PICACS: self-consistent modelling of galaxy cluster scaling relations

In this paper, we introduce PICACS, a physically-motivated, internally consistent model of scaling relations between galaxy cluster masses and their observable properties. This model can be used to constrain simultaneously the form, scatter (including its covariance) and evolution of the scaling relations, as well as the masses of the individual clusters. In this framework, scaling relations between observables (such as that between X-ray luminosity and temperature) are modelled explicitly in terms of the fundamental mass-observable scaling relations, and so are fully constrained without being fit directly. We apply the PICACS model to two observational datasets, and show that it performs as well as traditional regression methods for simply measuring individual scaling relation parameters, but reveals additional information on the processes that shape the relations while providing self-consistent mass constraints. Our analysis suggests that the observed combination of slopes of the scaling relations can be described by a deficit of gas in low-mass clusters that is compensated for by elevated gas temperatures, such that the total thermal energy of the gas in a cluster of given mass remains close to self-similar expectations. This is interpreted as the result of AGN feedback removing low entropy gas from low mass systems, while heating the remaining gas. We deconstruct the luminosity-temperature (LT) relation and show that its steepening compared to self-similar expectations can be explained solely by this combination of gas depletion and heating in low mass systems, without any additional contribution from a mass dependence of the gas structure. Finally, we demonstrate that a self-consistent analysis of the scaling relations leads to an expectation of self-similar evolution of the LT relation that is significantly weaker than is commonly assumed.Comment: Updated to match published version. Improvements to presentation of results, and treatment of scatter and covariance. Main conclusions unchange

The Lx-Yx Relation: Using Galaxy Cluster X-Ray Luminosity as a Robust, Low Scatter Mass Proxy

We use a sample of 115 galaxy clusters at 0.1<z<1.3 observed with Chandra ACIS-I to investigate the relation between luminosity and Yx (the product of gas mass and temperature). The scatter in the relation is dominated by cluster cores, and a tight LY relation (11% intrinsic scatter in Lx) is recovered if sufficiently large core regions (0.15R500) are excluded. The intrinsic scatter is well described by a lognormal distribution and the relations are consistent for relaxed and disturbed/merging clusters. We investigate the LY relation in low-quality data (e.g. for clusters detected in X-ray survey data) by estimating Lx from soft band count rates, and find that the scatter increases somewhat to 21%. We confirm the tight correlation between Yx and mass and the self-similar evolution of that scaling relation out to z=0.6 for a subset of clusters in our sample with mass estimates from the literature. This is used to estimate masses for the entire sample and hence measure the LM relation. We find that the scatter in the LM relation is much lower than previous estimates, due to the full removal of cluster cores and more robust mass estimates. For high-redshift clusters the scatter in the LM relation remains low if cluster cores are not excluded. These results suggest that cluster masses can be reliably estimated from simple luminosity measurements in low quality data where direct mass estimates, or measurements of Yx are not possible. This has important applications in the estimation of cosmological parameters from X-ray cluster surveys.Comment: 11 pages, 8 figures. ApJ in press. Replaced to match published version. Added new section testing the Yx-M relation for clusters with masses in literature. Scaling relation parameters are updated to reflect updates to the cluster sample. Conclusions unchange

The evolution of the cluster X-ray scaling relations in the WARPS sample at 0.6<z<1.0

The X-ray properties of a sample of 11 high-redshift (0.6<z<1.0) clusters observed with Chandra and/or XMM are used to investigate the evolution of the cluster scaling relations. The observed evolution of the L-T and M-L relations is consistent with simple self-similar predictions, in which the properties of clusters reflect the properties of the universe at their redshift of observation. When the systematic effect of assuming isothermality on the derived masses of the high-redshift clusters is taken into account, the high-redshift M-T and Mgas-T relations are also consistent with self-similar evolution. Under the assumption that the model of self-similar evolution is correct and that the local systems formed via a single spherical collapse, the high-redshift L-T relation is consistent with the high-z clusters having formed at a significantly higher redshift than the local systems. The data are also consistent with the more realistic scenario of clusters forming via the continuous accretion of material. The slope of the L-T relation at high-redshift (B=3.29+/-0.38) is consistent with the local relation, and significantly steeper then the self-similar prediction of B=2. This suggests that the non-gravitational processes causing the steepening occurred at z>1 or in the early stages of the clusters' formation, prior to their observation. The properties of the intra-cluster medium at high-redshift are found to be similar to those in the local universe. The mean surface-brightness profile slope for the sample is 0.66+/-0.05, the mean gas mass fractions within R2500 and R200 are 0.073+/-0.010 and 0.12+/-0.02 respectively, and the mean metallicity of the sample is 0.28+/-0.16 solar.Comment: 23 pages, 17 figures. Accepted for publication in MNRAS. Revised to match accepted version: reanalysed data with latest calibrations, several minor changes. Conclusions unchange

Images, structural properties and metal abundances of galaxy clusters observed with Chandra ACIS-I at 0.1<z<1.3

We have assembled a sample of 115 galaxy clusters at 0.1<z<1.3 with archived Chandra ACIS-I observations. We present X-ray images of the clusters and make available region files containing contours of the smoothed X-ray emission. The structural properties of the clusters were investigated and we found a significant absence of relaxed clusters (as determined by centroid shift measurements) at z>0.5. The slope of the surface brightness profiles at large radii were steeper on average by 15% than the slope obtained by fitting a simple beta-model to the emission. This slope was also found to be correlated with cluster temperature, with some indication that the correlation is weaker for the clusters at z>0.5. We measured the mean metal abundance of the cluster gas as a function of redshift and found significant evolution, with the abundances dropping by 50% between z=0.1 and z~1. This evolution was still present (although less significant) when the cluster cores were excluded from the abundance measurements, indicating that the evolution is not solely due to the disappearance of relaxed, cool core clusters (which are known to have enhanced core metal abundances) from the population at z>0.5.Comment: 23 pages, 12 figures. Accepted for publication in ApJS. Updated to match published version. Redshifts of two clusters (RXJ1701 and CL0848) corrected and two observations of MACSJ0744.8 have been combined into one. Conclusions unchanged. A version with images of all of the clusters is available at http://hea-www.harvard.edu/~bmaughan/clusters.htm

The WARPS Survey. VIII. Evolution of the Galaxy Cluster X-ray Luminosity Function

We present measurements of the galaxy cluster X-ray Luminosity Function (XLF) from the Wide Angle ROSAT Pointed Survey (WARPS) and quantify its evolution. WARPS is a serendipitous survey of the central region of ROSAT pointed observations and was carried out in two phases (WARPS-I and WARPS-II). The results here are based on a final sample of 124 clusters, complete above a flux limit of 6.5 10E-15 erg/s/cm2, with members out to redshift z ~ 1.05, and a sky coverage of 70.9 deg2. We find significant evidence for negative evolution of the XLF, which complements the majority of X-ray cluster surveys. To quantify the suggested evolution, we perform a maximum likelihood analysis and conclude that the evolution is driven by a decreasing number density of high luminosity clusters with redshift, while the bulk of the cluster population remains nearly unchanged out to redshift z ~ 1.1, as expected in a low density Universe. The results are found to be insensitive to a variety of sources of systematic uncertainty that affect the measurement of the XLF and determination of the survey selection function. We perform a Bayesian analysis of the XLF to fully account for uncertainties in the local XLF on the measured evolution, and find that the detected evolution remains significant at the 95% level. We observe a significant excess of clusters in the WARPS at 0.1 < z < 0.3 and LX ~ 2 10E42 erg/s compared with the reference low-redshift XLF, or our Bayesian fit to the WARPS data. We find that the excess cannot be explained by sample variance, or Eddington bias, and is unlikely to be due to problems with the survey selection function.Comment: 13 pages, 12 figures, accepted for publication in MNRA

Chandra Measurements of a Complete Sample of X-ray Luminous Galaxy Clusters: The Luminosity-Mass Relation

We present the results of work involving a statistically complete sample of 34 galaxy clusters, in the redshift range 0.15$\le$z$\le$0.3 observed with $Chandra$. We investigate the luminosity-mass ($LM$) relation for the cluster sample, with the masses obtained via a full hydrostatic mass analysis. We utilise a method to fully account for selection biases when modeling the $LM$ relation, and find that the $LM$ relation is significantly different than the relation modelled when not account for selection effects. We find that the luminosity of our clusters is 2.2$\pm$0.4 times higher (when accounting for selection effects) than the average for a given mass, its mass is 30% lower than the population average for a given luminosity. Equivalently, using the $LM$ relation measured from this sample without correcting for selection biases would lead to the underestimation by 40% of the average mass of a cluster with a given luminosity. Comparing the hydrostatic masses to mass estimates determined from the $Y_{X}$ parameter, we find that they are entirely consistent, irrespective of the dynamical state of the cluster.Comment: 31 pages, 43 figures, accepted for publication in MNRA

The XMM-LSS survey: the Class 1 cluster sample over the extended 11 deg2^2 and its spatial distribution

This paper presents 52 X-ray bright galaxy clusters selected within the 11 deg$^2$ XMM-LSS survey. 51 of them have spectroscopic redshifts ($0.05<z<1.06$), one is identified at $z_{\rm phot}=1.9$, and all together make the high-purity "Class 1" (C1) cluster sample of the XMM-LSS, the highest density sample of X-ray selected clusters with a monitored selection function. Their X-ray fluxes, averaged gas temperatures (median $T_X=2$ keV), luminosities (median $L_{X,500}=5\times10^{43}$ ergs/s) and total mass estimates (median $5\times10^{13} h^{-1} M_{\odot}$) are measured, adapting to the specific signal-to-noise regime of XMM-LSS observations. The redshift distribution of clusters shows a deficit of sources when compared to the cosmological expectations, regardless of whether WMAP-9 or Planck-2013 CMB parameters are assumed. This lack of sources is particularly noticeable at $0.4 \lesssim z \lesssim 0.9$. However, after quantifying uncertainties due to small number statistics and sample variance we are not able to put firm (i.e. $>3 \sigma$) constraints on the presence of a large void in the cluster distribution. We work out alternative hypotheses and demonstrate that a negative redshift evolution in the normalization of the $L_{X}-T_X$ relation (with respect to a self-similar evolution) is a plausible explanation for the observed deficit. We confirm this evolutionary trend by directly studying how C1 clusters populate the $L_{X}-T_X-z$ space, properly accounting for selection biases. We point out that a systematically evolving, unresolved, central component in clusters and groups (AGN contamination or cool core) can impact the classification as extended sources and be partly responsible for the observed redshift distribution.[abridged]Comment: 33 pages, 21 figures, 3 tables ; accepted for publication in MNRA

Separating the BL Lac and Cluster X-ray Emissions in Abell 689 with Chandra

We present the results of a Chandra observation of the galaxy cluster Abell 689 (z=0.279). Abell 689 is one of the most luminous clusters detected in the ROSAT All Sky Survey (RASS), but was flagged as possibly including significant point source contamination. The small PSF of the Chandra telescope allows us to confirm this and separate the point source from the extended cluster X-ray emission. For the cluster we determine a bolometric luminosity of L_{bol}=(3.3+/-0.3)x10^{44} erg s-1 and a temperature of kT=5.1^{+2.2}_{-1.3} keV when including a physically motivated background model. We compare our measured luminosity for A689 to that quoted in the Rosat All Sky Survey (RASS) and find L_{0.1-2.4,keV}=2.8x10^{44} erg s-1, a value \sim10 times lower than the ROSAT measurement. Our analysis of the point source shows evidence for significant pileup, with a pile-up fraction of ~60%. SDSS spectra and HST images lead us to the conclusion that the point source within Abell 689 is a BL Lac object. Using radio and optical observations from the VLA and HST archives, we determine {\alpha}_{ro}=0.50, {\alpha}_{ox}=0.77 and {\alpha}_{rx}=0.58 for the BL Lac, which would classify it as being of 'High-energy peak BL Lac' (HBL) type. Spectra extracted of A689 show a hard X-ray excess at energies above 6 keV that we interpret as inverse Compton emission from aged electrons that may have been transported into the cluster from the BL Lac.Comment: 11 pages, 15 figures, MNRAS in pres