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Lack of "co oling flow" clusters at z > 0.5
A. Vikhlinin1,2 , R. Burenin2 , W. R. Forman1 , C. Jones1 , A. Hornstrup3 , S. S. Murray1, and H. Quintana4
1 2 3 4

Harvard-Smithsonian Center for Astrophysics, Cambridge MA, USA Space Research Institute, Moscow, Russia Danish National Space Center Dep. de Astronomia y Astrofisica, Pontificia Universidad Catolica de Chile

The goal of this work is to study the incidence rate of "co oling flows" in the high redshift clusters using Chandra observations of z > 0.5 ob jects from a new large, X-ray selected catalog [1]. We find that only a very small fraction of high-z ob jects have cuspy X-ray brightness profiles, which is a characteristic feature of the co oling flow clusters at z 0. The observed lack of co oling flows is most likely a consequence of a higher rate of ma jor mergers at z > 0.5.

1 Introduction
The central regions in a large fraction of low-redshift clusters are clearly affected by radiative co oling [2]. Some estimates put the fraction of such co oling flow clusters to > 70% (e.g., [3]). A recent by Bauer et al. suggests that the cooling flow fraction remains high to z 0.4 [4]. However, this work is based on the ROSAT All-Sky Survey cluster sample, and so it can be strongly affected by Malmquist bias (strongly over-luminous clusters are preferentially selected because of the high flux threshold). Any evolution in the co oling flow fraction, if detected, must be taken into account in detailed physical mo dels of this phenomenon. We address this important question using a new distant cluster sample, derived from a sensitive survey based on the ROSAT pointed observations [1]. All ob jects were observed with Chandra, providing a uniform dataset which should be much less affected by selection effects than the previous samples.

2 Definition of the "cooling flow" cluster
First of all, we need to cho ose a definition of the "co oling flow" cluster that can be efficiently applied to the X-ray data of various statistical quality. The most common definition is based on the estimated central co oling time: co oltH (e.g., [3]). One could also use the mass depoing flow clusters have tcool sition rate given by the standard co oling flow mo del [2]; co oling flow clusters have M (10 - 100) M yr-1 [3]. These definitions rely on spatially-resolved spectroscopic measurements which is a serious disadvantage for application

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Fig. 1. X-ray surface brightness profiles typical for non-cooling flow (left ; A401) and cooling flow (right ; A85) clusters. Solid lines show the model X-ray brightness corresp onding to the b est-fit gas density model (see [5] for details).

at high redshifts. The data of sufficient quality to measure T (r) are available only for a small number of high-z ob jects. We, therefore, lo ok for a definition based solely on the X-imaging data. At low redshifts, there is a clear connection between the presence of the co oling flow and the X-ray morphology. Clusters with tcool tH have X-ray tH have characterbrightness profiles with flat cores while those with tcool istic central cusps in the X-ray brightness distribution (Fig. 1). The central cusp can be characterized by the power-law index of the gas density profile, = d log g /d log r. For uniformity, the radius at which is measured should be chosen at a fixed fraction of the cluster virial radius. This radius should be sufficiently small so that the effects of co oling are strong. At very small radii, however, the density profiles even in clusters with strong co oling flows can flatten because of the outflows from the central AGN (see many papers in these pro ceedings). Empirically, a go o d choice is r = 0.04 R500 ,5 and so we define the "cuspiness parameter", , as d log g d log r at r = 0.04 R500 (1)

Cuspiness can be measured by fitting a realistic 3-dimensional gas density mo del to the observed X-ray surface brightness (our pro cedure is described in [5]). Examples of the best-fit mo dels are shown by solid lines in Fig. 1. Such mo deling is feasible with mo derate-exposure Chandra observations of highredshift clusters. R500 can be estimated using low-scatter cluster mass proxies such as the average temperature (excluding the central cooling region). We use an even better proxy, the recently proposed YX parameter [6], which is
5 R500 is the radius at which the mean enclosed total mass overdensity is 500 relative to the critical density at the ob ject redshift. R500 0.5Rvir .

Lack of "cooling flow" clusters at z > 0.5

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Fig. 2. The distribution of the cuspiness parameter in the low-z cluster sample. Arrows indicate the values for some well-known clusters. The b oundary value of = 0.5 approximately separates cooling flow and non-cooling flow clusters.

remarkably insensitive to the cluster dynamical state and easily measured even in high-redshift clusters. Our low-redshift cluster sample is a flux-limited subsample of 48 ob jects from the HIFLUGCS catalog [7], all with the archival Chandra observations. The distribution of the cuspiness parameter for these ob jects is shown in Fig. 2. Clearly, the value of is closely connected to the more common co oling flow definitions. Clusters with > 0.7 (e.g., A2065, A478, A2029, A2597, 2A 0035, A133) are known to host strong co oling flows. The ob jects with < 0.5 (e.g., A2163, A399, A119, A2256, A754) are famous non co oling flow clusters. The clusters in the range 0.5 < < 0.7 (e.g., A2589, A3571) host weak co oling flows. Therefore, the cooling flow clusters are those with > 0.5. Approximately 2/3 of the low-redshift sample (31 of 48 ob jects) have cuspiness above this value, in line with the previous estimates of the co oling flow incidence rate (e.g. [3]).

3 High-redshift cluster sample
Our high-redshift sample is derived from the recently completed 400 deg2 ROSAT PSPC survey (400d; [1]). This is the largest-area survey based on the ROSAT pointed observations. Clusters are detected as extended X-ray sources in the central 17.5 of the PSPC FOV and required to have fluxes fx > 1.4 в 10-13 erg s-1 cm-2 . The X-ray sample is fully identified. It includes 266 optically confirmed clusters (95% of the X-ray candidate list). Spectroscopic redshifts are available for all ob jects.

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0.97

0.03

Fig. 3. (a) -- Detection efficiency of the 400d survey for idealized -model clusters as a function of total flux and core-radius. Dotted line shows the flux limit of the 400d catalog. Detection efficiency is reduced for rc 8 b ecause the such clusters are hard do distinguish from the p oint sources. The efficiency is also small for 150 b ecause they are "lost" in the cosmic X-ray background. ob jects with rc (b) Detection efficiency as a function of core-radius for fx = 2 в 10-13 erg s-1 cm-2 . Shaded histogram shows the distribution of core-radii in a low-redshift sample [8] scaled to z = 0.5.

A subsample of the high-z 400d clusters has been observed with Chandra. The exposure times were chosen to yield at least 2000 source counts, which is sufficient to measure the average cluster temperature with a 15% uncertainty and accurately trace the surface brightness profile to r R500 . Chandra 's angular resolution corresponds to a linear scale of < 8 kpc out to z = 1, fully sufficient to measure the cuspiness parameter. In this work, we use 400d clusters at z > 0.5, 20 in total. The typical mass of these ob jects corresponds to today's 4 keV clusters. The basic characteristics of the X-ray selection in the 400d survey have been extensively calibrated through exhaustive Monte-Carlo simulations (see [1] for details). The aspect most relevant for the present study is the sensitivity of the detection efficiency to the cluster size and structure. A precise two-dimensional map of the detection efficiency as a function of cluster size and core radius was derived for idealized -mo del clusters (Fig. 3a). 8 and rc 120 The detection efficiency drops significantly only for rc (see Fig. 3b which shows the slice through the detection probability map at fx = 2 в 10-13 erg s-1 cm-2 , just above the survey flux limit). The angular size range in which the 400d X-ray detection is sensitive encompasses the entire range of core-radii expected for the high-redshift clusters (c.f. shaded histogram in Fig. 3b). Therefore, the 400d selection will not bias the distribution of core-radii for -mo del clusters. The sensitivity of the 400d X-ray detection algorithm to co oling flow clusters with the cuspy X-ray brightness profiles requires a separate study.

Lack of "cooling flow" clusters at z > 0.5

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Fig. 4. (a) Chandra images of the 400d clusters with z > 0.5. Note a high fraction of ob jects that show clear signs of a ma jor merger. (b) Distribution of the cuspiness parameter for the z > 0.5 and z 0 samples.

This issue was addressed by a separate set of Monte-Carlo simulations in which instead of -mo dels, we used the real X-ray images of a complete sample of low-z clusters, scaled to different redshifts in the range 0.35 < z < 0.8 (see [1] for details). A short summary of the results from these simulations is that there is no significant difference in the detection efficiency for the -mo del and co oling flow clusters (see, e.g., Fig. 16 in [1]). For example, Hydra-A ( = 1.24) at z = 0.456 is detected with the probability 0.67; 2A 0335 ( = 1.26) at z = 0.45 has pdet = 0.54; A2029 ( = 0.90) at z = 0.8 has pdet = 0.69. These values are near the maximum efficiency for -mo del clusters of similar flux (Fig. 3b). Therefore, there should be no discrimination in the 400d survey against the ob jects similar to to day's co oling flow clusters.

4 Observed morphologies and cuspiness parameters of the high-redshift clusters
Chandra images of the evolution of the cluster signs of an on-going ma low-redshift sample is z > 0.5 ob jects from the 400d sample show a clear X-ray morphologies -- at least 15 of 20 ob jects shows jor merger (Fig. 4a); the corresponding fraction in the 30%. The same effect is apparent in the distribution

6 Redshifts here are chosen so that the observed fluxes would corresp ond to that in Fig. 3b, 2 в 10-13 erg s-1 cm-2 .

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of the cuspiness parameter shown in Fig. 4b. Only 3 of 20 high-z clusters have > 0.5 (i.e., above the boundary between co oling flow and non co oling clusters, see § 2), while in the low-z sample this fraction is 31 of 48 (65%). The are no clusters with > 0.7 (strong co oling flows) in the z > 0.5 sample, while the fraction of such clusters at z 0 is 46% (22 of 48 ob jects). The statistical significance of the difference in the distribution corresponds to a random fluctuation probability of only P 5 в 10-6 . Our results provide a tantalizing evidence for a strong evolution in the incidence rate of the cluster co oling flows at z > 0.5. This is apparently related to the higher cluster merging rate, indeed expected at these redshifts in the Dark Energy dominated, cold dark matter cosmological mo dels (e.g., [9]). The cluster co oling flows thus appear to be a relatively recent phenomenon, which becomes common only in the past 1/3 of the Hubble time.

References
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