{'fraction_non_alphanumeric': 0.03621283308173754, 'fraction_numerical': 0.028766728293502044, 'mean_word_length': 4.5219630982485715, 'pattern_counts': {'":': 0, '<': 9, '<?xml version=': 0, '>': 1, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 1, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 1, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A statistically-selected Chandra sample of 20 galaxy clusters -- II. Gas properties and cool-core/non-cool core bimodality

We investigate the thermodynamic and chemical structure of the intracluster medium (ICM) across a statistical sample of 20 galaxy clusters analysed with the Chandra X-ray satellite. In particular, we focus on the scaling properties of the gas density, metallicity and entropy and the comparison between clusters with and without cool cores (CCs). We find marked differences between the two categories except for the gas metallicity, which declines strongly with radius for all clusters (Z ~ r^{-0.31}), outside ~0.02 r500. The scaling of gas entropy is non-self-similar and we find clear evidence of bimodality in the distribution of logarithmic slopes of the entropy profiles. With only one exception, the steeper sloped entropy profiles are found in CC clusters whereas the flatter slope population are all non-CC clusters. We explore the role of thermal conduction in stabilizing the ICM and conclude that this mechanism alone is sufficient to balance cooling in non-CC clusters. However, CC clusters appear to form a distinct population in which heating from feedback is required in addition to conduction. Under the assumption that non-CC clusters are thermally stabilized by conduction alone, we find the distribution of Spitzer conduction suppression factors, f_c, to be log-normal, with a log (base 10) mean of -1.50+/-0.03 (i.e. f_c=0.032) and log standard deviation 0.39+/-0.02.


INTRODUCTION
The majority of baryons in collapsed massive haloes reside in a hot phase, in the form of a gaseous intracluster medium (ICM), with the remainder predominantly locked up in stars (Fukugita, Hogan & Peebles 1998;Gonzalez, Zaritsky & Zabludoff 2007). This hot gas serves as a reservoir of material to fuel not only star formation, but also black hole growth, as the ultimate endpoints of radiative cooling. Both these processes in turn give rise to feedback from subsequent supernova winds (Katz 1992;Strickland & Stevens 2000) and outbursts from active galactic nuclei (AGN; see McNamara & Nulsen 2007, for a recent review), respectively.
Given the considerable effectiveness of radiative cooling in depleting the hot gas, its dominance of the baryon budget in cluster haloes emphasizes the importance of feedback in order to restrict the excessive growth of galaxies (e.g. Cole 1991) and avoid a 'cooling crisis' (Balogh et al. 2001)-which has long plagued cosmological simulations in which the effects of non-gravitational heating are neglected (e.g. Katz & White 1993; Suginohara & Ostriker ⋆ E-mail: ajrs@star.sr.bham.ac.uk 1998). The same feedback mechanism(s) may also be responsible for arresting gas cooling in dense cluster cores (e.g. Peterson et al. 2001), where the development of a classical 'cooling flow' (Fabian 1994) appears to be truncated (Peterson & Fabian 2006).
A further indication of the importance of cooling is the discovery of short gas cooling times in the inner regions of even non-cool core clusters (Sanderson, Ponman & O'Sullivan 2006), as well as the quasi-universality of cooling time profiles across a wide range of cluster masses (Voigt & Fabian 2004;Bauer et al. 2005;Sanderson et al. 2006), despite the clear differences between the temperature profiles of cool-core and non-cool core clusters (e.g. Sanderson et al. 2006;Zhang et al. 2006;Pratt et al. 2007). The explanation for this dichotomy in the cluster population is the subject of current debate (e.g. McCarthy et al. 2008;Guo, Oh & Ruszkowski 2008), but is likely to involve galaxy feedback, given that cosmological simulations appear to overpredict the abundance of cool-cores in the cluster population (e.g. Kay et al. 2007) and that there is some question over the effectiveness of merging in permanently erasing cool cores (Poole et al. 2006). However, the lack of evidence for strong shock heating from most AGN outbursts in cluster cores (McNamara & Nulsen 2007) presents a challenge to understanding how feedback alone is sufficient to offset cooling losses.
It is clear that a more complete picture of the thermodynamic state of hot gas in clusters is needed, in order both to solve the cooling flow problem and tackle the broader issue of feedback between galaxies and the intracluster medium. In pursuing these goals it is necessary to map the thermodynamic state of the ICM across a wide mass range, including both cool core and non-cool core clusters, the latter of which are known to be under-represented in such detailed studies. This enables the gas entropy to be determined, which is a very sensitive probe of non-gravitational processes, as well the metallicity, which acts as a tracer of supernova enrichment and gas mixing. We aim to do this using Chandra observations of nearby clusters, which is the only instrument able to reliably probe core gas properties on kpc scales, where the effects of baryon physics are greatest. The basis for this investigation is the statistical sample of Sanderson et al. (2006, hereafter Paper I) comprising 20 galaxy clusters, in order to provide a representative survey of detailed cluster properties in the local universe.
Throughout this paper we adopt the following cosmological parameters: H0 = 70 km s −1 Mpc −1 , Ωm = 0.3 and ΩΛ = 0.7. Throughout our spectral analysis we have used XSPEC 11.3.2t, incorporating the solar abundance table of Grevesse & Sauval (1998), which is different from the default abundance table. Typically this results in larger Fe abundances, by a factor of ∼1.4. All errors are 1σ, unless otherwise stated.

SAMPLE SELECTION
The objects studied in this paper comprise the statistical sample of 20 galaxy clusters observed with Chandra presented in Paper I. The sample contains the 20 highest flux clusters drawn from the 63 cluster, flux-limited sample of Ikebe et al. (2002), excluding those objects with extremely large angular sizes (the Coma, Fornax and Centaurus clusters), which are difficult to observe with Chandra owing to its limited field of view. The Ikebe et al. fluxlimited sample was itself constructed from the HIFLUGS sample of , additionally selecting only those clusters lying above an absolute galactic latitude of 20 degrees and located outside of the Magellanic Clouds and the Virgo Cluster regions.

Re-analysis of Chandra data
Since the original analysis of the statistical sample data in Paper I, all but one of the Chandra observations have been reprocessed with uniform calibration by the Chandra X-ray Center (CXC) and we have reanalysed all the data accordingly. The only exception is Abell 2256 (ObsID 1386), which was observed at a frontend temperature of -110 C: thus far, only datasets observed at -120 C have been reprocessed, in order to provide a uniform calibration of most of the data in the Chandra archive 1 . Despite this, there is no indication that our results for Abell 2256 are anomalous in any way.
For the clusters Abell 401, Abell 496, Abell 1795, Abell 2142 and Abell 4038, longer observations are now available and, in the case of Abell 1795 & Abell 2142 these are with ACIS-I, giving the advantage of a wider field-of-view over the datasets analysed in Paper I. For Abell 478, however, we retain our original ACIS-S analysis (ObsID 1689) in favour of a newer ACIS-I observation, as the latter exposure is much shallower. Details of the new datasets analysed are given in Table 1 and key properties for the full sample are listed in Table 2. The data analysis and reduction were performed as detailed in Paper I, using version 3.4 of the standard software -Chandra Interactive Analysis of Observations (CIAO 2 ), incorporating CALDB version 3.4.2.

DATA ANALYSIS
Spectral fitting was performed as described in Sanderson et al. (2006), using weighted response matrix files (RMFs) generated with the CIAO task 'MKACISRMF' for all cases, except Abell 2256 -the only non-reprocessed dataset -where the older task 'MKRMF' was used instead. Spectra were fitted using an absorbed (WABS XSPEC component) APEC model over the energy range 0.5-7.0 keV for observations made with the ACIS-S detector, and 0.7-7.0 keV for those made with ACIS-I (as indicated in column 3 of Table 2). Spectra were grouped to a minimum of 20 counts per bin and fitted using the χ 2 statistic.

Cluster mean temperature and fiducial radius
Measurements of mean temperature, T , and fiducial scaling radii are very important in scaling studies, in order to permit fair a comparison of properties across a wide range of cluster mass. In Paper I we used an iterative scheme to determine both a core-excluded mean temperature and r500 (the radius enclosing a mean overdensity of 500 with respect to the critical density of the Universe), via the M − TX relation of Finoguenov et al. (2001). However, we have subsequently refined this method in the following two ways, to improve the reliability of our results. Firstly, we have adopted the newer, Chandra-derived M − TX relation of Vikhlinin et al. (2006) which is based on clusters with high quality observations, allowing direct measurements of gas properties at r500. Secondly, we have now excluded a larger central region of the data (0.15r500), to remove more completely any contaminating emission from strong central cooling that may occur in the core. Our chosen annular extraction region therefore spans the range 0.15-0.2r500; we use 0.2r500 to exclude outer regions where data incompleteness begins to affect our sample, due to the restricted Chandra field-of-view. None the less, one advantage of using an outer annulus of 0.1-0.2r500 is that it provides a better measure of any central temperature drop (within 0.1r500), as this range typically brackets the peak around the cool core radius. Therefore we retain the objective classifications of cool-core status determined in Paper I (and listed in Table 2), which were based on the significance of the temperature difference between the spectrum extracted in the range 0.1-0.2r500 compared to that measured inside 0.1r500.
The temperatures in the M − TX relation of Vikhlinin et al. (2006) were based on an aperture extending out to r500, excluding the central 70 kpc. Since cluster temperature profiles generally decline monotonically with radius outside of any cool core (e.g. Vikhlinin et al. 2005;Pratt et al. 2007), it is therefore necessary to allow for a bias factor that would shift temperature measurements within 0.2r500 higher compared to those made within r500. This was done by comparing the temperatures obtained using the iterative method of Paper I in the range 0.15-0.2r500 for 7 clusters from the sample of Vikhlinin et al. (2006) which were analysed in this work and in a companion analysis of galaxy groups (O'Sullivan et al. in prep.), namely Abell 262, 478, 1795, 2029. The aim of this process was to determine a multiplicative factor to apply uniformly to the temperatures measured in the range 0.15-0.2r500 to bring them into line with those measured in the Vikhlinin et al. aperture. The determination of this rescale factor was also iterative, and the procedure was as follows.
Firstly, a mean temperature (T ) was measured iteratively in the range 0.15-0.2r500 using the Vikhlinin et al. M − TX relation to achieve convergence for each of the 6 clusters common to both samples. Then a rescale factor was calculated as the mean ratio of these temperatures to the corresponding ones quoted in Vikhlinin et al. (2006). Secondly, the determination of T in the range 0.15-0.2r500 was repeated, using this rescale factor to adjust the measured temperature before using Equation 1 to calculate r500. The process was repeated until convergence of the rescale factor, f , whose final value was determined to be 0.96, i.e. temperatures measured in our aperture were 4 per cent hotter than those measured by Vikhlinin et al.. For a cluster of redshift, z, the radius is given by where f = 0.96 is a rescale factor to convert temperatures measured in the range 0.15-0.2r500 with those in the range 70 kpc-r500, and E(z) = (1 + z) 1 + (z Ωm) + ΩΛ (1 + z) 2 − ΩΛ . (2) A comparison between these new temperatures and those from the original Ikebe et al. (2002) parent sample is shown plotted in Fig. 1. There is slightly better agreement between our new temperatures and those of Ikebe et al. amongst the hottest clusters than was obtained using the measurements from Paper I, although the difference between this plot and figure 2 from Paper I is fairly small 3 The Ikebe et al. (2002) mean temperatures were based on a twocomponent spectral fit to the full cluster emission, which would likely result in lower T values for the hottest clusters, as pointed out in Paper I. An additional factor is a possible bias in temperature estimates for hotter clusters ( 4-5 keV) resulting from errors in the Chandra response matrix (as described in Sun et al. 2008, and references therein), which could lead to overestimates of T . Our final T values are listed in Table 2, together with the mean metallicity measured in the same aperture (see Section 4.3).
3 NB the cool-core status of the points in figure 2 of Sanderson et al. (2006) was incorrectly labelled. Although the M − TX relation of Vikhlinin et al. (2006) comprises clusters hotter than ∼2.3 keV, we none the less have verified that the masses of our cooler galaxy groups (O'Sullivan et al. in prep.) are consistent with it. Furthermore, we note that the recent Chandra study of 40 galaxy groups by Sun et al. (2008) finds only weak evidence (at the 1.5σ level) for a steepening of the M − TX relation in groups compared to clusters. This therefore justifies our inclusion of a mixture of clusters and groups in the 7 systems used to calibrate our modification of the Vikhlinin et al. M − TX relation for temperatures measured in the aperture 0.15-0.2r500.

Spectral profiles and deprojection analysis
The results which follow are based on the deprojection analysis method described in Paper I, to derive three-dimensional gas temperature and density profiles. To stablize the fitting, the Galactic absorbing column and gas metallicity were fixed at values obtained by fitting each annulus separately prior to the deprojection. Consequently, the gas metallicity results presented in Section 4.3 are projected quantities. For some clusters, it was necessary to freeze the absorbing column at the galactic HI value, since unfeasibly low values were otherwise obtained in many of the annular bins: full details can be found in Paper I. Similarly, in a number of cases the deprojected temperature had to be fixed at its projected value, to produce a stable fit, exactly as was done in Paper I. Fig. 2 shows the gas density as a function of scaled radius for the sample, colour-coded by mean temperature and split according to cool-core status. Following Sanderson et al. (2006), in order to clarify the underlying trend in each profile, the raw data points have  been fitted with a locally weighted regression in log-log space, using the task 'LOESS' in version 2.7 of the R statistical software environment package 4 (R Development Core Team 2008). It is immediately apparent from Fig. 2 that the profiles do not scale selfsimilarly, which would imply constant density at a given fraction of r500. There is a wide dispersion in the core, with a factor of ∼30 range in ρgas at 0.01r500, dropping to a factor of ∼5 spread at 0.1r500. At larger radius (beyond the peak in the temperature profile at ∼0.15r500; Paper I) there is a clear convergence in the profiles, despite the diminishing data coverage due to the limits of the Chandra field of view. It is clear from Fig. 2 that the cool-core (hereafter CC) clusters have systematically denser and more cuspy cores, consistent with the decline in gas temperature (scaling with r ∼0.4 ; Paper I) that must be counteracted by a rising density in order to maintain pressure equilibrium. The near power-law shape of the density profiles in the CC clusters is also consistent with a cooling dominated regime, as indicated by the simulations of Ettori & Brighenti (2008), who find ρgas ∝ r −1.2 for evolved cool-core clusters (after 10 Gyr). Within each cool-core category, there is also a systematic trend towards lower ICM densities in cooler systems. This may reflect gas depletion due to cooling out of the hot phase, or could be caused by non-gravitational heating expelling material out of the core. These findings are consistent with the recent study of Croston et al. (2008), based on a representative sample of 31 clusters analysed with XMM-Newton.

Gas entropy
The entropy of the gas is a key parameter, which provides a measure of the thermodynamic state of the ICM and is conserved in  Figure 2. Gas density profiles for each cluster, scaled to r 500 and coloured according to the mean cluster temperature, depicted by the inset histogram. Each curve represents a locally weighted fit to the data points, to suppress small-scale fluctuations (see the text for details).
any adiabatic process (see Bower 1997;Tozzi & Norman 2001;Voit et al. 2002, for example). We define entropy as S = kT /ρ 2/3 gas (e.g. Ponman, Cannon & Navarro 1999), which implies S ∝ kT for self-similar clusters. Within a virialized halo, the gas entropy is initially set by shock heating, which leads to a radial variation of the form S ∝ r 1.1 for a simple spherical collapse (Tozzi & Norman 2001). Despite radiative cooling in the cores of clusters lowering the entropy, its power-law variation with radius is nevertheless largely preserved, with approximately the same logarithmic slope as in the outskirts (e.g. Ettori & Brighenti 2008), leading to the expectation of a near-proportionality between entropy and physical (i.e. unscaled) radius, regardless of halo mass. This can be seen in Fig. 3 which shows gas entropy profiles as a function of radius in kpc for the sample, separated by cool-core status and colour-coded by mean temperature.
The distinction between CC and non-CC clusters is very clear from Fig. 3, with the latter having significantly higher entropy in the core and the divergence between the two types occurring within ∼40 kpc, at an entropy level of ∼80 keV cm 2 . The CC entropy profiles are tightly grouped and show no obvious sign of the transition between the shock heating regime in the outskirts and the cooling-dominated core. In contrast, the non-CC profiles show a much larger scatter in normalization, which may reflect the diversity of heating processes affecting them. Alternatively, it could be that cooling acts to regulate the entropy of CC clusters so as to suppress the scatter between them, which may also account for the apparent universality seen in the cooling time profiles of the sample (Paper I).

Entropy profile fitting
In order to characterize the form of the entropy profiles plotted in Fig. 3, we fitted power-laws to each cluster profile to quantify the logarithmic slope of the relationship. However, it can be seen from Fig. 3 that at small radii the profiles tend to flatten and therefore deviate from a simple power law form (see also Donahue et al. 2006, for example). Nevertheless, a power law provides a simple and reasonably effective description of the majority of the profile in all cases which enables the 'flatness' of the curves to be characterized. We have additionally employed a quantile regression technique to perform the fitting, in order to provide resistance to any such outliers. This form of regression minimizes the sum of absolute residuals, rather than the sum of squared residuals, and thus is analogous to determining the median as an estimator of the mean (Koenker 2005). The algorithm used is the 'RQ' function from the QUANTREG package in R 5 and was executed as an unweighted linear fit in log-log space. Table 2 lists the best-fit normalization (at 0.1r500) and power-law index (i.e. logarithmic slope) for each cluster, together with the corresponding 1σ errors.
To assess the suitability of a power law for describing the entropy profiles, we show in Fig. 4 the residuals from the best-fit model as a function of scaled radius, for each cluster. We have normalized the residuals by the predicted model values rather than the measurement errors on the entropy, since the fit was performed using unweighted quantile regression rather than by minimizing χ 2 . This approach allows for the fact that real clusters exhibit intrinsic deviations from simple radial models in excess of the statistical scatter associated with measurement errors. It can be seen that in general the power law fits do a reasonable job of describing the data, with the majority of residuals contained within ∼5 per cent of the best fit. However, while there is no obvious sign of any strong systematic trends with radius, there is some indication of an excess entropy above the model at very small radii ( 0.03r500) for a few of the clusters, consistent with the flattening in the entropy profiles of nine cool core clusters found by Donahue et al. (2006). Nevertheless, we restrict our use of the power law fits to the entropy profile to a larger radius (0.1r500), which is not affected by any such systematic departure from a power law form.
There is no evidence of any systematic variation in the logarithmic slope of the entropy profile with mean temperature across the sample, as plotted in Fig. 5. However CC and non-CC clusters are clearly segregated in the plot, occupying higher and lower values of the entropy index, respectively. The only exception is Abell 2142 -the archetypal 'cold front' cluster (Markevitch et al., 2000) -which was classified as a non-CC cluster in Paper I, as its cool core ratio was found to be only marginally significant (∼ 2σ; Paper I). Notwithstanding the cool core status of the clusters, it is reasonable to ask if there is any evidence for bimodality in the distribution of logarithmic slope values in Fig. 5, and we address this specific issue in Section 5.

Entropy scaling
The effectiveness of entropy as a probe of non-gravitational physics in the ICM is best exploited by studying its variation with mean temperature, which is expected to be linear in the case of simple self-similarity. However, the strong dependence of entropy on radius, raises the issue of at what point to measure entropy in order to consider its variation from cluster to cluster. The issue is further complicated by the fact that the gas entropy within a cluster bridges two distinct regimes: the cooling-dominated core and the outskirts, where the effects of shock-heating from infall prevail. The first measurements of entropy scaling were made at a fiducial radius of 0.1r200 (Ponman et al. 1999;Lloyd-Davies, Ponman & Canon 2000) in order to sample the region between these two regimes. However, Pratt, Arnaud & Pointecouteau (2006) find consistent results for the scaling with temperature of entropy when measured a range of radii at fractions of r200 of 0.1, 0.2, 0.3 and 0.5 in the range b = 0.5-0.6 for S ∝ T b .
Taking the power-law fits to the entropy profiles performed above we plot in Fig. 6 entropy vs. T for the sample using the normalization value, corresponding to a fiducial radius of 0.1r500. Also shown are power-law fits to the CC and non-CC clusters separately, performed in log-log space using the BCES weighted orthogonal regression method of Akritas & Bershady (1996). The logarithmic slopes of these lines correspond to an entropy scaling of the form S ∝ T b with b = 0.66 ± 0.10 and 0.71 ± 0.21 for the CC and non-CC clusters, respectively. These results are in good agreement with the value of 0.65 ± 0.05 similarly determined by Ponman, Sanderson & Finoguenov (2003), at a fiducial radius of 0.1r200, as well as with the values found by Pratt et al. (2006) at a series of radii and using a number of regression methods. The CC and non-CC points are generally well separated with respect to their corresponding best-fit power laws in Fig. 6. However, in the case of the CC cluster Abell 262, the (albeit large) error bar overlaps significantly with the non-CC best-fit line. While this poor cluster does have a strong negative central temperature gradient, it is also known to possess a number of cavity and ripple features coincident with low frequency radio emission (Blanton et al. 2004). It is therefore possible that AGN activity in the core might have boosted the entropy at 0.1r500 to shift this cluster towards the non-CC regression line. Nevertheless, a number of the other CC clusters also host ghost cavities (see table 2 in Paper I), which evidently have not significantly biased their location in Fig. 6. While the separate fits to the CC and non-CC clusters in Fig. 6 yields results consistent with a non-self similar entropy scaling, the two sets of points are clearly offset from each other. It is interesting to note that a BCES orthogonal regression fit to all the 20 clusters combined yields a much steeper logarithmic slope of 0.92 ± 0.12, which is consistent with self-similar scaling. To check this result, we repeated the individual power-law fits using a pivot-point of 0.15r500, and performed the same regression of the normalization versus mean temperature to obtain the following logarithmic slopes: 1.06 ± 0.16 (all clusters combined) 0.65 ± 0.10 (CC) 0.65 ± 0.26 (non-CC).
Thus it is possible that similarity breaking can occur in the separate CC/non-CC cluster sub-populations in such a way as to produce fully self-similar scaling in an analysis which combines the two types. On the other hand, if we exclude the coolest system (NGC 5044) from the fit, the resulting best-fit slope for the whole sample (0.89 ± 0.22) is consistent at the 1σ level with the values obtained for the separate CC and non-CC sub-samples.
Given the broad agreement in the dependence on temperature of the entropy scaling, we show in Fig. 7 entropy profiles as a function of r / r500 normalized by the factor T 0.65 from Ponman et al. (2003). It can be seen that this empirical scaling brings the curves into fairly close alignment. There is, however, some indication of a systematic dispersion in the profiles, indicating that gas entropy may vary less strongly with cluster mean temperature than T 0.65 , as also suggested by the results of Pratt et al. (2006) when measuring entropy at 0.1r200. In order to explore the entropy scaling across a range of radii, rather than at at particular spot value, we modelled the variation of entropy in terms of both scaled radius and mean temperature using the following expression:

Sample
S ′ ( keV cm 2 ) a b ( This parametrization has the advantage of allowing the scaling of entropy with both radius and temperature to be determined simultaneously. The results of performing an unweighted quantile regression fit in log-log space of Equation 3 to the entire sample are summarised in Table 3. Only data in the range 0.02 < r/r500 < 0.2 were included, to ensure completeness in the radial coverage. The resulting values of a agree well with the results from the individual power law fits to each cluster described previously, in Section 4.2.1. It can also be seen that the fit to the entire sample yields a dependency on mean temperature such that S ∝ T b , with b = 0.56 +0.11 −0.08 slightly lower but still in agreement with the scaling of T 0.65±0.05 found by Ponman et al. (2003), which was evaluated at a radius of 0.1r200 -roughly 0.15r500 . A fit to the combined CC and non-CC clusters separately yields values of b = 0.49 +0.07 −0.13 and b = 0.52 +0.08 −0.07 , respectively, demonstrating that this weaker dependence of entropy on system temperature persists. This result is strongly inconsistent with a selfsimilar scaling of S ∝ T (i.e. b = 1) demonstrating the impact of non-gravitational physics in influencing the hot gas (see Ponman et al. 2003, for example, for further discussion), but extends beyond the finding of Ponman et al. in that it applies across a range of radii spanning an order of magnitude, as opposed to being determined at only a fixed spot value. Furthermore, the fact that this result is essentially unchanged when fitting the CC and non-CC clusters separately (see Table 3), demonstrates the uni- versality of this modified entropy scaling, at least in the range 0.02 < r/r500 < 0.2. However, the difference between CC and non-CC clusters is very clear when considering the variation of entropy with radius, S ∝ r a . Here the corresponding logarithmic slopes are a = 1.05 +0.07 −0.15 and 0.51 +0.09 −0.06 , respectively, compared to 0.95 +0.10 −0.08 for the entire sample. The flatness of the best-fit non-CC entropy profile compared to that for the CC clusters is further underscored by the difference in normalization at the fiducial 'pivot point' in Equation 3 (at 0.1r500 for T = 5 keV), yielding values of S ′ = 259 +6 −4 keV cm 2 compared to 161 +7 −10 keV cm 2 , respectively. The results from the combined fit of Equation 3 are in good agreement with the results from the power-law fits to the individual cluster entropy profiles. They are also consistent with the logarithmic slope of 0.95±0.02 (Piffaretti et al. 2005) and 1.08±0.04 (Pratt et al. 2006) from two separate XMM-Newton analyses of cool-core clusters, as well as the values of slopes in the range 1-1.3 from the Chandra analysis of 9 CC clusters by Donahue et al. (2006).

Metallicity of the ICM
The metallicity of the ICM is an important tracer of galaxy feedback via supernova-driven winds, which eject both metals and energy into the hot gas (e.g. Strickland & Stevens 2000). Fig. 8 shows the mean metallicity against mean temperature for the sample (see Table 2), both evaluated in the range 0.15 r/r500 0.2, identified according to cool-core status. There is no indication of any trend in the data or of any systematic difference between CC and non-CC clusters; the mean value across the entire sample is 0.55 Solar, with a standard deviation of 0.22.
To explore radial trends we use the metallicity values determined in the projected annular spectral fitting, which were taken as fixed inputs in the deprojection analysis as described in Section 3.2 and Paper I. The fact that these values are not deprojected will tend to smooth out gradients slightly. However, Rasmussen & Ponman (2007) demonstrate that this is a small effect and that deprojected metallicity data typically suffer from large instabilities which add significantly to the noise, particularly given the poorer constraints on this parameter compared to temperature or density. Fig. 9 shows the individual projected metallicity profiles as a function of scaled radius for the sample, split by cool-core status and colour-coded by mean temperature. The curves represent a locally-weighted fit to the data, using the LOESS function described in Section 4.1 and it can clearly be seen that the metallicity declines with radius beyond ∼0.01-0.02r500 in almost every case, for both CC and non-CC clusters. Within this radius the dispersion in metallicity increases noticeably; some clusters show a strongly peaked metallicity profile (in particular Abell 85 and Abell 2029), whereas others have metal-deficient central cores. More specifically, the three most peaked profiles are all hot clusters, whereas the coolest clusters show sharp central declines. It is not clear what is responsible for this strong divergence in behaviour, but it occurs on a scale of roughly 0.02r500 (∼20-30 kpc), which is comparable to the size of the central galaxy. This also coincides with the region where the gas density and entropy profiles also become widely dispersed (Figs. 2 and 7).
Regardless of any difference between CC and non-CC clusters at small radii, it is clear that the point where the metallicity begins to decline strongly towards the cluster outskirts lies well within the typical cooling radius of ∼0.15r500 (Paper I). The fact that the metallicity profiles of all the clusters are quite similar beyond this point suggests that the enrichment of the ICM is insensitive to those factors responsible for determining coolcore status. The finding that metallicity declines strongly with radius in all the clusters is apparently at odds with the study of De Grandi & Molendi (2001), who concluded that the abundance profiles for the 8 non-CC clusters in their BeppoSAX sample were consistent with being constant. However, examination of figure 2 from De Grandi & Molendi (2001) shows that, with the exception of only a few outliers, there is an indication of a general decline in metallicity with increasing radius in their non-CC clusters. Furthermore, we note that Baldi et al. (2007) also found no difference between CC and non-CC gas metallicity profiles, outside ∼0.1r180 in their analysis of 12 hot clusters observed with Chandra.
To highlight the trend in metallicity with radius we show the mean CC and non-CC profiles in Fig. 10, grouped to a total of 5 bins in each case, with error bars indicating the standard deviation within each bin. Apart from a slightly larger dispersion in the non-CC bins, there is very little difference between the two profiles and no indication in either case of any flattening off at large radii. Interestingly, the BeppoSAX average CC profile of De Grandi et al. (2004) shows a sharp levelling off in metallicity at around 0.4 Solar (Grevesse & Sauval 1998, abundances) at 0.2r200, which corresponds to roughly 0.3r500 -close to the limit of our Chandra data but otherwise consistent with the outer bin of Fig. 10, so we cannot rule out a flattening beyond this point. However, in contrast, the De Grandi et al. (2004) non-CC profile is both flatter and lower in normalization (albeit only at ∼2σ) and thus rather different from our own. Of their 10 non-CC clusters, only three are present in our sample (A1367, A2256 and A3266; they classifiy A2142 and A3571 as CC clusters), and their profiles for these systems appear to be reasonably consistent with our own, within the region covered by Chandra. The differences between CC and non-CC clusters seen by De Grandi et al. (2004) appear to originate in the somewhat low and fairly flat abundance profiles of several non-CC clusters in their sample, whereas the non-CC clusters in our sample don't appear to include such cases. Notwithstanding this difference in samples, we note that Baldi et al. (2007) measure a similar radial decline to us, with essentially no difference between CC and non-CC clusters, albeit with the exception of their central bin. As mentioned above, cluster metallicity profiles appear to exhibit greater dispersion on the scale of the central galaxy, so some difference from sample to sample is to be expected in this region.
The data in Fig. 10 appear to be reasonably consistent with a power law, so we have fitted such a function in log-log space, using the quantile regression method outlined in Section 4.2.1. In order to exclude the core region where the profile flattens and the profile diverge substantially (r ∼ 0.014r500; Fig. 9), we performed separate fits inside and outside this radius, combining both the CC and non-CC data. The results for the inner region (r < 0.014r500) are By comparison, the metallicity profiles of galaxy groups appear to be somewhat steeper in their decline at large radii. The recent analysis of 15 groups with Chandra data by Rasmussen & Ponman (2007)-also using Grevesse & Sauval (1998) abundances-found logarithmic slopes of -0.66 ± 0.05 and -0.44 for the combined radial profiles of iron and silicon, respectively, across their sample, compared to our slope of -0.31 +0.03 −0.05 for the mean metallicity (see Fig. 10). At a radius of r500, Rasmussen & Ponman estimate an average iron abundance in groups to be ∼0.1, whereas the extrapolation of the above best fit implies a mean metallicity of Z ∼ 0.15 in clusters at the same radius.
The similar abundance patterns between CC and non-CC clusters can be seen by examining the gas metallicity as a function of entropy, plotted in Fig. 11. Also plotted are locally-weighted curves for the combined points in each category, which demonstrate that there is very little difference between them, aside from the greater radial coverage in the centres of CC clusters. Since the gas entropy scales roughly linearly with radius (Fig. 3), the trend between metallicity and entropy mimics that seen in Fig. 9. However, a striking aspect of Fig. 11 is the almost complete absence of low-metallicity gas (i.e. < 0.4-0.5 Solar) with low entropy (S < 200 keV cm 2 ). In general it appears that the most enriched gas has low entropy, although the smoothed local regression suggests a turnover in this trend towards lower metallicity below ∼30 keV cm 2 . Interestingly, this entropy level corresponds to the threshold below which star formation appears to take place in the central galaxies of CC clusters Rafferty, McNamara & Nulsen 2008). Thus, a reversal of the inverse trend between entropy and metallicity may reflect the loss of the most enriched gas from the hot phase in fuelling such star formation.

CLUSTER BIMODALITY AND THERMAL CONDUCTION
Clusters can be divided according to the presence or absence of a cool core, and it is clear that the properties of these two categories differ substantially in terms of their temperature, density and entropy profiles. However, an important question to ask is, are these two types merely separate parts of the same continuous distribution, or do they really constitute distinct populations? If the latter holds true, then this would have interesting implications for models of self-similarity breaking via feedback and/or other non-gravitational processes.
To address this issue, we return to the power-law fits to the entropy profiles described in Section 4.2.1. The probability distribution of logarithmic slopes is plotted as a kernel density estimate in Fig. 12, with the positions of the raw values also indicated. It can be seen that two peaks are visible in the distribution, suggestive of bimodality in the cluster population. We performed a maximum likelihood fit to the unbinned entropy slope values with both a single and a pair of (equally-weighted) Gaussians, using the FIT-DISTR function in the MASS package in R. The single Gaussian best-fit mean value was µ = 0.70 ± 0.05 with standard deviation of σ = 0.25 ± 0.04, and the best fit double-Gaussian values were: µ1 = 0.48 ± 0.04 σ1 = 0.10 ± 0.03 µ2 = 0.92 ± 0.04 σ2 = 0.11 ± 0.03.
The two separate Gaussians are plotted as dashed curves in Fig. 12 and align closely with the peaks in the smoothed density distribution; the cross-over point between these two Gaussians is 0.69 and is plotted as the dashed horizontal line in Fig. 5.
In order to provide a quantitative assessment of the putative bimodality in the population, we calculated both the Akaike information criterion (AIC, Akaike 1974) and the Bayesian information criterion (BIC, Schwarz 1978). These are standard statistics used in model selection (e.g. see Liddle 2007, for a discussion of their relative merits), based on the negative log-likelihood penalised according to the number of free parameters, with the model having the lowest value always being preferred. The corresponding values obtained are AIC = 4.65 (-0.49) and BIC = 6.64 (3.49) for the single (double) Gaussian model, implying a change in BIC of 4.0 in favour of the two component fit. Differences in BIC of between 2 and 6 indicate positive evidence against the model with the greater BIC value, with values above 6 indicating strong evidence against the model with the greater BIC value (e.g. Mukherjee et al. 1998), demonstrating that a bimodal distribution is clearly favoured over a unimodal distribution. Given that the sample was statistically selected, this therefore implies that two distinct categories of cluster exist.
The two separate distributions of entropy profile logarithmic slopes match the cool-core classification (with the exception of Abell 2142; see Section 4.2.1), show similar dispersion (σ ∼ 0.1) and are well-separated (the means differ by ∼4 standard deviations). The means of the distributions are also in good agreement with the results obtained by fitting Equation 3 to the CC and non-CC clusters separately, as summarised in table 3.
While a power law fit describes the entropy profiles of CC clusters quite well, it can be seen from Fig. 7 that the non-CC profiles appear to flatten increasingly at small radii. This raises the possibility that estimating the gradient from a power law fit (albeit robustly) could bias the results. Therefore, to check our conclusions regarding bimodality, we have also evaluated the entropy profile logarithmic slope at 0.05r500 as estimated from a locallyweighted fit to the data (in log-log space), using the LOESS task in R (c.f. Fig. 7), with a heavier smoothing (using a value of the 'span' parameter of 2), to increase the stability of the gradient measurements. Repeating the above analysis leads to best fit bimodal populations, given by µ1 ′ = 0.26 ± 0.09 σ1 ′ = 0.28 ± 0.07 µ2 ′ = 0.97 ± 0.03 σ2 ′ = 0.08 ± 0.02.
The corresponding values obtained are AIC = 25.4 (18.4) and BIC = 27.4 (22.4) for the single (double) Gaussian model, implying a change in BIC of 5.0 in favour of the two component fit. It can be seen that the non-CC slope is indeed flatter at this smaller radius (although with much greater dispersion), but that the conclusion that the population is bimodal is verified.

Conduction and thermal balance
One of the most intriguing aspects of the ICM is its resistance to runaway radiative cooling. Although galaxy feedback is a plausible mechanism for maintaining (or nearly maintaining) thermal balance in the centres of cool-core clusters, it is less clear if it can similarly affect non-CC clusters, which none the less also have short cooling times in their inner regions (Paper I). This is because non-CC clusters show no sign of mass drop-out necessary to fuel AGN outbursts or supernova winds. However, heat transport by thermal conduction is likely to play an important role in such cases and is also very effective at stabilizing cooling within CC regions, provided the gas density is not too high (e.g. Conroy & Ostriker 2008;Guo et al. 2008).
Circumstantial evidence for the effectiveness of thermal conduction in counteracting cooling can be seen in the temperature profiles of CC clusters. As pointed out by Voigt et al. (2002), cool cores at the limit of stablization by conduction would have temperature gradients of the form T ∝ r 0.4 in the case of bremsstrahlung emission, flattening to T ∝ r 0.3 for line-dominated emission, which concurs well with observations of CC clusters (Paper I) and groups (O'Sullivan et al. in prep.), respectively. Furthermore, recent work by Voit et al. (2008) and Rafferty et al. (2008) indicates that star formation in the cores of clusters, resulting from unchecked cooling, only occurs when the gas entropy drops below a certain level ( 30 keV cm 2 ) which matches the threshold below which gas becomes thermally unstable against conduction.
The critical scale for thermal conduction is given by the Field length, which must exceed the characteristic size of the system in order to allow thermal balance to be maintained by smoothing out temperature fluctuations (Field 1965 Figure 13. Implied Spitzer conductivity suppression factor as a function of scaled radius, grouped by cool-core type and plotted with identical axes. Each curve represents a locally weighted fit to the data points, to suppress small-scale fluctuations (see the text for details). λF = κT ρ 2 gas Λ 1/2 ≈ 4 kpc S 10 keV cm 2 where κ is the Spitzer conduction coefficient with suppression factor fc. This relation applies for the case of bremsstrahlung emission, where the cooling function varies with temperature, T , such that Λ ∝ T 1/2 , which renders λF a function of entropy only (Donahue et al. 2005).
In the limit of conductive thermal balance, where r = λF, Equation 4 can be rearranged to yield an expression for the corresponding implied suppression factor: in terms of the radius, r (in kpc) and the entropy, S (in keV cm 2 ). The variation of this quantity with scaled radius is plotted for each cluster in Fig. 13, smoothed using the LOESS function in R and split by cool core status. Also shown is the threshold of thermal stability, corresponding to conduction at the Spitzer rate, when fc = 1. The striking aspect of Fig. 13 is the clear difference between the profiles of CC and non-CC clusters, in terms of both their shapes and locations on the plot: CC clusters having higher normalization and largely negative gradients compared to non-CC profiles, which all lie well within the conductively stable region with mostly positive gradients. Once again, the outlier cluster Abell 2142 (as seen in Fig. 5) stands out as an anomaly (the only non-CC curve aligned from bottom right to top left), which nevertheless retains similarities to both categories in that it lies within the range of the non-CC profiles while bearing closer resemblance to the CC profiles in shape.
The implication of Fig. 13 is that non-CC clusters are certainly capable of being stablilized by conduction alone, operating at no more than ∼10 per cent of the Spitzer rate and even much less effectively than that within their inner regions. By contrast, the CC clusters require values of fc 0.1 within the peak temperature radius (∼ 0.15r500; Paper I), rising sharply towards the centre and in some cases crossing into the region of thermal instability, corresponding to fc > 1 (for NGC 5044, Abell 262, Abell 478, Abell 496 and 2A 0335+096). For these five clusters, an additional heat source would be required in order to maintain thermal balance. With the exception of A478, these are 4 of the 5 coolest CC clusters (see Table 2), which is unsurprising, since thermal conduction operates much less effectively at lower temperatures as the Spitzer conductivity, κ ∝ T 5/2 . Furthermore, all except Abell 496 show evidence of AGN-related disturbance in the form of X-ray cavities (Bîrzan et al. 2004) and both X-ray and radio disturbance in the case of NGC 5044 (David et al, in prep.). These results are in agreement with the findings of Voigt & Fabian (2004), who studied four of the same clusters: for Abell 2029 & Abell 1795 they also concluded that conductivity at or below the Spitzer level was able to balance cooling everywhere inside the cooling radius, whereas this was not the case for Abell 478 and 2A 0335+096.
Theoretical considerations indicate that magnetohydrodynamic turbulence in the ICM could give rise to conduction suppression factors of ∼0.2 (Narayan & Medvedev 2001), which is also consistent with results from the direct numerical simulations of Maron, Chandran & Blackman (2004), who favour fc ∼ 0.1-0.2. This would imply conductive stability for the non-CC clusters at all radii and for all CC clusters outside ∼0.05-0.1r500 (Fig. 13). Taking all the fc values for the non-CC clusters, we find the spread of values to be well fitted by lognormal distribution with a mean log (base 10) of −1.50±0.03 and log standard deviation of 0.39±0.02 corresponding to 0.032 with a 1σ range of 0.013-0.077.
Why, though, should a threshold for conduction stability give rise to a well-separated bimodal distribution of clusters, with a 'zone of avoidance' in between? Donahue et al. (2005) point out that clusters exceeding the threshold for conductive stability will continue to cool until some other form of heating intervenes, which would therefore lead to diverging populations. In which case, the fact that the non-CC fc profiles are themselves not flat suggests that this threshold is spatially varying. Since the likely dominant cause of conduction suppression is magnetic fields, it follows that the configuration of magnetic field lines varies significatly with radius. Consequently, it is possible that the variation of fc profiles amongst the non-CC clusters reflects the intrinsic variation in intracluster magnetic field configurations in the cluster population. In any case, the non-CC fc profiles (except for A2142) all drop sharply inside ∼0.1r500, reaching values within the typical scale of the central cluster galaxy (∼0.02r500) consistent with the higher suppression factors of 0.01 present in the interstellar medium of cluster galaxy coronae (Sun et al. 2007). This indicates that the transition within the ICM to higher suppression factors on galaxy scales may occur smoothly, suggesting a gradual variation in magnetic fields.
By contrast, the presence of cold fronts in the ICM implies sharply discontinuous magnetic fields, especially considering that such features occur at larger cluster radii, where fc is greater. For example, in the case of Abell 2142, detailed analysis of the temperature gradient across the cold front indicates that conduction must be suppressed by at a factor of 250-2500 (Ettori & Fabian 2000), which is certainly far below the levels implied in Fig. 13, although these amount to globally-averaged estimates. Such discontinuous configurations are possible in this case, since the magnetic field is likely to be stretched by tangental gas motions near the cold front, making it stronger and changing its structure compared to the rest of the ICM (Vikhlinin, Markevitch & Murray 2001).
A notable feature of Fig. 13 is the absence of any substantially flat profiles, in between the strongly negative gradients of the CC clusters and the mostly strongly positive (except for A2142) gradients of the non-CC clusters. A flat profile, lying along the conduction-stabilized threshold with a constant value of fc 1, would imply an entropy profile of the form S ∝ r 2/3 (Donahue et al. 2005), which is close to the cross-over point of 0.69 between the two distributions of entropy profile logartithic slopes found in Section 5 (also plotted as the dashed horizontal line in Fig. 5). Thus the divergence between CC and non-CC profiles seen in Fig. 13 mirrors the bimodality seen in the slopes of the entropy profiles described above.

DISCUSSION
The above results clearly indicate that bimodality is present in the cluster population, structured along the dichotomy between cool core and non-cool core clusters. Furthermore, the implication is that thermal conduction alone is a plausible mechanism for stabilizing the intracluster medium in non-CC clusters, whereas additional heating from galaxy feedback is necessary to achieve the same in CC clusters-a conclusion also reached by Guo et al. (2008). Conductive heat transfer could certainly explain why no significant temperature decline is observed in non-CC clusters, despite the short cooling times of gas in their cores (Paper I). However, by contributing to the heating of the cluster core, conduction also acts to reduce the amount of energy input required from additional sources such as AGN, in order to maintain thermal stability. This may therefore account for the observed lack of evidence for strong AGN heating in clusters (McNamara & Nulsen 2007).
Nevertheless, while feedback heating may not be necessary to stabilize non-CC clusters, it is clear from the results of the entropytemperature scaling analysis in Section 4.2.2 that both CC and non-CC clusters show significant departures from self-similarity. Such similarity breaking is the unmistakable signature of nongravitational physics, which suggests that the non-CC clusters must also have been impacted significantly by feedback (if not also radiative cooling) in their lifetimes. This possibility is consistent with the theoretical model of McCarthy et al. (2008), where non-CC clusters are formed from material that has experienced higher levels of preheating. In this picture, the influence of conduction could help to segregate the cluster population and stave off the formation of cool cores in the most strongly preheated systems.
A related aspect is the role of mergers in cluster evolution, particularly given the close association between signatures of recent disruption, such as radio halos, and the absence of a cool core (e.g. Million & Allen 2008). Although suggesting a key role for thermal conduction in sustaining non-CC clusters, our results nevertheless certainly do not rule out merging as an alternative explanation for their existence. While recent simulations have concluded that cluster mergers cannot permanently erase cool cores (Poole et al. 2006), it is possible that the additional influence of conduction could achieve this outcome and thereby provide an alternative path to a non-CC state. In this situation, the temporary fragmentation of a cool core that can take place in a merger (Poole et al. 2008) could plausibly lead to conductive dissipation of the resulting blobs of cool gas, whose size can easily fall below the Field length, provided the magnetic field configuration is favourable. Since conduction lowers the threshold necessary to transition from a state where additional feedback is required (i.e. in a cool core), to one where conduction alone can maintain stability (i.e. a non-cool core), the transformation from CC to non-CC status is correspondingly more achievable.
However, notwithstanding this appealing explanation of bi-modal populations, it is also clear that the key role that conduction can play in stabilizing clusters against cooling instabilities cannot easily extend to galaxy groups, where the lower gas temperatures render it much less effective (the conduction coefficient, κ ∝ T 5/2 ). Therefore, the impact of merging activity may be more short lived in galaxy groups, without the contribution of significant conductive heat transfer to impede re-formation of a cool core. This suggests that non-cool core groups are likely to have been recently disrupted; by contrast, conduction in clusters could sustain a non-CC state in post mergers long after disruption. Nevertheless, it remains to be seen whether a consistent thermodynamic picture of ICM evolution in both groups and clusters can be developed. The similarity of the ICM metallicity in CC and non-CC clusters is noteworthy as the only property of the gas that does not differ significantly between the two types, at least within the region of overlap seen in this sample. This fact alone provides evidence that strong mixing of gas cannot preferentially have affected non-CC clusters-as a result of merging activity, for example. However, the width of the metallicity peak in the cluster cores appears significantly ( 2×) broader than the stellar distribution of the brightest cluster galaxy (BCG), as previously noted by Rebusco et al. (2005), which implies some mechanism to transport metals into the ICM. Rebusco et al. speculate that this might be caused by AGN-driven gas motion, as also favoured by the recent theoretical modelling of Rasera et al. (2008). However, if AGN are responsible for diffusing the enriched gas then the similarity of cluster metallicity profiles implies an equally prominent role for AGN outflows in non-CC clusters, despite the lack of evidence for significant AGN disruption in such cases.

CONCLUSIONS
Using the statistically-selected sample of 20 galaxy clusters presented in Sanderson et al. (2006), we have studied the density, entropy and metallicity of the intracluster medium as a function of radius, focussing on the comparison between clusters with coolcores (CC) and those without. We describe an improved method of estimating the cluster mean temperature and fiducial scaling radius r500, which we use to explore systematic trends in cluster gas properties across the sample.
We find that the gas density is systematically higher in the cores of CC clusters, and that the ICM is progressively depleted in less massive systems. We also find a clear departure from selfsimilar scaling in the gas entropy which is consistent with the modified scaling of S ∝ T b with b = 0.65 from Ponman et al. (2003): at 0.1r500 the best-fit scaling is b = 0.66 ± 0.10 and 0.71 ± 0.21 for CC and non-CC clusters, respectively. However, the dependency on temperature strenghens when all the clusters are combined, to a nearly self similar value of b = 0.92 ± 0.12, and similar results are obtained in all three cases for entropy measured at 0.15r500 versus mean temperature. This demonstrates that similarity breaking (i.e. S ∝ T ∼2/3 ) can exist in the separate populations of CC and non-CC clusters, even while the combined population shows consistency with self-similarity.
The metallicity of the gas shows no evidence of a systematic variation with T , but declines with radius such that Z ∝ r −0.31±0.04 outside 0.014r500 (comparable to the size of any central dominant galaxy), for both CC and non-CC clusters alike. Inside this point there is substantial divergence in the metallicity, with a few CC clusters showing sharply decreasing Z towards the centre while others possess continually rising profiles. At large radii, there is no indication of any flattening in the metallicity profile to at least ∼0.5r500, where the Chandra field-of-view limits the data. We study gas metallicity as a function of entropy and find a striking lack of low-metallicity gas (i.e. < 0.4-0.5 Solar) with low entropy (S < 200 keV cm 2 ). Above ∼100 keV cm 2 the metallicity declines with increasing entropy in an identical fashion for both CC and non-CC clusters.
We address the issue of bimodality in cluster properties by studing the distribution of logarithmic slopes obtained from powerlaw fits to individual cluster entropy profiles (i.e. S ∝ r a ). We find that a double-Gaussian distribution is strongly preferred over a unimodal Gaussian distribution, using maximum likelihood fits to the unbinned values, employing both the Bayesian and Akaike Information Criteria model selection tests. The best fitting means of the two distributions are a = 0.92 ± 0.04 and 0.48 ± 0.04, with a standard deviations of 0.1 in both cases. Given the statistically selected nature of the sample, this demonstrates that two distinct categories of cluster exist, which has important implications for models of galaxy feedback and cluster similarity breaking.
We explore the impact of thermal conduction on the ICM by studying the implied conduction suppression factor, fc, as a function of radius. We find that the profiles of fc differ sharply between CC and non-CC clusters consistent with two distinct populations. We conclude that conduction alone is capable of stabilizing non-CC clusters against catastrophic cooling, while in CC clusters some feedback is required in addition to conduction to maintain thermal balance, in agreement with the findings of Guo et al. (2008). Taking all the fc values for the non-CC clusters, we find the spread of values to be well fitted by lognormal distribution with a mean log (base 10) of −1.50±0.03 and log standard deviation of 0.39±0.02 corresponding to 0.032 with a 1σ range of 0.013-0.077.