Cluster growth: X-ray scaling relations

The Observed Growth of Massive Galaxy Clusters II: X-ray Scaling Relations

A. Mantz, S. W. Allen, H. Ebeling, D. Rapetti and A. Drlica-Wagner
Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, 452 Lomita Mall, Stanford, CA 94305-4085, USA
SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA 94025, USA
Institute for Astronomy, 2680 Woodlawn Drive, Honolulu, HI 96822, USA
E-mail: amantz@slac.stanford.edu
Accepted 2010 April 28. Received 2010 March 14; in original form 2009 August 30
Abstract

This is the second in a series of papers in which we derive simultaneous constraints on cosmology and X-ray scaling relations using observations of massive, X-ray flux-selected galaxy clusters. The data set consists of 238 clusters with 0.1–2.4 luminosities , and incorporates follow-up observations of 94 of those clusters using the Chandra X-ray Observatory or ROSAT (11 were observed with both). The clusters are drawn from three samples based on the ROSAT All-Sky Survey: the ROSAT Brightest Cluster Sample (78/37 clusters detected/followed-up), the ROSAT-ESO Flux-Limited X-ray sample (126/25), and the bright sub-sample of the Massive Cluster Survey (34/32). Our analysis accounts self-consistently for all selection effects, covariances and systematic uncertainties. Here we describe the reduction of the follow-up X-ray observations, present results on the cluster scaling relations, and discuss their implications. Our constraints on the luminosity–mass and temperature–mass relations, measured within , lead to three important results. First, the data support the conclusion that excess heating of the intracluster medium (or a combination of heating and condensation of the coldest gas) has altered its thermodynamic state from that expected in a simple, gravitationally dominated system; however, this excess heat is primarily limited to the central regions of clusters (). Second, the intrinsic scatter in the center-excised luminosity–mass relation is remarkably small, being bounded at the per cent level in current data; for the hot, massive clusters under investigation, this scatter is smaller than in either the temperature–mass or –mass relations (10–15 per cent). Third, the evolution with redshift of the scaling relations is consistent with the predictions of simple, self-similar models of gravitational collapse, indicating that the mechanism responsible for heating the central regions of clusters was in operation before redshift 0.5 (the limit of our data) and that its effects on global cluster properties have not evolved strongly since then. Our results provide a new benchmark for comparison with numerical simulations of cluster formation and evolution.

keywords:
large-scale structure of Universe – X-rays: galaxies: clusters.
pagerange: The Observed Growth of Massive Galaxy Clusters II: X-ray Scaling RelationsBpubyear: 2010

1 Introduction

Establishing the relationship between total mass and observable quantities is a crucial step in deriving cosmological constraints from the growth of cosmic structure using galaxy clusters. Not only can these scaling relations provide useful proxies for mass, but they are also fundamentally important in accounting for selection effects such as Eddington bias and Malmquist bias.

The construction of X-ray flux-selected cluster samples out to redshift and beyond has now enabled investigations of dark energy using these data (Mantz et al. 2008, hereafter M08; Vikhlinin et al. 2009b). However, the task of calibrating X-ray scaling relations has become correspondingly more complex; the evolution with cosmic time of the scaling relations and their scatter must be well understood, since such evolution can be degenerate with the effects of dark energy. The effect on cosmological constraints of systematic uncertainties in the scaling relations has been discussed in the context of future surveys by, e.g., Sahlén et al. (2009).

Fortunately, as we describe below, it is possible to simultaneously constrain both the evolution of the scaling relations and cosmological parameters, using a flux-limited sample of which some clusters have been targeted by detailed, follow-up X-ray observations. To distinguish X-ray methods from other measures of the growth of cosmic structure, including those using optically selected clusters, we refer to the resulting data set as the cluster X-ray luminosity function (XLF), although, strictly speaking, it contains a great deal more information than the luminosity function alone.

This is the second of a series of papers in which we address these issues. In a companion paper (Mantz et al., 2009, hereafter Paper I) we describe the statistical methods required to simultaneously constrain the scaling relations and cosmology, self-consistently accounting for all selection effects111Throughout this paper, we refer to “selection effects” or “selection biases” relative to a mass-limited sample, since we are primarily interested in deriving scaling relations as a function of cluster mass. and systematic uncertainties, and present the cosmological results from our analysis. This paper focuses on the reduction of the follow-up X-ray observations, and the constraints on the scaling relations from the simultaneous analysis. In Papers III (Rapetti et al., 2009) and IV (Mantz, Allen, & Rapetti, 2009), we respectively apply our analysis to investigations of modified gravity and neutrino properties.

In addition to their utility for cosmological investigations, cluster scaling relations are of significant astrophysical importance. Of primary interest is the heating mechanism that prevents cooling gas in dense cluster cores from condensing into stars and molecular gas at much higher rates than are observed (for reviews, see Peterson & Fabian, 2006; McNamara & Nulsen, 2007). The shape and evolution of the scaling relations, and specifically any departures from the simplest predictions for gravitationally dominated systems, can provide information on the physical mechanisms responsible for averting strong cooling and star formation.

The details of the cluster sample selection, the follow-up observations, and their reduction are discussed in Section 2. Sections 3 describes the scaling relation model and Section 4 our statistical method, which is more comprehensively detailed in Paper I. In Section 5, we present constraints on the scaling relations, and investigate various extensions to the simplest model, including possible evolution with redshift and asymmetric scatter. Section 6 contains a discussion of the influence of cool, X-ray bright gas in cluster centers on the scaling relations. Implications of our results for the astrophysics of the intracluster medium (ICM) are discussed in Section 7.

Unless otherwise noted, masses, luminosities and distances in tables and figures are calculated with respect to a reference cosmology, defined to be spatially flat, with Hubble constant , present mean matter density with respect to the critical density , and dark energy in the form of a cosmological constant. We adopt the conventional definition of cluster radius in terms of the critical density of the Universe; thus, is the radius within which the mean density of the cluster is times the critical density at the redshift of the cluster.

2 Data

2.1 Cluster samples

Figure 1: Luminosity–redshift distribution of clusters in the BCS (blue, filled circles), REFLEX (black, open circles) and Bright MACS (red triangles) samples which are above the respective flux limits (see text). The adopted minimum luminosity of is indicated by the dashed line. Luminosities in this plot are calculated from survey fluxes, assuming our reference cosmology, and refer to the 0.1–2.4 band in the cluster rest frame. Error bars are not shown.

Our data are drawn from three wide-area cluster samples derived from the ROSAT All-Sky Survey (RASS; Trümper, 1993): the ROSAT Brightest Cluster Sample (BCS; Ebeling et al., 1998), the ROSAT-ESO Flux-Limited X-ray sample (REFLEX; Böhringer et al., 2004), and the bright sub-sample of the Massive Cluster Survey (Bright MACS; Ebeling, Edge, & Henry 2001; Ebeling et al. 2010). Each sample covers a distinct volume of the Universe: the BCS covers the northern sky at , REFLEX covers the southern sky222The coverage of REFLEX actually extends slightly into the northern hemisphere. In this study, we restrict REFLEX to declinations and adjust the sky coverage fraction accordingly. at , and Bright MACS covers higher redshifts, , at declinations . The distributions of cluster detections from each sample in redshift and luminosity are shown in Figure 1 (here luminosities in the rest frame 0.1–2.4 band are calculated straightforwardly from the survey fluxes, assuming our reference cosmology).

The flux limits, , defining the samples are respectively , and in the 0.1–2.4 keV ROSAT energy band. In order to restrict the data set to massive clusters, for which the scaling relations can be described simply, we select only clusters whose flux in this band satisfies

(1)

where

(2)

approximately corresponds to a fixed, intrinsic luminosity of in the 0.1–2.4 band for our reference cosmology. Using this selection criterion, the BCS, REFLEX and MACS samples respectively contribute 78, 126 and 34 clusters to our data set.333Our previous analysis in M08 included 130 REFLEX sources using similar selection criteria. Published catalog entries RX J0117.8-5455 and RX J2251.7-3206 were eliminated from the present study, since high-resolution Chandra imaging reveals their emission to be point-like rather than extended. Source RX J0507.6-0238 satisfies our criteria after correcting its redshift (Dale Kocevski, private communication) from that published in Böhringer et al. (2004), and was therefore added. Three other sources (all Abell clusters), RX J0552.8-2103, RX J1959.1-3454 and RX J2331.2-3630, were removed because they do not satisfy the flux limit defined in Equations 1 and 2, reflecting a small difference between our K-correction and that used by Böhringer et al. (2004), and the fact that Equation 2 is not precisely identical to a fixed luminosity. The BCS and MACS sources selected are the same as in M08. Within the redshift and flux range defined above, all three samples are thought to be approximately 100 per cent complete and pure.444In the sense that the published selection function for each sample, the likelihood for cluster detection as a function of redshift and flux, is accurate. See additional comments in M08.

2.2 Follow-up X-ray observations

Additional information about a subset of the flux-selected clusters is available from follow-up X-ray observations. These observations enable more precise measurements of cluster luminosities, as well as measurements of morphology, temperature, and gas mass, which is an excellent proxy for total mass.

We incorporate Chandra data for clusters at where it is available. Below this redshift, the Chandra Advanced CCD Imaging Spectrometer (ACIS) field of view is typically too small to allow measurements at , a canonical radius at which simulations indicate that the scaling relations are well behaved (Evrard et al., 2008). For , we do, however, incorporate follow-up ROSAT Position Sensitive Proportional Counter (PSPC) observations. The ROSAT and Chandra observations were cross-calibrated using clusters in the redshift range that were observed with both instruments (Section 2.2.4). Details of the follow-up observations can be found in Tables 14; the total good exposure time of the follow-up data, including both ROSAT and Chandra observations, is 3.3 Ms, distributed over 94 clusters. The reduction and analysis of these data are described in the following sections.

Name RA (J2000) Dec (J2000) Date Detector Mode Exposure (ks)
Abell 2256 17 04 02.3 +78 38 14 1990 Jun 17 PSPC        16. 4
Abell 1795 13 48 53.1 +26 35 38 1991 Jul 01 PSPC 15. 1
1992 Jan 04 PSPC 33. 1
Abell 401 02 58 57.2 +13 34 46 1992 Jan 23 PSPC 5. 3
1992 Jul 30 PSPC 6. 9
Abell 2029 15 10 55.9 +05 44 44 1992 Aug 10 PSPC 8. 7
Abell 2255 17 12 50.0 +64 03 43 1993 Aug 24 PSPC 11. 8
Abell 478 04 13 25.2 +10 28 00 1991 Aug 31 PSPC 21. 9
Abell 2142 15 58 21.1 +27 13 45 1992 Aug 25 PSPC 5. 9
1992 Aug 26 PSPC 4. 8
1993 Jul 23 PSPC 4. 4
Abell 2244 17 02 42.0 +34 03 24 1992 Sep 21 PSPC 2. 9
Abell 2034 15 10 12.6 +33 30 45 1993 Jan 31 PSPC 4. 9
Abell 1068 10 40 44.4 +39 57 13 1992 Nov 30 PSPC 9. 8
Abell 2204 16 32 47.2 +05 34 33 1992 Sep 04 PSPC 5. 2
Abell 2218 16 35 53.0 +66 12 36 1991 May 25 PSPC 31. 9
Abell 1914 14 26 01.0 +37 49 37 1992 Jul 20 PSPC 6. 3
Abell 665 08 30 58.1 +65 51 02 1991 Apr 10 PSPC 32. 0
Abell 520 04 54 09.0 +02 55 18 1993 Sep 06 PSPC 4. 8
2000 Oct 10 ACISI VFAINT 9. 4
2003 Dec 04 ACISI VFAINT 57. 8
2007 Jan 01 ACISI VFAINT 5. 1
Abell 963 10 17 03.6 +39 02 52 1993 Oct 28 PSPC 9. 1
2000 Oct 11 ACISS FAINT 36. 3
2007 Feb 18 ACISI VFAINT 5. 0
RX J0439.0+0520 04 39 02.2 +05 20 42 2000 Aug 29 ACISI VFAINT 9. 6
2007 Nov 12 ACISI VFAINT 16. 2
2007 Nov 15 ACISI VFAINT 7. 9
Abell 1423 11 57 17.4 +33 36 40 2000 Jul 07 ACISI VFAINT 9. 9
Zwicky 2701 09 52 49.2 +51 53 06 2001 Nov 04 ACISS VFAINT 25. 9
Abell 773 09 17 52.7 +51 43 36 1991 Oct 28 PSPC 11. 0
2000 Sep 05 ACISI VFAINT 10. 9
2003 Jan 25 ACISI VFAINT 7. 6
2004 Jan 21 ACISI VFAINT 19. 8
Abell 2261 17 22 27.0 +32 07 58 1999 Dec 11 ACISI VFAINT 6. 7
2004 Jan 14 ACISI VFAINT 23. 3
Abell 1682 13 06 50.7 +46 33 30 2002 Oct 19 ACISI VFAINT 1. 8
Abell 1763 13 35 19.0 +40 59 59 1992 Jun 23 PSPC 12. 7
2003 Aug 28 ACISI VFAINT 19. 3
Abell 2219 16 40 20.3 +46 42 30 1993 Aug 02 PSPC 8. 5
2000 Mar 31 ACISS FAINT 42. 2
Abell 2111 15 39 41.1 +34 25 07 1993 Jul 23 PSPC 6. 7
2000 Mar 22 ACISI FAINT 9. 5
Zwicky 5247 12 34 22.1 +09 47 05 2000 Mar 23 ACISI VFAINT 9. 3
Abell 267 01 52 42.2 +01 00 30 1999 Oct 16 ACISI FAINT 7. 1
2003 Dec 07 ACISI VFAINT 17. 8
Abell 2390 21 53 37.1 +17 41 45 1993 Nov 13 PSPC 8. 4
1999 Nov 05 ACISS FAINT 8. 0
2000 Oct 08 ACISS FAINT 9. 8
2003 Sep 11 ACISS VFAINT 74. 6
Zwicky 2089 09 00 36.8 +20 53 40 2006 Dec 23 ACISI VFAINT 9. 1
RX J2129.6+0005 21 29 39.7 +00 05 18 2000 Oct 21 ACISI VFAINT 8. 7
RX J0439.0+0715 04 39 00.6 +07 16 00 1999 Oct 16 ACISI FAINT 6. 3
1999 Oct 16 ACISI VFAINT 1. 6
2003 Jan 04 ACISI VFAINT 19. 0
Abell 1835 14 01 01.9 +02 52 40 1993 Jul 03 PSPC 6. 1
1994 Jul 05 PSPC 2. 5
2005 Dec 07 ACISI VFAINT 36. 3
2006 Jul 24 ACISI VFAINT 39. 5
2006 Aug 25 ACISI VFAINT 117. 9
Abell 68 00 37 05.9 +09 09 36 2002 Sep 07 ACISI VFAINT 10. 0
Table 1: Details of the follow-up observations of BCS clusters. The detector column indicates whether the observation used the ROSAT PSPC or the one of the Chandra ACIS CCD cameras.
Name RA (J2000) Dec (J2000) Date Detector Mode Exposure (ks)
MS J1455.0+2232 14 57 15.1 +22 20 33 2000 May 19 ACISI FAINT        9. 9
2003 Sep 05 ACISI VFAINT 91. 9
2007 Mar 23 ACISI VFAINT 7. 1
Abell 697 08 42 57.6 +36 21 57 1991 Apr 10 PSPC 9. 6
2002 Dec 15 ACISI VFAINT 17. 5
Zwicky 3146 10 23 39.6 +04 11 12 1993 Nov 13 PSPC 8. 1
2000 May 10 ACISI FAINT 42. 4
2008 Jan 18 ACISI VFAINT 31. 2
Abell 781 09 20 25.3 +30 30 11 2000 Oct 03 ACISI VFAINT 8. 7
Table 2: continued
Name RA (J2000) Dec (J2000) Date Detector Mode Exposure (ks)
Abell 3558 13 27 58.4 31 30 04 1991 Jul 17 PSPC        24. 0
Abell 85 00 41 50.1 09 18 22 1992 Jun 11 PSPC 3. 2
1992 Jul 01 PSPC 8. 3
Abell 3667 20 12 31.2 56 49 47 1992 Oct 09 PSPC 6. 3
Abell 3266 04 31 21.5 61 26 21 1992 Apr 30 PSPC 6. 6
1993 Aug 19 PSPC 13. 2
Abell 3112 03 17 58.2 44 14 07 1992 Dec 17 PSPC 7. 0
Abell 2597 23 25 19.6 12 07 27 1991 Nov 27 PSPC 6. 7
Abell 3921 22 49 57.0 64 25 53 1992 Nov 15 PSPC 11. 5
MS J1111.8 11 14 12.7 38 11 25 1993 Jan 11 PSPC 18. 5
Abell 1689 13 11 29.6 01 20 28 1992 Jul 18 PSPC 13. 5
Abell 2163 16 15 46.0 06 08 54 1992 Feb 28 PSPC 3. 1
1992 Sep 01 PSPC 7. 0
2000 Jul 29 ACISI VFAINT 9. 4
2001 Jun 16 ACISI VFAINT 67. 4
Abell 209 01 31 53.1 13 36 48 2000 Sep 09 ACISI VFAINT 8. 7
2003 Aug 03 ACISI VFAINT 9. 6
RX J1504.10248 15 04 07.6 02 48 16 2004 Jan 07 ACISI FAINT 12. 0
2005 Mar 20 ACISI VFAINT 33. 8
RX J0304.13656 03 04 03.3 36 56 30 2008 Mar 16 ACISI VFAINT 19. 9
RX J0237.42630 02 37 27.4 26 30 28 2008 Mar 03 ACISI VFAINT 7. 4
Abell 2667 23 51 39.7 26 04 60 1992 Dec 05 PSPC 2. 0
1992 Dec 05 PSPC 3. 0
2001 Jun 19 ACISS VFAINT 9. 4
RX J0638.75358 06 38 47.3 53 58 28 2008 Apr 11 ACISI VFAINT 19. 9
RX J0220.93829 02 20 56.5 38 28 52 2008 Feb 29 ACISI VFAINT 19. 9
Abell 521 04 54 07.4 10 13 24 1999 Dec 23 ACISI VFAINT 36. 8
2000 Oct 13 ACISS VFAINT 18. 6
RX J0307.02840 03 07 02.0 28 39 56 2008 Mar 13 ACISI VFAINT 18. 1
RX J2011.35725 20 11 27.2 57 25 10 2004 Jun 08 ACISI VFAINT 22. 3
RX J0232.24420 02 32 17.7 44 20 55 2004 Jun 08 ACISI VFAINT 7. 9
RX J0528.93927 05 28 53.3 39 28 19 2004 Mar 10 ACISI VFAINT 15. 9
RX J0043.42037 00 43 24.8 20 37 24 2008 Feb 02 ACISI VFAINT 19. 7
1ES 0657558 06 58 27.5 55 56 32 1997 Feb 28 PSPC 4. 5
2000 Oct 16 ACISI FAINT 25. 3
2002 Jul 12 ACISI VFAINT 81. 1
2004 Aug 10 ACISI VFAINT 21. 3
2004 Aug 11 ACISI VFAINT 93. 9
2004 Aug 14 ACISI VFAINT 77. 5
2004 Aug 15 ACISI VFAINT 31. 2
2004 Aug 17 ACISI VFAINT 79. 8
2004 Aug 19 ACISI VFAINT 70. 7
2004 Aug 23 ACISI VFAINT 22. 9
2004 Aug 25 ACISI VFAINT 39. 1
Abell 2537 23 08 22.0 02 11 30 2004 Sep 09 ACISS VFAINT 36. 2
Table 3: Details of the follow-up observations of REFLEX clusters (see caption for Table 1).
Name RA (J2000) Dec (J2000) Date Detector Mode Exposure (ks)
MACS J2245.0+2637 22 45 04.6 +26 38 04 2002 Nov 24 ACISI VFAINT        13. 9
MACS J1131.81955 11 31 55.6 19 55 45 1993 Jun 27 PSPC 7. 2
2002 Jun 14 ACISI VFAINT 13. 1
MACS J0014.33022 00 14 18.8 30 23 18 1992 Jun 16 PSPC 13. 6
2001 Sep 03 ACISS VFAINT 23. 8
2006 Nov 08 ACISI VFAINT 12. 3
2007 Jun 10 ACISI VFAINT 37. 7
2007 Jun 14 ACISI VFAINT 23. 9
MACS J2140.22339 21 40 15.2 23 39 40 1993 Nov 07 PSPC 9. 2
1999 Nov 18 ACISS VFAINT 40. 5
2003 Nov 18 ACISS VFAINT 24. 0
MACS J0242.52132 02 42 35.9 21 32 26 2002 Feb 07 ACISI VFAINT 9. 6
MACS J1427.62521 14 27 39.5 25 21 03 2002 Jun 29 ACISI VFAINT 14. 6
2008 Jun 11 ACISI VFAINT 26. 3
MACS J0547.03904 05 47 01.5 39 04 26 2002 Oct 20 ACISI VFAINT 20. 9
MACS J0257.62209 02 57 41.3 22 09 13 2001 Nov 12 ACISI VFAINT 20. 5
MACS J2049.93217 20 49 55.3 32 16 49 2002 Dec 08 ACISI VFAINT 22. 9
MACS J2229.72755 22 29 45.2 27 55 36 2002 Nov 13 ACISI VFAINT 12. 9
2007 Dec 09 ACISI VFAINT 13. 3
MACS J1319.9+7003 13 20 07.5 +70 04 37 2002 Sep 15 ACISI VFAINT 8. 7
MACS J0520.71328 05 20 42.2 13 28 47 2002 Feb 10 ACISI VFAINT 19. 0
MACS J1931.82634 19 31 49.6 26 34 34 2002 Oct 20 ACISI VFAINT 13. 1
MACS J0035.42015 00 35 26.2 20 15 46 2003 Jan 22 ACISI VFAINT 20. 8
MACS J0947.2+7623 09 47 13.0 +76 23 14 2000 Oct 20 ACISI VFAINT 11. 7
MACS J1115.8+0129 11 15 51.9 +01 29 55 2003 Jan 23 ACISI VFAINT 8. 7
2008 Feb 03 ACISI VFAINT 34. 7
MACS J0308.9+2645 03 08 56.0 +26 45 35 2002 Mar 10 ACISI VFAINT 23. 4
MACS J0404.6+1109 04 04 32.7 +11 08 11 2002 Feb 20 ACISI VFAINT 17. 6
MACS J1532.8+3021 15 32 53.8 +30 20 59 2001 Aug 26 ACISS VFAINT 9. 4
2001 Sep 06 ACISI VFAINT 10. 0
MACS J0011.71523 00 11 42.8 15 23 22 2002 Nov 20 ACISI VFAINT 20. 8
2005 Jun 28 ACISI VFAINT 37. 2
MACS J0949.8+1708 09 49 51.8 +17 07 08 2002 Nov 06 ACISI VFAINT 14. 3
MACS J1720.2+3536 17 20 16.7 +35 36 23 2002 Nov 03 ACISI VFAINT 19. 8
2005 Nov 22 ACISI VFAINT 29. 5
MACS J1731.6+2252 17 31 39.2 +22 51 50 2002 Nov 03 ACISI VFAINT 18. 5
MACS J2211.70349 22 11 45.9 03 49 42 2002 Oct 08 ACISI VFAINT 15. 2
MACS J0429.60253 04 29 36.0 02 53 06 2002 Feb 07 ACISI VFAINT 22. 1
MACS J0159.80849 01 59 49.4 08 49 60 2002 Oct 02 ACISI VFAINT 17. 4
2004 Dec 04 ACISI VFAINT 35. 3
MACS J2228.5+2036 22 28 32.8 +20 37 15 2003 Jan 22 ACISI VFAINT 19. 9
MACS J0152.52852 01 52 33.9 28 53 33 2002 Sep 17 ACISI VFAINT 17. 3
MACS J1206.20847 12 06 12.3 08 48 06 2002 Dec 15 ACISI VFAINT 23. 5
MACS J0417.51154 04 17 34.3 11 54 27 2002 Mar 10 ACISI VFAINT 11. 2
MACS J2243.30935 22 43 21.4 09 35 43 2002 Dec 23 ACISI VFAINT 20. 2
MACS J1347.51144 13 47 30.8 11 45 09 2000 Mar 05 ACISS VFAINT 8. 9
2000 Apr 29 ACISS FAINT 10. 0
2001 May 10 ACISS VFAINT 89. 6
2003 Sep 03 ACISI VFAINT 55. 8
MACS J0358.82955 03 58 51.2 29 55 22 2009 Oct 18 ACISI VFAINT 8. 7
MACS J2311.5+0338 23 11 35.3 +03 38 25 2002 Sep 07 ACISI VFAINT 6. 5
Table 4: Details of the follow-up observations of Bright MACS clusters (see caption for Table 1). The last two observations listed are not used in this paper: the MACS J0358 observation took place after this paper was initially submitted, and we conservatively chose to exclude the MACS J2311 observation because it coincides with a long-duration background flare. Their derived properties are nevertheless included in Table 7 so that the complete sample of Ebeling et al. (2010) is represented.

2.2.1 Chandra data analysis

The standard level-1 event files distributed by the Chandra X-ray Center (CXC) were reprocessed in accordance with CXC recommendations, using the ciao software package555http://cxc.harvard.edu/ciao/ (version 4.1.1, CALDB 4.1.2). This processing includes removal of bad pixels, corrections for cosmic ray afterglows and charge transfer inefficiency, and application of standard grade and status filters, using appropriate time-dependent gain and calibration products. The extra information available for observations taken in VFAINT mode (the majority) was used to improve cosmic ray rejection. The data were cleaned to remove times of high or unstable background using the energy ranges and time bins recommended by the CXC. Blank-field data sets made available by the CXC were tailored to each observation and cleaned in an identical manner to the real data. The normalizations of these blank-sky files were scaled to match the count rates in the target observations measured in the 9.5–12 keV band.

After identifying and masking point sources, flat-fielded images and background-subtracted surface brightness profiles were prepared in the 0.7–2.0 energy band. The emissivity in this band is largely insensitive to the gas temperature, , provided (as is the case for all the clusters studied here), making it the preferred energy range for determining the gas mass. The center of each cluster was identified with the centroid of 0.7–2.0 emission after masking point sources.

Our spectral analysis is a two-stage process. In the first stage, spectra in the 0.8–7.0 band were extracted in an annulus about the cluster centers. The inner radii of all annuli were set to 100 in order to prevent relatively cool gas in the cores from strongly influencing the spectral fits. The outer radii were initially chosen to be the radii at which the signal-to-noise ratio apparent in the 0.8–7.0 surface brightness profiles falls to 2. Background spectra were extracted from the blank-sky fields for targets at , and from source-free regions of the detector for targets. When required, e.g. due to the presence of strong excess soft emission in the field, a model for additional, soft thermal emission was included in the spectral modeling of the background. Photon-weighted response matrices and effective area files were generated for each observation using calibration files for the appropriate period.

The spectral analysis was performed using xspec.666http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/ The spectra were fit to a single-temperature, optically thin thermal emission model evaluated with the mekal code (Kaastra & Mewe 1993; Mewe, Kaastra, & Liedahl 1995, incorporating the Fe-L calculations of Liedahl, Osterheld, & Goldstein 1995), including a model for photoelectric absorption due to Galactic hydrogen (Balucinska-Church & McCammon, 1992). Column densities were fixed to the Galactic values determined from the H survey of Kalberla et al. (2005), unless the published value exceeded , in which case they were fit as free parameters.777We note that the choice of column density does not have a significant impact on our derived luminosities, temperatures and masses. In particular, the energy bands used (), and the use of locally determined backgrounds for the surface brightness analysis (Section 2.2.3) and, when possible, for the spectral analysis, make our results relatively insensitive to uncertainties in the soft X-ray background. Residual uncertainties are within the systematic tolerances defined in Section 2.2.3. The abundances of all metals were assumed to vary with a common ratio, , relative to solar values (Anders & Grevesse, 1989), which was a free parameter in the fit for each cluster. We minimized the modified C-statistic (Cash, 1979; Arnaud, 1996) rather than , as is appropriate for spectra with few counts per bin. Once a best fitting model was identified, the parameter space was explored using Markov Chain Monte Carlo; these Monte Carlo samples were used to propagate the uncertainty due to the fit in the conversion of 0.7–2.0 count rate to 0.1–2.4 flux for each observation. We note that, since both the count rate and flux in this conversion are at soft energies, the conversion is only weakly dependent on temperature and has negligible dependence on metallicity, provided that the temperature is sufficiently high ().

The second stage of the spectral analysis uses an estimate for , obtained as described in Section 2.2.3 below. New spectra in the annuli (0.15–0.5) and (0.15–1) were extracted and fit as above. For observations of nearby clusters where a large fraction of the (0.15–1) region falls outside the detector, only the (0.15–0.5) region was analyzed; we then estimated the (0.15–1) temperature using the relation , fit from the other clusters. (This result is consistent with that of Vikhlinin et al. 2009a, who followed a similar procedure; see Section 4.1.1 and Figure 6 of that work.) This final step is motivated by the desire to measure a temperature within , for consistency with the mass and luminosity measurements (Section 2.2.3), while still reliably excising the cool core, if one is present. We note, however, that this level of detail is not entirely necessary; the per cent reduction in temperature within compared with the temperature measurement from the first stage of the analysis is within statistical errors for most systems and has negligible impact on the determination of masses and luminosities. We therefore do not further iterate the determination of using this new temperature estimate. The resulting temperature measurements are referred to as in the following, the subscript indicating “center-excised”, and are listed in Tables 57.

We note that the uncertainties on temperatures measured within are necessarily somewhat larger than those on our initial estimates from higher signal-to-noise regions. Ultimately, however, this has negligible effect on our results, since this additional uncertainty is smaller than the systematic allowances associated with instrument calibration and mass estimations (Section 2.2.3).

Name
(Mpc) (keV) ref
Abell 2256 0.0581 1
Abell 1795 0.0622 2
Abell 401 0.0743 2
Abell 2029 0.0779 2
Abell 2255 0.0809 1
Abell 478 0.0881 2
Abell 2142 0.0904 2
Abell 2244 0.0989 2
Abell 2034 0.113 1
Abell 1068 0.1386 1
Abell 2204 0.1511 2
Abell 2218 0.171 1
Abell 1914 0.1712 1
Abell 665 0.1818 1
Abell 520 0.203 3
Abell 963 0.206 3
RX J0439.0+0520 0.208 3
Abell 1423 0.213 3
Zwicky 2701 0.214 3
Abell 773 0.217 3
Abell 2261 0.224 3
Abell 1682 0.226 3
Abell 1763 0.2279 3
Abell 2219 0.2281 3
Zwicky 5247 0.229 3
Abell 2111 0.229 3
Abell 267 0.230 3
Abell 2390 0.2329 3
Zwicky 2089 0.2347 3
RX J2129.6+0005 0.235 3
RX J0439.0+0715 0.2443 3
Abell 1835 0.2528 3
Abell 68 0.2546 3
MS J1455.0+2232 0.2578 3
Abell 697 0.282 3
Zwicky 3146 0.2906 3
Abell 781 0.2984 3
Table 5: Redshifts and derived properties of BCS clusters from follow-up observations. Temperatures in this work are measured in the aperture (0.15–1). Luminosities are in the 0.1–2.4 band in the cluster rest frame and have been cross-calibrated to the standard of ROSAT (Section 2.2.4). Gas masses measured with Chandra have similarly been calibrated to the ROSAT standard. Total masses are independent of this cross-calibration, but do depend on the value of , which is assumed here to be 0.1104 at . As discussed in the text, recent Chandra calibration updates favor an increase in the measured values of at by 5–10 per cent, implying reductions of 3–5 per cent in and 7–15 per cent in and , with respect to the values listed here. This dependence is accounted for fully in our analysis (see also Paper I). Error bars in this table do not include contributions due to systematic uncertainty in , or uncertainty in the overall instrument calibration, whose effects are correlated across all clusters. references: [1] Horner (2001), [2] Vikhlinin et al. (2009a), [3] this work.
Name
(Mpc) (keV) ref
Abell 3558 0.048 1
Abell 85 0.0557 2
Abell 3667 0.0557 2
Abell 3266 0.0602 2
Abell 3112 0.0752 1
Abell 2597 0.0852 1
Abell 3921 0.094 1
MS J1111.8 0.1306 1
Abell 1689 0.1832 1
Abell 2163 0.203 3
Abell 209 0.206 3
RX J1504.10248 0.2153 3
RX J0304.13656 0.2192 3
RX J0237.42630 0.2216 3
Abell 2667 0.2264 3
RX J0638.75358 0.2266 3
RX J0220.93829 0.228 3
Abell 521 0.2475 3
RX J0307.02840 0.2537 3
RX J2011.35725 0.2786 3
RX J0232.24420 0.2836 3
RX J0528.93927 0.2839 3
RX J0043.42037 0.2924 3
1ES 0657558 0.2965 3
Abell 2537 0.2966 3
Table 6: Redshifts and derived properties of REFLEX clusters from follow-up observations (see caption for Table 5).
Name
(Mpc) (keV) ref
MACS J2245.0+2637 0.301 3
MACS J1131.81955 0.306 3
MACS J0014.33022 0.308 3
MACS J2140.22339 0.313