Chandra Analysis of a Possible Cooling Core Galaxy Cluster at z = 1.03

Chandra Analysis of a Possible Cooling Core Galaxy Cluster at z = 1.03 Kyle Dolan Institute for Astronomy, University of Hawaii at Manoa (Dated: 12 August 2005) We present an analysis of Chandra observations of a massive cluster of galaxies at high redshift, Cl J1415+3612 at z = 1.03, investigating whether the cluster possesses a cooling core. If the cluster does possess a cooling core, it will be the earliest known example of a massive cooling core cluster. We find Cl J1415+3612 to be of a relaxed morphology through the use of a two-dimensional X-ray surface brightness model, and we use spectral fitting to find that the temperature of the cluster is kt = 5.7 ± 0.49 kev. Spectral fitting gives a temperature of 7.03 ± 1.01 kev for the core and 4.45 ± 0.58 kev for the outer cluster, which suggests that the core is warmer than the rest of the cluster, but too few counts are available for the spectral fits to be definitive. We find through one-dimensional spatial modeling that the radial surface brightness profile of the cluster cannot be satisfactorily modeled without some strong central peak in addition to the standard β model, which is suggestive of the presence of a cooling core. We find the total mass of the cluster to be (1.28 ± 0.67) 10 15 M which indicates that it is one of the more massive known clusters. The bolometric luminosity of the cluster (within the defined spectral radius) was found to be L(r s) = 7.73 10 44 ergs s 1. The use of spectrally normalized exposure maps is also discussed, and we mention the importance of correcting for the degradation of the Chandra ACIS low-energy quantum efficiency when performing spectral fits to energies below 1 kev. I. INTRODUCTION For the current astronomical community, few studies provide more opportunities for the advancement of cosmology than X-ray observations of massive, distant galaxy clusters. These clusters are the largest gravitationally bound systems in the universe, and their properties such as luminosity, mass, and temperature, along with their abundances at different redshifts, allow astronomers to test and refine current theories on cosmology and structure formation in the early universe. X-ray observations of distant galaxy clusters provide valuable information on the structure of the universe due to the fact that diffuse matter observed to be luminous in the X-ray band acts as a tracer for the distribution of dark matter in and around the visible galaxies. Since approximately 80% of the universes matter is dark matter, tracing the distribution of dark matter through X-rays allows a much more complete analysis of the structure of the galaxy clusters than would be possible with optical observations. During the past few years, the instruments on board the Chandra X-Ray Observatory have allowed astronomers to make some of the most detailed observations of distant, X-ray luminous galaxy clusters in history. The observatory continues to provide groundbreaking images and data, such as its data on the distant galaxy cluster Cl J1415.1+3612 (Perlman et al. 2002) at a redshift of z = 1.03 (see Fig. 1). Based on this redshift, the images from Chandra show Cl J1415.1+3612 as it was when the universe was two-fifths its current age ( 5.7 Gyr), but the cluster appears to be more relaxed than all other clusters at comparable redshift. In fact, as will be discussed below, the cluster resembles clusters in the final stages of relaxation, which are known as cooling core clusters. Galaxy clusters form cooling cores when they have not merged with other clusters for at least one billion years. As they recover from mergers with smaller clusters of galaxies, massive clusters approach hydrostatic equilibrium and rather than having an elliptical or irregular morphology (see Fig. 2), they gain a spherically symmetric appearance and have a sharp central peak in X-ray luminosity (see Fig. 3). Clusters that reach this state are called relaxed or virialized, as no major changes in the distribution of matter occur at this point. A cooling core develops when the gas density in a cluster s core increases to a point where the core cools more rapidly than the gas in the outer regions of the cluster. When this happens, the gas pressure in the core is no longer sufficient to support the core and the matter in the outer regions begins to flow inward. Since cooling cores take such a long time to form, if Cl J1415.1+3612 is in fact a cooling core cluster it would mean that the cluster is at least one billion years older than the image we have of it. This would be an unprecedented discovery, as the most distant known massive cooling core cluster is at z = 0.55 (when the universe was 8.1 Gyr old) and the most distant observed galaxy cluster of any kind is at z = 1.4 (when the universe was 4.4 Gyr old). The accepted epoch of cluster formation would have to extend further back in history to accommodate the discovery of a cluster being fully relaxed so early in the universe s history. The research project for this summer was to examine the Chandra images of Cl J1415.1+3612 and do a quantitative analysis of the clusters physical properties, with the particular goal of answering the question of whether or not the cluster possesses a cooling core. The CIAO software package was used to prepare the raw data for

2 06 00 13 00 05 00 Declination 12 00 04 00 11 00 250 kpc 31.1" 36 10 15s 10s 14h 15m 05s 24 03 0 55s 14h 23m 45s Right Ascension FIG. 1: Optical image of the cluster Cl J1415+3612 at a redshift of z = 1.03 with overlaid contours indicating the clusters X-ray surface brightness. This luminosity acts as a tracer of the dark matter in the cluster, which makes up most of the cluster s mass. FIG. 3: Optical image of the cluster MACSJ1423.8+2404 at redshift z=0.55 with overlaid contour lines indicating X-ray surface brightness. The contour lines show that this cluster has a relaxed morphology and a sharp central peak, the conditions necessary for a cooling core to form (Ebeling, Edge, and Henry 2001). II. 47 DATA PREPARATION AND ANALYSIS Cl J1415.1+3612 was observed using the ACIS-I array of the Chandra X-Ray Observatory on 18 September, 2003. The data were reprocessed by the standard software pipeline, removing any flaring events and calibrating by the latest files in CIAO 3.2.1. The useful time for the observation was 89 ks after removal of the flaring events. Point sources were recognized by the CIAO algorithm celldetect and removed from the data set for all subsequent analyses (see Fig. 4). 46 50s 45 44 A. Spectral Analysis Methods 250 kpc 37 43 40s 35s 30s 25s 07h 17m 20s FIG. 2: Optical image of the cluster MACSJ0717.5+3745 at redshift z=0.55 with overlaid contour lines indicating X-ray surface brightness. As is shown, the cluster has an irregular morphology and is not relaxed(ebeling, Edge, and Henry 2001). analysis, and IDL and Sherpa were used to analyze the prepared data The analysis shown in this paper closely follows the methods illustrated in Maughan et al., 2003. After Sherpa was used to make a preliminary twodimensional spatial fit of the data, the resulting radial profile of the cluster s luminosity was used to define the region where radiation from the cluster dominates over the background (S/N ratio 3σ). CIAO was then used to extract the spectrum of the cluster from this region, which was defined as a circle centered on the cluster s Xray centroid and with radius 52 (known as the spectral radius, or rs from now on)(see Fig. 4). ACISSPEC, a routine within CIAO, was used to create Ancillary Reponse Files (ARFs) and Redistribution Matrix Files (RMFs) for use in the spectral analysis. RMFs define the relationship between the energy of the photons striking the CCD and the actual energy output from the instrument, while ARF s define the relationship between the energy of the

3 15 15 10 10 36 05 36 05 45 s 30 s 15 s 15 m 00 s 14 h 14 m 45 s 45 s 30 s 15 s 15 m 00 s 14 h 14 m 45 s FIG. 4: X-ray image of the cluster Cl J1415+3612 with pixels of 0.492. The green circle shown here is the region from which the cluster s energy spectrum was extracted for spectral analysis. The orange regions mark all of the point sources which were removed from the emission data in order to isolate the cluster and the quiescent background from other emission sources. FIG. 5: X-ray image of Cl J1415+3612 with pixels of 0.492. The circular regions used for spectral analysis are shown, with the upper left region used to extract the source spectrum and the other three regions used for the background spectrum. The chip gaps are faintly visible in between the circles, showing that the regions are reflected images of each other over those chip gaps. photons and the effective area of the detector. ARFs and RMFs were produced for all of the user-defined regions to allow an accurate calibration of the spatial variations in the detector response. In order to define regions in the data from which to extract background spectra, we place one region of identical geometry in the same relative position on each of the adjacent CCDs (see Fig. 5). This method has the advantage of obtaining both the source spectrum and the background spectrum from the same observation, which eliminates any time-dependent systematic errors. Also, since the regions are placed in the same relative positions on each chip, the spatial variations in the energy responses and effective areas of the CCDs are also eliminated. In an attempt to demonstrate radial temperature variations in the cluster, additional regions were defined, dividing the cluster into a smaller circle of radius 21 for the cluster core and an annulus for the outer regions extending from the defined core radius of 21 to the spectral radius of 52. Spectra were then extracted, both from these regions and from their corresponding background regions. In order to compensate for decreased accuracy in the ACIS low-energy quantum efficiency (QE) due to the continuous particle buildup on Chandra s detector, the command MKACISRMF was used. In CIAO, this command allows a user to create RMF s that take the particle buildup into account, so that the spectra can be modelled correctly at energies below 1.0 kev. Without the updated RMF s, additional absorption would occur below 1.0 kev, causing the overestimation of cluster temperatures. After the spectra were extracted, they were fitted in Sherpa to an absorbed MEKAL plasma emission model (Mewe, Kaastra, Liedahl 1995) in order to produce temperature fits for each given region. B. Spatial Analysis Methods During the spatial analysis of the cluster, Sherpa was used to produce both two-dimensional and onedimensional models of the cluster s surface brightness distribution. The energy range 0.5-7.0 kev was used because it reduces the contribution from background events, while no significant cluster emission is observed outside this range, thus yielding the highest possible signal to noise ratios (see Fig. 6). A two-dimensional model was fitted to an image of the cluster, both in order to define the spectral radius of the cluster (see above) and to test the cluster s ellipticity. While a two-dimensional model allows the preservation of the image s exact Poisson statistics, very few (or zero) counts are contained in a pixel in a given Chandra image. Thus, the analysis is limited to the C statistic (Cash 1979) which does not allow an absolute measure of the goodness of fit for the model. For these reasons, a onedimensional model is preferred over a two-dimensional model for clusters of a significantly spherical distribution.

original data values as possible. Since exposure maps of this kind vary only by 5% over the cluster region, we are justified in assuming the validity of Gaussian statistics in our analysis. The model commonly used for spherically symmetric, relaxed galaxy clusters is called the β profile (Cavaliere and Fusco-Femiano 1976), and if a cluster conforms to this model it has the density profile 4 ( ) ] 2 3β/2 r ρ(r) = ρ 0 [1 + (i) r c where ρ(r) is the gas density at radius r and ρ 0 is the central gas density. The brightness distribution under the β profile is given as ( ) ] 2 3β+1/2 r S(r) = S 0 [1 + (ii) r c FIG. 6: The energy spectra of the particle background; the spectrum for the ACIS-I chips is shown by the lowermost line of black points (denoted 1023). The 0.5-7.0 kev range provides the best signal to noise ratios when subtracting background spectra from source spectra (Chandra Proposers Observatory Guide). A one-dimensional model assumes that the cluster is spherical, which limits its range of application to those clusters of a low enough ellipticity, but by ensuring that 20 counts are in each of the model s radial bins, Gaussian errors can be assumed in analyzing the cluster. Hence, if each bin has 20 counts, the χ 2 statistic may be used. Unlike the C statistic, the χ 2 statistic provides an absolute measure for the goodness of fit for the radial model. In order to create a good spatial model for the cluster, the Chandra emission data first had to be normalized to compensate for telescope vignetting and variations in the telescope s effective area with respect to both energy and CCD position. CCD gaps and the dithering of the satellite had also to be taken into account. To compensate for all of these factors, a spectrally-weighted exposure map was used. Exposure maps, as they are used with Chandra data, are images that indicate the position-dependent effective exposure time across the surface of the detector in units of s cm 2. An energy spectrum can be used to weight the exposure map with respect to a set of energy ranges, essentially producing an average of many exposure maps that are weighted by the relative number of counts in each of the given energy ranges. In this way, the final exposure map can account for energy dependence as well as location dependence in the emission data. The image data were divided by the completed exposure map, after first normalizing the exposure map to its own highest value so as to preserve as much of the Where S(r) is the surface brightness at radius r and S 0 is the central surface brightness. For both equations, r c is the core radius and β describes the slope of the profile at large radii. The preceding two parameters are derived from the data for Cl J1415.1+3612 in the following section. Operating under the assumptions that the cluster is spherically symmetric, is in hydrostatic equilibrium, and fits the β profile found in Sherpa; and that the mean molecular weight of the gas is 0.59m p, where m p is the proton mass, the total mass within the cluster out to a radius r is M(r) = 1.13 10 14 β T r (r/r c ) 2 kev Mpc 1 + (r/r c ) 2 M (iii) To evaluate the total mass of the cluster, we need to find the cluster s virial radius. Using the formalism of Arnaud, Aghanim, and Neumann (2002) and applying it to a flat (Ω 0 + Λ = 1) cosmology with Ω 0 = 0.3 and Λ = 0.7, we have that ( ) 1/2 r v = 3.80β 1/2 kt T 1/2 z (1 + z) 3/2 h 1 50 Mpc, 10 kev (iv) where z = ( c Ω 0 )/(18π 2 Ω z ),β T = 1.05 is a normalization, taken from Evrard, Metzler, and Navarro (1996), and the density contrast c is given by c = 18π 2 + 82(Ω z 1) 39(Ω z 1) 2 (v) for a flat universe. The matter density at redshift z, Ω z, is given by Ω z = Ω 0 (1 + z) 3 Ω 0 (1 + z) 3 + (1 Ω 0 Λ)(1 + z) 2 + Λ. (vi)

5 III. RESULTS A. Spectral Results Using the spectral radius of 52 initially suggested by the preliminary spatial model, a circular region of this size was centered on the X-ray centroid of the cluster (α = 14 h 15 m 11 s.234, δ = +36 12 01.81) and used to produce a spectrum of 1945 net counts. The spectrum was grouped into bins of at least 30 counts each using CIAO. The binned version of the file was then read into Sherpa where it was background-subtracted using the background regions, and fitted by an absorbed MEKAL model. The absorbing equivalent hydrogen column density was frozen at the Galactic value of 1.14 10 20 cm 2. The redshift was frozen at 1.03 and the abundance was frozen at 0.3. All of the fits were calculated with an energy range of 0.5-7.0 kev. The spectrum and fit are shown in Fig. 7. The best fit to the spectrum gave a temperature value of kt = 5.7±0.49 kev with a reduced χ 2 value of 0.526(53 degrees of freedom). Thawing the redshift parameter led to a best-fit for a redshift of z = 0.98 ± 0.032, which is lower than the optically derived z = 1.01 but not significantly so. Similar discrepancies in redshifts have been observed in Chandra analyses of other clusters (see, e.g., Schindler et al. 2001) and are credited to calibration errors. This fit of the background-subtracted source spectrum is a poor one, which is likely due to the low number of available counts which makes it impossible to get enough bins with 30 counts to do rigorous statistical analysis. Noting the low number of counts, spectral fitting was nevertheless done on two regions within the larger circular region: a circle of radius 21 containing 1021 counts; and an annulus with inner radius 21 and outer radius 52 containing 924 counts. This spectral fitting was done with the same parameters and binning values as the larger circle, in an effort to see any suggestion of cooling within the core of the cluster. For the circle of radius 21, the best spectral fit gave a temperature value of 7.03 ± 1.01 kev, with a reduced statistic value of 0.977(28 degrees of freedom). We see that this spectral fit does not suggest a cooling core, as the temperature given is above the calculated temperature of the whole cluster which we just found. Though the statistic value is better for this fit than the fit for the radius 52 circle, the number of counts is much lower so we cannot claim that the fit for the radius 21 circle is a rigorous fit. For the annulus from radius 21 to radius 52, the best spectral fit gave a temperature value of 4.45 ± 0.58 kev, with a reduced statistic value of 0.485(27 degrees of freedom). With this fit for the annulus, we have the suggestion that the core is warmer than the outer regions of the cluster instead of cooling faster than the outer regions. Using our best fit for the spectrum of the entire cluster FIG. 7: Spectrum and best-fit model of Cl J1415+3612 region, we find the total unabsorbed cluster flux in the observed 0.5-7.0 kev band to be the unabsorbed total cluster flux in the observed 0.5-7.0 kev energy band to be F(r s ) = 1.38 10 13 ergs s 1 cm 2. For the 0.1-2.4 kev band, we find this flux to be F(r s ) = 8.54 10 14 ergs s 1 cm 2. In the 0.5-2.0 kev band, this same flux value is F(r s ) = 7.43 10 14 ergs s 1 cm 2, and in the bolometric (0.01-100 kev) energy band we have F(r s ) = 1.38 10 13 ergs s 1 cm 2. The observed fluxes were then calibrated to the redshift of the cluster so that the luminosity of the cluster could be calculated. For the observed 0.5-7.0 kev energy band, we obtained F(r s ) = 1.09 10 13 ergs s 1 cm 2, corresponding to a luminosity of L(r s ) = 6.15 10 44 ergs s 1. In the 0.1-2.4 kev band, the redshift-adjusted flux is F(r s ) = 4.28 10 14 ergs s 1 cm 2, corresponding to a luminosity of L(r s ) = 2.41 10 44 ergs s 1. In the 0.5-2.0 kev band, we have F(r s ) = 3.29 10 14 ergs s 1 cm 2, corresponding to a luminosity of L(r s ) = 1.85 10 44 ergs s 1. Finally, using the bolometric 0.01-100 kev band, we have an unabsorbed flux of F(r s ) = 1.38 10 13 ergs s 1 cm 2, corresponding to a luminosity of L(r s ) = 7.73 10 44 ergs s 1. B. Spatial Results In fitting our two-dimensional model (see Fig. 8)to the radial brightness profile for the cluster, the model s ellipticity was found to be only 0.14, which is low enough for us to assume that the cluster is spherical and proceed with a one-dimensional spatial fit. First, however, a normalized image must be prepared through the use of an exposure map. In Sherpa, the cluster best-fit X-ray spectrum was used to create a weights file for a spectrally

6 20 15 10 36 05 45 s 30 s 15 s 15 m 00 s 45 s 14 h 14 m 30 s FIG. 8: A preliminary two-dimensional fit to the radial surface brightness profile of Cl J1415+3612. Using this fit, we can define the cluster s region of dominance to have a radius of 105 pixels (52 ). Also, the low ellipticity of this model allows us to assume that the cluster has a spherical morphology. weighted exposure map. Next, CIAO was used to create that exposure map (see Fig. 9)and divide an image of the emission data (with all of the point sources removed) by a normalized version of the exposure map. In IDL, a set of nested annuli (radial bins) was defined with logarithmically increasing radii, a maximum radius of 246 and centered on the X-ray centroid. The inner annuli were adjusted so that all of the annuli had at least 20 counts, to ensure that Gaussian statistics could be used. Next, the number of counts in each radial bin was divided by the area of the bin (after subtracting the area that was removed when the point sources were subtracted from the bin). The result was a series of data points defining the radial surface brightness profile of the cluster in terms of counts per pixel per second. First, an attempt was made to fit the profile to a composite model with a β profile and a constant background flux. The best fit for this model gave a β value of 0.58 ± 0.03 and an r c value of 7.95 ± 1.46 (63.8 kpc ±10.24) while the background flux was given as 0.013 ± 1.9 10 4 counts pixel 1 second 1 and the reduced χ 2 value was given as 2.52(34 degrees of freedom). This high χ 2 value indicates a poor fit, and Fig. 10 shows that the model cannot fit several data points close to the core. This discrepancy between the model and the data suggests that an additional central component may be necessary to reconcile the model with the profile. A central Gaussian peak was added to the one-dimensional model in Sherpa, and the best-fit model for the profile gave a β value of 0.82±0.16 and an r c value of 19.9 ±5.5 (160 ±44 kpc). The Gaussian peak has a full width at half maximum value of 6.02 ± 1.7 (48 ±14 kpc), and FIG. 9: This exposure map, normalized by the source cluster s spectrum and created in CIAO, shows the telscope s effective exposure time in units of s cm 2, with highest effective exposure time shown in black and lowest effective exposure time shown in white. The telescope s vignetting effect can be seen, as the effective exposure time is greater at the center of the ACIS-I detector than at the corners. The chip gaps are also quite visible, due to the loss of sensitivity between the CCD chips. FIG. 10: Radial brightness profile of Cl J1415+3612. The solid line shows the best-fit one-dimensional model consisting of a β profile and a constant background flux component. Several data points near the center do not fit with the model, suggesting that an additional component may be necessary to fit the data.

7 IV. CONCLUSIONS FIG. 11: Radial brightness profile of Cl J1415+3612. The solid line shows the best-fit one-dimensional model consisting of a β profile, a constant background flux component, and a central gaussian peak. This model fits with the first data points close to the center much better than does the previous model, which does not include the gaussian component. the χ 2 statistic has a value of 1.07(31 degrees of freedom). This model is a significantly better fit for the profile than the model without a gaussian component, and as Fig. 11 shows, this new composite model fits the central data points much better than the previous model. The relative success of this new model including a central Gaussian peak suggests the presence of the strong central brightness peak that is characteristic of cooling core clusters. Unfortunately, the fact that only about 2000 photon counts are available in the cluster s region of dominance (52 or 415 kpc) means that not enough counts are present to provide a definitive model for this central peak. If we take r c and β from the second model and use their known values and uncertainties along with T (for the cluster within r s ),and if we take r to be the spectral radius (r s = 415 kpc), we can use Equation (iii). to state that the mass of the galaxy cluster within the spectral radius is M(r s ) = (1.90 ± 0.87) 10 14 M. Next, using Equation(iv), we find the virial radius of the cluster to be r v = 2.44±0.21 Mpc, and the total mass within r v is then found to be M(r v ) = (1.28 ± 0.67) 10 15 M. This mass is comparable to the mass of the massive, relaxed cluster ClJ1226.9+3332, which has been found to be (1.4±0.5) 10 15 M (Maughan et al. 2005). We have analyzed Chandra observations of Cl J1415+3612 at z = 1.03 in an effort to determine whether or not the the cluster possesses a cooling core. Due to its extreme distance, the number of photon counts available to us to perform this analysis is not enough for a definitive answer to the question of whether a cooling core is present, but the evidence we do have is suggestive. In the course of our investigations, we have used the CIAO software package as well as Sherpa and IDL to prepare and analyze the data, both in terms of its energy spectra and the spatial positions of the photon counts. We determined the mass and luminosity of the cluster, giving us a means to compare this cluster s global properties to those of other known clusters. In our spatial analysis, we found that we did not have enough counts to perform a rigorous analysis on the energy spectrum of the cluster, as the entire spectral region only possessed slightly less than 2000 counts. Spectral fits of the core of the cluster suggest that the core is warmer than the rest of the cluster, but the small number of photon counts in the core ( 1000) prevents the data from convincing us that a cooling core cannot be present. The initial spatial analysis we performed on the cluster shows that the cluster is of a sphericity that suggests the relaxed morphology of a cooling core, and the cluster s spherical symmetry also allowed us to perform a onedimensional spatial fit. This one-dimensional fit suggests that the cluster data may not be properly modeled with a β profile unless a strong, central peak is also included in the model. Since a strong central brightness peak is one of the key characteristics of a cooling core cluster, our spatial analysis suggests that a cooling core is likely. More observations will be necessary, however, before we can constrain our spectral model and improve our spatial model to determine whether a cooling core is present. If a cooling core is not present, the cluster may be in the process of merging with a minor galaxy cluster that has fallen into the larger cluster s core, creating shockwaves in the X-ray luminous gas and raising the larger cluster s core temperature. The cluster could also be in a state of development slightly before the development of a cooling core, which would also explain why the core appears warmer than the rest of the cluster. V. ACKNOWLEDGEMENTS Special thanks to Harald Ebeling, Elizabeth Barrett, and Joshua Ruderman for their help on this project, and thanks also to the University of Hawaii at Manoa and the National Science Foundation.

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