temperature gradients.

We also conﬁrm the presence of unusual, very complex temperature proﬁles noted by

Humphrey et al. (2006). These unusual proﬁles exhibit a reversal in the sign of the

temperature gradient at some intermediate radius.

We categorize the observed temperature gradients into four major groups, but

note that the transition from one category is not clear-cut. Each row in Figure 6.2

shows two representative examples for each category.

Positive Gradients. These temperature proﬁles show a positive gradient at all radii, i.e. the temperature continuously rises outwardly. These proﬁles resemble those found in clusters of galaxies, which generally harbor cool cores.

Negative Gradients. The temperature proﬁles show a negative gradient at all radii, i.e. temperatures monotonically decline outward. This phenomenon is less well-known, and has only recently been reported by independent observers (Randall

et al. 2006; Fukazawa et al. 2006; Humphrey et al. 2006; Khosroshahi et al. 2004).

Hybrid. These peculiar cases exhibit a dramatic change in the temperature gradients. The gradient changes its sign from negative to positive at some intermediate radius, generally between 1−3RJ. These galaxies have warm centers, outside of which 193

their temperatures drop to a minimum level and rise back up again. These proﬁles

have ﬁrst been noted by Humphrey et al. (2006).

Quasi-Isothermal. The radial temperature proﬁles in this category are consistent

with being almost ﬂat at all radii. These galaxies form the transition point between

galaxies with positive and negative gradients.

We only observe hybrid temperature proﬁles that change their gradient from neg-

ative to positive. Some cooling ﬂow clusters have been found to exhibit the opposite

behavior (Piﬀaretti et al. 2005). Their temperature proﬁles show a cool center, then

rise to a peak temperature and fall back down on the outskirts. This “break” usually

happens at around 10% of the virial radius, which is larger than the radii that we

are probing in normal galaxies. A ROSAT study by O’Sullivan et al. (2003) exhibits

similar trends for elliptical galaxies at larger radii.

We split the proﬁles into two radial regions and analyze the inner and outer

temperature gradients separately. As most hybrid proﬁles exhibit their turnover in

slope somewhere around 2RJ, we use this radius as the boundary between our two

regions. Accordingly, we deﬁne the inner region from outside the central point source

extending out to 2RJ and the outer region between 2 − 4RJ. We then fit each part of the profile with a power law to derive effective temperature gradients for each region.

We will refer to the logarithmic gradients d ln T/d ln R evaluated within 2RJ and from

2 − 4 RJ as α02 and α24, respectively. 194

The best-ﬁt values for α02 and α24 are listed in Table 6.1. The reported errors are

the formal 1σ statistical errors obtained from the fitting procedure. For cases with only 2 valid data points within the fitting range, we use the difference between these two points to derive a gradient; the errors are derived by propagating the statistical errors of the individual temperature measurements.

6.3.2 The Inner Temperature Gradient α02

Figure 6.1 shows a plot of all radial temperature proﬁles, with each colored accord-

ing to its luminosity weighted temperature TX within 3 optical radii. The coloring

changes smoothly from top to bottom, indicating overall positive gradients for intrin-

sically hotter galaxies and negative gradients for cooler galaxies. We plot α02 as a function of TX in Figure 6.3. The plot shows a tight correlation of the form

T α = 0.868 X + 0.18. (6.1) 02 keV

This correlation reﬂects the fact that we observe only a very small range in central

temperatures between 0.6 − 0.7 keV (Figure 6.1). Thus, any average temperature will

obviously be strongly correlated with the gradient. The transition from positive to

negative temperatures happens at a mean temperature around 0.62 keV

To establish the underlying cause for the negative inner temperature gradients,

we perform a correlation analysis with various galaxy properties, the most interesting

of which are listed in Table 6.1+6.2: X-ray gas luminosities LX,gas, absolute K mag- 195

Figure 6.1: Combined plot of all projected temperature profiles, as a function of radius scaled by the J-band effective radius RJ. Error bars are omitted for clarity; for typical error estimates, refer to Figure 6.2. The profiles are colored according to the luminosity weighted average temperature of the galaxy within 3 optical radii TX, as indicated by the color scale bar. Note how the temperature gradient changes continuously from positive gradients at the top to isothermal and hybrid profiles to negative gradient profiles at the bottom, along with the average temperature.

nitudes MK, central velocity dispersions σ, radio luminosities at 20cm (LNVSS) and

6cm (L6cm), and environmental measures of local galaxy density, ρ2MASS and ρTully.

We fit the dependency of α02 on each of these properties with a robust linear fitting algorithm. During the fits, the parameters are scaled logarithmically, except for MK, 196

Figure 6.2: Examples of different projected temperature profiles as a function of radius. Temperature profile types can be divided into 4 major groups (top to bottom rows): (1) Positive gradient (outwardly rising) at all radii; (2) Negative gradient (outwardly falling) at all radii; (3) Hybrid, negative gradient in the core and positive gradient at larger radii; (4) Quasi-isothermal, no apparent temperature change with radius. 197

while α02 is left linear. The top half of Table 6.3 lists the best-ﬁt parameters for

the linear ﬁts. The list is ordered by decreasing statistical signiﬁcance, as indicated

by a Spearman rank analysis. The probability for the null hypothesis (PNull) of no

correlation is given in the far right column. The x0 column indicates where the best

ﬁt puts the transition from negative to positive temperature gradients. The results

from linear ﬁts that yield slopes that are statistically consistent with zero are omitted.

The strongest correlation is with the 20 cm radio luminosity, which we show in

the left panel of Figure 6.4. A Spearman rank analysis rejects the null hypothesis

for LNVSS and α02 at the 99.9% conﬁdence level. The correlation with the 6 cm radio

luminosity is equally tight, but has a lower signiﬁcance, due to the smaller sample size

with 6 cm radio luminosity measurements. We further ﬁnd slightly weaker correlations

with σ, MK, and LX,gas. As a representative example of the scatter associated with these correlations, we show the MK–α02 relation in the right panel of Figure 6.4.

We do not ﬁnd any evidence that α02 is correlated with the environmental galaxy

densities ρ2MASS or ρTully. The ρ2MASS–α02 plot is shown in the bottom panel of

Figure 6.5. We conclude that the inner temperature gradients are not the result of

interactions with ambient intragroup or intracluster gas. Instead, we ﬁnd that they are

connected to intrinsic galaxy properties. We can generally characterize galaxies with

negative inner temperature gradients as being smaller, optically fainter galaxies with

lower velocity dispersions, lower X-ray gas luminosities, lower average temperatures,

and lower radio luminosities than their positive gradient counterparts. 198

Unfortunately, all of these galaxy properties are intimately connected with each other through well-known correlations such as the TX–σ relation (e.g. O’Sullivan et al.

2003), the Faber-Jackson relation (Faber and Jackson 1976), the LX,gas–TX relation

(e.g. O’Sullivan et al. 2003) and the LRadio–σ relation (e.g. Snellen et al. 2003). This makes it diﬃcult to distinguish between fundamental correlations that are really responsible for determining the inner temperature structure and others that are simply

“riding along” via the other correlations. A manual inspection of the scatter in the correlations and the low PNull value suggests that the radio-luminosity dependence is strongest.

We check the robustness of our results by deriving inner temperature gradients for different cutoff radii and find that all of the observed trends are confirmed, as long as the cutoff-radius does not exceed ∼ 3RJ. In particular, we find that for smaller cutoff-radii (e.g. 1RJ), the significance of the correlations with σ, MK and

LX,gas slightly decreases, while the correlations with the radio luminosities LNVSS and

L6cm strengthen even further. This increases our conﬁdence that the correlations with radio luminosities are intrinsically the strongest. Figure 6.6 shows a combined plot of all temperature proﬁles, similar to Figure 6.1, but this time colored according to the NVSS radio luminosities. A trend with radio luminosity is clearly evident. We will discuss the implications of our results in §6.6. 199

Table 6.3. Correlations involving inner and outer temperature gradients.

y x a b x0 PNull

α02 log LNVSS 0.086 ± 0.020 −2.67 ± 0.11 31.0 0.1% α02 log σ 1.171 ± 0.386 −2.77 ± 0.60 2.37 0.9% α02 log LGB6 0.087 ± 0.039 −2.70 ± 0.13 31.0 1.7% α02 MK −0.138 ± 0.046 −3.44 ± 1.18 −24.9 2.2% α02 log LX,gas 0.073 ± 0.043 −2.98 ± 0.27 40.8 3.7% α02 log ρ ········· 24.9% α02 log ρTully ········· 50.9%

α24 log ρ 0.493 ± 0.138 −1.51 ± 0.25 3.06 0.4% α24 log ρTully 0.230 ± 0.114 0.06 ± 0.06 0.26 3.4% α24 MK ········· 60.3% α24 log σ ········· 76.4% α24 log LNVSS ········· 79.1% α24 log LX,gas ········· 90.9% α24 log LGB6 ······ 96.2%

Note. — All correlations are given in order of correlation strength. All correlations are linear ﬁts of the form y = ax + b. x0 denotes the point where the correlation yields 0, i.e. where the gradients change sign. PNull is the probability for the null hypothesis of no correlation.

6.3.3 The Outer Temperature Gradient α24

˙ We now repeat the same analysis for the outer temperature gradient α24The results of the correlation analysis are listed in the bottom half of Table 6.1+6.2. Surpris- ingly, we find very different correlations, suggesting that inner and outer temperature gradients are essentially decoupled. In contrast to α02, α24 does not depend on the intrinsic galaxy properties LNVSS, L6cm, σ, or MK. Instead, we find strong evidence that 200

α24 depends only on the environmental density parameters ρ2MASS and ρTully. This trend with environment is statistically even stronger than the one with the luminosity weighted temperature TX, even though those parameters are not independent measurements.

To check the robustness of these results, we repeat our analysis using larger outer radial boundaries and confirm all trends. The significance of the environmental dependence gets even stronger when restricting the analysis to for larger radii. These relations are strongest, with a 99.5% significance for ρ2MASS and 98.9% for ρTully,

when one ﬁts temperature gradients to all radii beyond 2RJ, without an outer radial

limit. However, since the gradients tend to get stronger with radius, and our galaxies

have very different cutoff radii owing to different surface brightness profiles, we do

not report the functional form of the ﬁt, as it is driven by the brightest galaxies.

Nevertheless, this strengthens the conﬁdence in the observed correlation.

We conclude that the inner and outer temperature gradients are essentially de-

coupled. While the inner gradient depends only on intrinsic galaxy properties, the

outer gradient shows no correlations but with the environment.

6.3.4 Two-dimensional Temperature Maps

To our knowledge, only one temperature map of a normal elliptical galaxy has been published so far in the literature (NGC4636, O’Sullivan et al. 2005). We believe

that temperature maps can be powerful tools to elucidate the heating mechanism for 201 the hot gas. The right panels in Figure 6.7 show the two-dimensional temperature maps for the 12 galaxies with the highest signal-to-noise ratios in our sample: IC 1262,

NGC 0507, NGC 0533, NGC 1399, NGC 1404, NGC 4406, NGC 4472, NGC 4636,

NGC 4649, NGC 5044, and NGC 5846. Each temperature map has an individually chosen, logarithmic temperature scale associated to bring out as much detail as possible. The temperature range generally covers about a factor of ∼ 2. The left panels show the adaptively binned gas distribution for comparison.

The majority of these bright galaxies show strong positive gradients consistent with the observed trend that the inner temperature gradient is a function of X-ray luminosity. Unfortunately, no galaxy with a strong negative temperature gradient has suﬃcient signal to produce a meaningful temperature map. We include NGC 720,

NGC 1404 and NGC 4649, despite the poorer spatial resolution of their temperature maps. These galaxies are nearly-isothermal, with slight increases in temperature toward the centers.

The most striking aspect of Figure 6.7 is that most of the temperature distributions look heavily disturbed, particularly NGC 4406, NGC 0507, NGC 4636 or NGC 5044.

In each of these galaxies, the asymmetries in the temperature maps are associated with asymmetries in the surface brightness to their left, a trend which holds for all galaxies in Figure 6.7, except for the galaxies NGC 1404, NGC 720 and NGC 4649, which unfortunately have poor spatial resolution at the center. Our morphological analysis in Paper II showed that morphological disturbances in the gas maps are 202 primarily caused by activity of the central AGN. The fact that these asymmetric features now have counterparts in the temperature maps may support the importance of the AGN in reheating the cores of elliptical galaxies.

However, we cannot claim that this is direct evidence for AGN heating of the ISM.

These observations may also be consistent with the AGN simply stirring the hot gas, blowing bubbles and compressing the surrounding material, without heating the gas.

This compression would raise the density in the rim region, shorten the cooling time and could lead to rapid cooling in these regions. The evacuated cavities might then simply appear hotter due to projection eﬀects (O’Sullivan et al. 2005). 203

Figure 6.3: Inner temperature gradient within 2 RJ as a function of the luminosity weighted temperature within 3 optical radii. The dashed line indicates the best ﬁt. 204

Figure 6.4: Inner temperature gradient within 2 RJ as a function of 20 cm NVSS radio luminosity (left) and absolute K magnitude (or stellar mass, right). The dashed lines indicate the best-ﬁt correlations. Note the increased scatter in the MK plot, compared to the stronger correlation. 205

Figure 6.5: Projected galaxy number density ρ2MASS vs. outer (α24, top panel) and inner (α02, bottom panel) temperature gradients. Note how α02 is completely un- aﬀected by the environment, whereas α24 depends strongly on the presence of hot ambient gas. 206

Figure 6.6: Identical to Figure 6.1, but colors now indicate NVSS 20 cm continuum radio luminosity within 3RJ, as indicated by the colorbar. Note how the radio luminosity changes smoothly, as one works its way down from positive to negative temperature gradients. 207 . 2 − arcsec 2 − cm 1 − photons sec 7 − 10 × to 3 11 − 10 × Note how disturbed bothassociated gas with images the and asymmetries temperature in maps the are, temperature and distribution. how disturbances in the gas map often are often Figure 6.7: Projected temperaturesample. maps (right), The together temperature withcolor maps their bars. are gas Black maps scaled areas (left)gas logarithmically, denote for with images regions the their are outside 12 individual brightest scaled the galaxies temperature field on in of ranges the our view, indicated same or by logarithmic bins the scale, for which ranging the from spectral 5 fit did not converge. All 208 Figure 6.7: Continued 209 Figure 6.7: Continued 210 6.4 Density and Cooling Time Profiles

Figure 6.8 shows a combined plot of all electron density proﬁles in our sample, as

a function of radius in kpc. The diﬀerent colors in the plot denote the galaxy’s X-ray

luminosity, as indicated by the color bar. Note that low-luminosity galaxies generally

have lower densities. In particular, X-ray bright galaxies show much larger densities

at large radii. The observed small range in densities is probably caused at least in

part by a selection eﬀect: our analysis requires suﬃcient signal to make a deprojection

possible. In fact, nine of the galaxies in our full sample have gas detections below the

3σ conﬁdence level, four of which fall even below the 1σ conﬁdence level, statistically

consistent with being completely devoid of gas (Paper I).

Figure 6.9 shows a similar plot for the cooling times present in our galaxy sample, also colored by the X-ray gas luminosity. X-ray faint galaxies tend to have somewhat longer cooling times on average, primarily caused by their lower electron densities.

All galaxies have cooling times < 108 yr in the inner 2 kpc, emphasizing the need for

a central heat source.

6.5 Entropy Proﬁles

We combine our deprojected density proﬁles (§6.2.4) with our projected temper-

ature proﬁles (§6.2.2) to generate radial entropy proﬁles. We adopt the common

−2/3 convention to deﬁne entropy as S = kT ne , a quantity proportional to the log- 211

Figure 6.8: Combined plot of all electron density proﬁles as a function of physical radius. Each plot is colored according to the galaxy’s X-ray gas luminosity. X-ray faint galaxies tend to have generally lower densities and are less extended, which may be a sign that X-ray fain galaxies have lost a signiﬁcant fraction of their gas through winds.

arithm of the correct definition of entropy in thermodynamics, and offset with an additive constant. Figure 6.10 shows a combined plot of all entropy profiles in our sample as a function of physical radius. Each plot is colored according to X-ray gas luminosity, as indicated by the scale bar. One can see a trend for X-ray fainter objects to have higher entropy, due to their lower electron densities. 212

Figure 6.9: Combined plot of all cooling time proﬁles as a function of physical radius. Each plot is colored according to the galaxy’s X-ray gas luminosity. X-ray faint galaxies tend to have longer cooling times at large radii, due to their lower electron densities. The cooling times reach values as low as only 10Myr in the centers.

We note the absence of an entropy ﬂoor in the centers of normal elliptical galaxies, contrary to what is generally observed in clusters of galaxies (e.g. Balogh et al. 2006;

Voit et al. 2002; Donahue et al. 2005). In clusters, this ﬂoor has been interpreted as a sign of preheating of the intracluster gas (Voit et al. 2003), eﬀervescent heating by the central AGN (Roychowdhury et al. 2004) or radiative cooling (e.g. Xue and Wu 2003).

However, our galaxies are very diﬀerent physical systems, and the gas has a very 213

diﬀerent hydrodynamic history. A signiﬁcant fraction of the gas in normal ellipticals

is believed to be due to stellar-mass loss in the galaxies themselves, which may provide

a source of low-entropy material and destroy an entropy ﬂoor. Furthermore, entropy

ﬂoors in clusters are usually observed at a level of over ∼ 100 keV cm2, much higher

than the regime our galaxies occupy.

To highlight average trends in the entropy proﬁles, we bin all of proﬁles into

logarithmically spaced radial bins and compute unweighted logarithmic means, shown

as solid black circles in the plot. The mean proﬁle is monotonic and is adequately

described by a single slope at all radii: S ∝ r0.78±0.02. However, the profile does steepen at large radii and flatten at small radii. A linear fit to the inner profile within 1 kpc yields a shallower slope of 0.61 ± 0.01, and a fit to larger radii between

5 kpc − 25 kpc gives a steeper slope of 0.97 ± 0.12.

The dashed line in Figure 6.10 indicates a logarithmic gradient d ln S/d ln r = 1.1,

which is predicted for gas in clusters of galaxies that is heated via shock-dominated

external accretion (Tozzi and Norman 2001). The gradients in the outer galaxy

entropy proﬁles seem to be approaching this slope. As our analysis of the outer

temperature gradients in §6.3.3 suggests the presence of hotter ambient medium which

inﬂuences α24, this may a sign for accretion or interaction with ambient gas. 214

Figure 6.10: Combined plot of all circularly averaged entropy profiles as a function of physical radius. The profiles are colored according to the galaxy’s X-ray gas luminosity, revealing a slightly higher entropy levels for fainter galaxies due to their lower densities. The solid circles show the average of all profiles, obtained from binning all profiles into radial segments and averaging over the data points. The combined profiles shows a slope of ∼ 0.61 within 1 kpc, which steepens to ∼ 0.98 between 5−25 kpc. All profiles exhibit similar shapes and none show evidence for an “entropy floor” in their cores. The dashed line indicates a slope of 1.1, a prediction of shock-heated accretion models, developed for galaxy clusters. 215

6.5.1 Eﬀects on the L-T diagram

The radial structure of galaxy clusters and groups are completely deﬁned by the

shape of the gravitational potential and the shape of the radial entropy proﬁle (e.g.

Tozzi and Norman 2001; Voit et al. 2002). One of the major successes of entropy pro-

ﬁles in clusters of galaxies is that they break self-similarity and are able to reproduce

the shape of the X-ray luminosity–temperature (LX–TX) diagram (e.g. Balogh et al.

2006). In general, these models predict a sharp turn-oﬀ around 1 keV, at the group

scale.

In Figure 6.11, we update the LX–TX diagram and combine our data for ellip-

tical galaxies (black diamonds) with group data from Helsdon and Ponman (grey

circles, 2000) and cluster data from Wu et al. (grey triangles, 1999). The solid line

indicates the best ﬁt from Wu et al. (1999) for the cluster sample only, yielding a slope d ln L/d ln T = 2.72. Groups and galaxies are known to drop well below the cluster relation (e.g. Mulchaey 2000). The dashed line is the best-ﬁt from Helsdon

and Ponman (2000) to the LX–TX relation for their group sample only. They ﬁnd

that a steeper slope of 4.3 best matches their data. Our data for normal galaxies

fall systematically below their relation, demanding an even further steepening of the

LX–TX relation on the galaxy scale.

The steepening of the LX–TX relation is consistent with the study of O’Sullivan

et al. (2003), who ﬁnd a slope of 5.9 ± 1.3, when they exclude galaxies with strong

positive temperature gradients. As our analysis of temperature gradients has shown, 216

this choice eﬀectively restricts their sample to intrinsically fainter galaxies. Thus the

steepening of the LX–TX relation in their subsample is consistent with a general steep-

ening of the relation toward lower luminosities. In addition, O’Sullivan et al. (2003)

do not correct their luminosities for the contribution of unresolved point sources,

which is relatively larger for lower X-ray luminosities. Correcting for this overesti-

mate of the true gas luminosities for X-ray faint systems will steepen this relation

even further.

The steepening is also consistent with the X-ray gas fundamental plane (XGFP;

Diehl and Statler 2005), a relation between X-ray half-light radius, surface brightness and luminosity weighted temperature. A pure LX–TX relation is a nearly edge-on view of the XGFP. A covariance analysis of their best-ﬁt fundamental plane yields the closest LX–TX relation to have a slope of 8.5, while a principal component analysis yields a shallower slope of 5.9.

6.6 Discussion

6.6.1 Implications for Cooling Flows

Cooling ﬂow models have gone somewhat out of fashion recently due to extensive work on galaxy clusters, which show insuﬃcient amounts of cooling gas at the center

(Peterson and Fabian 2006). Simple steady-state cooling ﬂow models are unlikely to

apply to X-ray bright elliptical galaxies either. We showed in Paper II that the hot gas 217

Figure 6.11: The Logarithm of the X-ray temperature as a function of X-ray luminosity. Black, filled diamonds are our X-ray data for elliptical galaxies. The grey symbols are group data (circles) from Helsdon and Ponman (2000) and cluster data (triangles) from (Wu et al. 1999), reproduced from a review by Mulchaey (2000). Clusters, groups and normal elliptical galaxies form a continuous relation, with groups and galaxies dropping off from the best-fit for the cluster data (solid line, adopted from Wu et al. 1999), continuously steepening the LX–TX relation at lower luminosities. 218

in these systems is almost always disturbed, and we are able to trace the origin of these

disturbances to the central AGN. The analysis of the two-dimensional temperature

distribution of the 12 X-ray brightest galaxies in our sample only strengthens this

point.

However, it is far from proven that the same is true for the situation in low-

luminosity galaxies, in which we ﬁnd negative inner temperature gradients. Com-

pressive heating during a gradually cooling inﬂow of relatively cool gas may be able

to oﬀset radiative losses for low-temperature gas in steep gravitational potentials (e.g.

Mathews and Brighenti 2003a). This counter-intuitively results in a cooling flow that gets heated during inflow and may even produce a hot center, i.e. a negative temperature gradient. We also find in Paper II that these systems are generally much less disturbed, which would make a steady state cooling flow solution at least possible.

Khosroshahi et al. (2004) observe a falling temperature proﬁle for the fossil group

candidate NGC 6482 and successfully ﬁt a steady-state cooling ﬂow model with a rea-

˙ −1 sonable cooling rate of M = 2M yr . However, they derive the inner gravitational potential from the X-ray proﬁles themselves assuming hydrostatic equilibrium, which yields a steep inner potential gradient. They then use this potential to ﬁt the cooling

ﬂow model to the negative temperature gradient. This could be circular reasoning: a central temperature peak together with the assumption of hydrostatic equilibrium implies a steep gravitational potential, which leads to increased compressional heating

(e.g. Mathews and Brighenti 2003a) and a central temperature peak. In addition, we 219

have shown in Papers I and II that hydrostatic equilibrium in elliptical galaxies does

not generally hold. It would be much safer to derive the gravitational potential from

independent stellar dynamics, as the inner region is most likely stellar-mass domi-

nated, at least within two eﬀective radii (e.g. Mamon andLokas 2005). In any event,

NGC 6482 is the only negative-gradient object that has been successfully ﬁtted with a cooling ﬂow model so far. Only modeling a more complete sample will show if this idea can generally hold.

Negative temperature gradients have been recognized only recently (e.g. Mathews and Brighenti 2003a). Because earlier observations revealed only positive gradients, many theoretical flow models have been dismissed on the grounds that they produce negative gradients. Instead, theoretical effort has focused on finding an explanation for this prevalence of positive gradients. Brighenti and Mathews (1998) argue that a hot circumgalactic gas reservoir is able to reverse a negative temperature gradient.

This explanation is consistent with our observations that the outer temperature gradient is correlated with the environment. Whether models with circumgalactic gas can quantitatively account for the more complex hybrid temperature proﬁles remains to be seen.

6.6.2 Implications for Supernova Feedback

One proposed means of producing negative temperature gradients involves supernova (SN) feedback. Since star formation should be negligible in elliptical galaxies, 220

this mechanism would involve only contributions from type Ia SN. Early proposed

wind models involving SN feedback (Binney and Tabor 1995) were later dismissed, since a main feature was a negative temperature gradient throughout their evolution, which had not been observed at that time. However, Mathews and Brighenti

(2003a) point out that these models are able to reproduce observed gas proﬁles only for a very short period of time (∼ 108 yr) just before a cooling catastrophe sets in.

Furthermore, these models are sensitive to the assumed SN rate, resulting in abrupt

transitions to SN driven winds, and thus require ﬁne-tuning. This ﬁne-tuning problem

can be circumvented by the presence of circumgalactic gas (Mathews and Brighenti

2003a). However, our observations of purely negative gradients without an outer rise in temperature cannot be explained by this idea.

In addition, the predicted metallicities in galactic wind models are generally super- solar, signiﬁcantly exceeding the historically observed extremely low abundances in the hot gas (Arimoto et al. 1997). A Chandra spectral analysis of abundance gradients

in a sample of 28 elliptical galaxies by Humphrey and Buote (2006), on the other

hand, no longer shows strongly sub-solar abundances. They attribute this diﬀerence

to previously imperfect modeling of the spectra, mainly caused by the neglect of the

unresolved point source component and attempting to ﬁt multi-temperature gas with

a single-temperature model, the so-called iron-bias. Nevertheless, they conclude that

their abundances are still far too low to be consistent with galactic wind models, and

favor the circulation ﬂow model of Mathews et al. (2004) instead. 221

However, if we consider only the energy input by SNIa feedback, we ﬁnd that SN feedback could play a role in heating the hot gas. The SNIa rate for elliptical and S0

−1 10 −1 galaxies is rSN = 0.18 ± 0.06 (100 yr) (10 LB ) (Cappellaro et al. 1999). With an average energy injection of ∼ 1051 ergs per SN, this results in a SN heating rate of

30 −1 LSN = 5.7 × 10 (LB/LB, ) erg s . An inspection of the LX,gas–LB diagram in Paper

I shows that LSN > LX,gas for galaxies below the blue luminosity where the inner

10 temperature gradients turn from negative to positive (∼ 4 × 10 LB ). Although this is somewhat suggestive, the large scatter in X-ray luminosity of almost 2 orders of magnitude at a given blue luminosity, combined with the also rather large scatter in the LB–α02 relation, make it impossible to tell if this is simply coincidence.

The LX,gas/LSN ratio only weakly correlates with the inner temperature gradient.

A Spearman rank analysis yields an inconclusive 8.9% probability for the null hypothesis. The barely positive slope is non-zero on the 1.3σ level. We conclude that supernova feedback may be important for balancing part of the radiative losses in

X-ray faint galaxies, but is most likely not the dominant factor.

6.6.3 Implications for AGN feedback

In Paper II we have measured the amount of asymmetry in the hot gas, and ﬁnd a strong correlation between asymmetry and AGN power. This correlation persists all the way down to the weakest AGN luminosities at the detection limit of the NVSS

20 cm survey. In this paper, we ﬁnd that these disturbances are not restricted to 222 the gas surface brightness, but are also intimately connected with asymmetries in the two-dimensional temperature maps. We infer that the central AGN is responsible for establishing both the gas morphology and temperature structure.

However, we cannot rule out compressionally heated cooling ﬂows to explain the prevalence of negative temperature gradients. Thus, we propose two possible scenarios involving AGN feedback to explain our observations:

(1) We suggest that weak AGN with smaller black holes heat the ISM locally, while the higher-luminosity sources feed powerful jets that distribute the heat globally by blowing large cavities into the ISM. This is consistent with the observation that smaller elliptical galaxies have rather weak AGN and generally less extended radio emission, and also in agreement with our ﬁndings from Papers I and II that the amount of asymmetry correlates with AGN luminosity. In this scenario, weak

AGN would still be disturbing the gas, but on a scale and surface brightness level that is simply less detectable, resulting in a lower asymmetry. Negative temperature gradients could then be a sign of very localized heating by the central AGN.

(2) AGN are responsible for globally heating the hot gas only in X-ray bright galaxies with positive temperature gradients. The onset of negative inner temperature gradients marks the point where AGN heating becomes unimportant, relative to other sources. These other sources could include compressional heating or supernovae. 223

We also cannot dismiss the idea that the observed temperature gradients are snapshots of diﬀerent stages of a time-dependent ﬂow, which cyclically reverses the temperature gradient over time.

The possible importance of heating by AGN for elliptical galaxies has also recently been pointed out by Best et al. (2006). They combine two empirical results to derive an estimate of time-averaged heating by radio sources in galaxies. They use a result by

Bˆırzanet al. (2004) for galaxy clusters that empirically links the pdV work associated with inflating X-ray cavities into the intracluster medium with the observed 20 cm radio continuum power of the associated radio source. Although this correlation exhibits significant scatter, Best et al. derive a linear fit and use it to convert their radio powers to mechanical energy. In an earlier study, Best et al. (2005) find that the fraction of elliptical galaxies hosting radio-loud AGN correlates with black hole mass and radio luminosity. Assuming that all elliptical galaxies have AGN at their centers, Best et al. interpret the fraction of galaxies with active AGN as the fraction of time that they are turned on. By combining the computed mechanical work per unit radio luminosity derived from Bˆırzanet al. (2004) with the fraction of time the radio source is turned on, Best et al. calculate the time-averaged mechanical heat input of the AGN. A comparison with the LX,gas–LB relation for normal ellipticals shows a remarkable agreement between the time-average AGN heat input and the averaged radiative losses of elliptical galaxies (Best et al. 2006, Figure 2 in). This good agreement is actually surprising, since the conversion factor from radio power 224

to mechanical energy has a rather large scatter and is only based on observations of

cluster cavities.

Further support for AGN heating has been provided by Allen et al. (2006), who

measure the mechanical energy associated with X-ray cavities in 9 X-ray luminous

elliptical galaxies. They compare this value to the Bondi accretion rate, which they

derive from deprojected density and temperature proﬁles, evaluated at the accretion

radius. The black hole masses are computed from the MBH–σ relation from Tremaine

et al. (2002). Allen et al. ﬁnd a tight correlation between the Bondi accretion rate

and the mechanical energy injected into the ISM, and ﬁnd that this energy input may

be suﬃcient to prevent the gas from cooling.

6.6.4 What is so special about ∼ 0.6 keV?

A close inspection of Figure 6.1 shows a remarkably small range in central temperature, which fall between 0.6 to 0.7 keV. The upper limit owes its origin to our explicit exclusion of brightest cluster galaxies, with higher temperatures, from our sample. Including cluster cDs in our sample would add the missing proﬁles, adding positive temperature gradients with higher central temperatures.

However, the lower limit is quite mysterious. We find it unlikely that this is simply a Chandra sensitivity effect. We know that our temperature fits are sensitive to lower temperatures, as we can see them in fits to the outer regions of the same objects. Another idea would be that this represents a selection effect, imposed on the 225

Chandra archive through the proposal process, which disfavors proposed observations of systems with lower temperature due to the drop in instrument sensitivity below this temperature. We find this explanation also difficult to believe, as galaxies with negative gradients would have been characterized simply as having a lower mean temperature, since ROSAT would not have been able to detect the rise in temperature toward the center. However, we do see that the faintest galaxies in our sample exclusively build the lower envelope in the temperature profiles, with luminosity weighted temperatures of ∼ 0.4 keV. Thus, fainter galaxies could lower this envelope even further, and with it the central temperature. The lower envelope may also mark the transition to a galactic wind, which would render the temperature gradient for these galaxies unobservable due to low gas densities.

Nevertheless, something is special about ∼ 0.6 keV. First, we do not observe any central temperature below this value. Second, the hybrid temperature profiles all drop below 0.6 keV at some intermediate radius and then rise back up again. And third, the best fit for the TX–α02 relation puts the transition between negative and positive gradients at 0.62 keV. Any flow model on the galaxy scale has to be able to reproduce these properties.

6.7 Conclusions

We examine the radial temperature, density and entropy proﬁles for a sample of

39 elliptical galaxies observed with the ACIS-S instrument on Chandra. The galaxy 226 entropy profiles show strong differences compared to cluster entropy profiles in their general shape and absolute values. In particular, we do not observe an entropy floor, as is often observed in clusters of galaxies (Voit et al. 2003), but find that the entropy monotonically drops toward the center. In fact, the central entropy values get as low as ∼ 2 keV cm2, about a factor of ∼ 50 below the level of the cluster entropy floor.

An average entropy proﬁle yields a slope of ∼ 0.61 in the central 1 kpc, steepening to

∼ 0.97 between 5 − 25 kpc, approaching the slope of 1.1 expected from shock-heated accretion in clusters (Tozzi and Norman 2001). Since the outer temperature gradient is related to the environment, this may be interpreted as a sign of interaction with ambient gas. The lack of an entropy floor, on the other hand, may be a reflection of the very different hydrodynamic history of the gas in elliptical galaxies, believed to be mainly the result of stellar mass-loss. Thus, the gas would have originally cooled all the way down to condense into stars, then been ejected in a stellar wind and reheated to X-ray temperatures through weak shocks, whereas cluster gas has been primarily heated at the cosmological accretion shock.

Our temperature profiles show a variety of different profile types: purely positive gradients, purely negative gradients, quasi-isothermal and even hybrid profiles. To understand this complexity, we derive mean temperature gradients for an inner region within 2RJ, excluding the central point source, and an outer region between 2 −

4RJ. We ﬁnd that the outer temperature gradient is independent of intrinsic galaxy properties, but a strong function of environment, such that positive outer temperature 227

gradients are restricted to cluster and group environments. This suggests that the

outer gradients are caused by interaction with hotter ambient gas, whereas galaxies

with negative outer gradients are in less dense environments and lack this intergalactic

gas reservoir.

The inner temperature gradient, on the other hand, is completely decoupled from

the outer gradient and the environmental inﬂuence. Instead, we ﬁnd that it is corre-

lated with a number of intrinsic galaxy properties; in decreasing order of signiﬁcance,

the 20 cm radio luminosity, the central velocity dispersion, the 6 cm radio luminosity,

the absolute K magnitude, and the X-ray gas luminosity.

Our data cannot rule out the idea that negative gradients can be produced by compressional heating in low-temperature systems, during a slow cooling inflow in a steep gravitational potential. We find that SN feedback may also potentially provide sufficient energy to offset cooling in X-ray faint galaxies, but we find no direct evidence that SN heating dominates.

Our preferred feedback model, however, involves the central AGN. We produce temperature maps for the 12 brightest galaxies in our sample and ﬁnd strong evidence that the temperature structure is intimately connected to asymmetries in the gas maps, suggesting a common cause. We observed these surface brightness asymmetries already in Paper I, and linked their origin to AGN activity in Paper II. Furthermore, the strongest dependencies for the inner temperature gradient are radio luminosities and the central velocity dispersion, which may be interpreted as a surrogate for black 228 hole mass (Tremaine et al. 2002). The nature of these correlations is such that weak AGN hosts show negative temperature gradients, whereas more luminous AGN exclusively live in positive gradient systems. Thus, we propose two scenarios, to explain the observed features. (1) Weak AGN distribute their heat locally, whereas luminous AGN heat the gas more globally with their extended jets. (2) The onset of negative gradients marks the point where AGN heating becomes unimportant, and compressional heating or SN feedback becomes dominant. 229 Chapter 7

Conclusions

7.1 Summary

7.1.1 Morphological Evidence for AGN Feedback

The general perception of the X-ray emission of normal elliptical galaxies in the

ROSAT and Einstein era was that of round, calm and hydrostatic objects. This picture has radically changed with our analysis of 54 elliptical galaxies taken from the Chandra public archive. Due to the high spatial resolution capabilities of Chandra, it is possible to resolve a large fraction of the X-ray emission in elliptical galaxies into individual point sources, which has not only given a clearer view of the diﬀuse gas, but also deepened the general understanding of the point source population. This has led to the development of our new isolation technique for the gas, providing the opportunity to study the true gas morphology alone for the ﬁrst time.

We use our new WVT binning technique to adaptively bin the the gas-only images, and to produce the Chandra gas gallery of elliptical galaxies (Figure 4.2). The gallery has revealed many unexpected features and demonstrated how disturbed and asymmetric the gas distribution in elliptical galaxies really is. A one-by-one comparison between the X-ray gas maps and optical DSS images shows immediately how 230

little the gas distribution has in common with the shape of the starlight, and a quan-

titative analysis of optical and X-ray ellipticity proﬁles conﬁrms this observation. A

comparison of the mean X-ray and optical ellipticities shows absolutely no correlation

between the two quantities (Figure 4.4), in sharp contrast to what is expected from

gas sitting in hydrostatic equilibrium with the stellar potential.

The fact that the gas is not in hydrostatic equilibrium has far reaching conse-

quences. All X-ray tools that support the presence of dark matter in ellipticals out to

large radii are based on this very assumption. One technique, called the “geometrical

test for dark matter” (Buote and Canizares 1994), relies on measuring the elliptical isophotes of the hot gas, to infer the shape of the underlying potential. Our results show without a doubt that the hot gas is simply too disturbed and too far out of equilibrium for this test to work. Unfortunately, this also refutes the validity for the important result by Buote et al. (2002), who use this test to claim the existence of

a highly ﬂattened dark matter halo for the elliptical galaxy NGC 720. The presence

of disturbances in the hot ISM indicates the existence of at least localized over- or

underpressurized regions. The fact that even the large-scale morphologies, i.e. the

ellipticities, are correlated with the small-scale asymmetries implies that these eﬀects

are likely not to be restricted to small areas. Thus, even radial total mass proﬁles

that rely on hydrostatic equilibrium may be aﬀected, and in error by a factor of a

few. 231

With the help of a statistical measure of asymmetry, the asymmetry index η, we

trace the origin of these disturbances back to the activity of the central AGN. The

most striking observation that we make is that this AGN–morphology connection

persists all the way down the weakest AGN luminosities (Figure 5.9). Most likely,

the AGN is continually stirring the hot gas, inﬂating bubbles into the ISM with its

radio jet during intermittent outbursts. The fact that this may be even true for

extremely weak radio sources, which are often not even resolved as extended sources,

comes as a surprise and provides support for AGN-based feedback models to reheat

the gas even in normal elliptical galaxies.

7.1.2 Toward a Solution of the Cooling Problem

Our ﬁndings for the prevalence of morphological disturbances in the hot ISM of

elliptical galaxies, and their connection to the activity of the central AGN, may have

important consequences for the overall radial structure and energy budget for the hot

gas in elliptical galaxies. If the AGN also deposits signiﬁcant amounts of heat into

the gas while disturbing it, and prevents it from cooling at the center (e.g. Bregman

et al. 2006), our observations may be a ﬁrst step toward a solution for the long- standing “cooling ﬂow problem” on a galactic scale. The prospect that the AGN may be involved as a central heat source, even for normal elliptical galaxies, is promising.

To find spectral evidence of heating, we compute radial temperature profiles for our sample, revealing a surprising variety of different temperature profile types. We 232

are able to explain this complexity by dividing the temperature proﬁles into two radial

ranges, and analyzing these two temperature gradients separately. While our correla-

tion analysis shows that the outer temperature gradient (2−4RJ) galaxies is dictated

by the environment, and thus most likely indicates the presence of hot ambient inter-

galactic gas (Figure 6.5), we ﬁnd that the inner gradient (< 2RJ) is a consequence of

only intrinsic galaxy properties. In fact, the three strongest correlations that we ﬁnd

can all be interpreted as dependencies on AGN properties: the radio luminosities at

20 cm and 6 cm continuum wavelengths, and the velocity dispersion, which is believed

to be a surrogate of black hole mass (Tremaine et al. 2002).

The correlation between the inner temperature gradient and the AGN properties is such that negative inner temperature gradients are only found in galaxies with very weak central AGN, while powerful AGN are exclusively found in galaxies with cool cores. To explain this observation through AGN feedback, we propose two diﬀerent scenarios, that are consistent with our observations:

(1) Weak AGN distribute their heat locally, causing a central negative temperature

gradient, while more powerful AGN distribute their heat more globally. This

idea is also consistent with the fact that weaker AGN have smaller radio sources,

often consistent with point sources. Stronger AGN however drive powerful jets

and may interact with the AGN on larger scales.

(2) Alternatively, at the point where negative inner temperature gradients begin to

dominate, AGN heating may become unimportant. A cooling ﬂow may develop 233

and compressive pdV work in a steep potential may heat the gas to produce the

negative inner temperature gradients. Alternatively, supernovae heating may

become important at this point

We propose that the central AGN is the dominant factor that determines the

morphological as well as the thermodynamic structure of the hot gas in elliptical

galaxies.

7.1.3 Feedback and the X-ray Gas Fundamental Plane

We have discovered a new fundamental relationship between the X-ray gas half-

light radius, averaged surface brightness and luminosity weighted temperature. This

“X-ray gas fundamental plane” – or XGFP – is surprisingly tight, with an intrinsic

scatter as low as in the important stellar fundamental plane (SFP). In fact, it is

probably one of the tightest X-ray–only relationships that exist to date. We show

that our XGFP parameters are decoupled from the optical SFP parameters and that

the XGFP is not implying hydrostatic equilibrium. While this came as a surprise at

ﬁrst, it is obvious now with the new evidence for a complete decoupling of X-ray and

optical morphology from our Chandra gas gallery analysis. However, it is a mystery how most elliptical galaxies can appear extremely disturbed in their gas emission, while still forming an extremely tight relationship when one derives the three XGFP parameters from circularly average proﬁles. 234

Since the gas morphology is dictated by AGN feedback, this also suggests the involvement of the central AGN as the underlying cause of the XGFP. We have shown that the average temperature TX is strongly correlated with the inner temperature gradient, which in turn is correlated with AGN strength. If the process of AGN heating depends on X-ray luminosity, for which our change in temperature gradients may be an indication, the AGN may systematically aﬀect the half-light radius, surface brightness and average temperature, and thus create the XGFP. On the other hand, we show that our temperature structure also evolves with environment, with positive outer gradients indicating the presence of ambient intracluster or intragroup gas.

If this circumgalactic gas is pressure-confining the inner gas, it may very well be affecting the extent of the galaxy’s gas by stifling outflows, providing another possible explanation for the XGFP.

There are many theories for inﬂows, outﬂows, or even simultaneous in- and out-

ﬂows (see Mathews and Brighenti 2003a, for a review), some representing steady-state solutions, some providing the basis for a time-dependent evolution. Any of these theories may be able to explain the existence of the XGFP, but so far none has given deﬁnite predictions about the correlation between our XGFP parameters. Neverthe- less, we think that the XGFP has the potential of determining the validity of these models, as it puts a very stringent constraint on the X-ray structure of the hot gas.

The XGFP may be speciﬁc to normal galaxies, but on the other hand, it is closely related to the LX − TX relation, smoothly connecting the trend for extremely massive 235 clusters to that of groups and normal galaxies. It is unclear at which point and why this 2-parameter relation splits up and becomes a tilted plane in a 3-dimensional space. It may very well be that it is a 3-D correlation even at cluster luminosities, which has been pointed out by several authors (Adami et al. 1998; Fritsch and Buchert

1999; Miller et al. 1999; Fujita and Takahara 1999b). Finding the cause of the XGFP may be challenging, but nevertheless it may prove to be a powerful tool to test the hydrodynamic state or evolution of the hot gas in elliptical galaxies and groups.

7.2 Open Questions

Even though our understanding of the hot gas in elliptical galaxies has vastly improved in recent years, many questions still remain unanswered.

What exactly is the dynamical state of the hot gas? Since we have now established that the gas is disturbed, and not in equilibrium, we have to ﬁnd out what the eﬀects of this phenomenon are. How far out of equilibrium is the hot gas?

Is this causing the gas to ﬂow inward or rather outward? Or could it even drive gas in both directions at the same time, as proposed by circulation ﬂow models by Mathews et al. (2004)?

Where does the angular momentum of the gas go? A prediction of cooling

ﬂow models is that the gas retains its angular momentum while it slowly ﬂows inward. 236

Thus, the gas should generally settle into a cooling disk, a prediction which we have ruled out in our Chandra data. Does the activity of the AGN disrupt existing disks or mask their existence? Or have they never existed in the ﬁrst place?

What is the underlying cause behind the X-ray gas fundamental plane?

Winds? AGN feedback? Circumgalactic gas? Cooling ﬂows? Outﬂows? Circulation

Flows?

How exactly does the AGN deposit energy into the hot gas? Theoretical and observational efforts have provided promising solutions on the cluster scale, such as effervescent heating (Roychowdhury et al. 2004), shocks (Mathews et al. 2006), heat conduction (Voigt and Fabian 2004), or sound waves (Fabian et al. 2006). How- ever, it is unclear how these explanations will hold in the context of the different temperatures, densities, or black hole masses on the galactic scale.

What is the fueling mechanism for the black hole? Recent studies by Allen et al. (2006) suggest a remarkably tight relationship between a scaled Bondi accretion rate and the mechanical power output from radio sources. However, this is the ﬁrst study of this kind with a small sample of galaxies and needs reconﬁrmation. It would actually be surprising if a spherically symmetric, steady accretion model would turn out to explain every property satisfactorily. 237

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