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Register a new userA theoretical study of the luminosity temperature relation for clusters of galaxies
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Antonino del Popolo
Publication date
2005
fields
Physics
and research's language is
English
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A luminosity-temperature relation for clusters of galaxies is derived. The two models used, take into account the angular momentum acquisition by the proto-structures during their expansion and collapse. The first one is a modification of the self-similar model (SSM) while the second one is a modification of the Punctuated Equilibria Model (Cavaliere et al. 1999). In both models the mass-temperature relation (M-T) used is based on the calculations of Del Popolo (2002b). We show that the above models lead, in X-rays, to a luminosity-temperature relation that scales as L propto T^5, at scale of groups, flattening to L propto T^3 for rich clusters and converging to L propto T^2 at higher temperatures. However a fundamental result of our paper is that the non-similarity in the L-T relation, can be explained by a simple model that takes into account the amount of the angular momentum of a proto-structure. This result is in disagreement with the widely accepted idea that the above non-similarity is due to non-gravitating processes as those of heating/cooling.
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We have obtained the first large sample of accurate temperatures for clusters at z>0.14 from ASCA. We compare the luminosity temperature (L-T) distribution for these clusters with the low redshift sample of David et al (1993) and find that there is no evidence for evolution. We also find that the intrinsic variance in this relation is roughly constant with redshift. Additionally, there is no detectable change in the relationship of optical velocity dispersion to X-ray temperature with redshift. Most cosmological simulations driven primarily by gravity predict substantial changes in the L-T relation due to the recent rapid growth of clusters. Our results are consistent either with models in which the cluster core entropy is dominated by pre-heating, or with low Omega models in which cluster structure does not evolve strongly with time. The intrinsic variance in the L-T relation at a fixed redshift can be due a variety of possibilites e.g. a change in the baryonic fraction from cluster to cluster, variation in the fraction of the total energy in the system arising from shocks or supernova heating or variations in the emission measure distributions in multiphase gas.
We present our discovery observations and analysis of RDCS1317+2911, z = 0.805, and RDCS1350+6007, z= 0.804, two clusters of galaxies identified through X-ray emission in the ROSAT Deep Cluster Survey (RDCS). We find a temperature of 3.7 +1.5 -0.9 keV and a bolometric luminosity of 8.2e43 +1.7e43 -1.6e43 erg/s for RDCS1317+2911, and a temperature of 4.9 +1.3 -0.9 keV and a bolometric luminosity of 4.1e44 +0.5e44 -0.4e44 erg/s for RDCS1350+6007. Our weak lensing analysis of RDCS1350+6007 confirms the general shape of the inner density profile but predicts twice the mass of the model based on the X-ray profile. We combine the X-ray luminosities and temperatures for RDCS clusters of galaxies with such measurements of other clusters at high redshift (z>0.7) and fit the luminosity-temperature relation. We find no statistically significant evolution in the slope or zero-point of this relation at a median of z=0.83. This result is in agreement with models of intracluster medium evolution with significant pre-heating or high initial entropy values. We discuss how low temperature, high redshift clusters of galaxies will allow us to improve on this result and announce the discovery of two such objects, CXOU J0910.1+5419 and CXOU J1316.9+2914.
We investigate the relationship between soft xray luminosity and mass for low redshift clusters of galaxies by comparing observed number counts to expectations of $Lambda$CDM cosmologies. We use a three-parameter model for the conditional probability of luminosity given mass and epoch, described as a log-normal distribution of fixed width centered on a power-law scaling relation, $L spropto M^prhoc^s(z)$. We use an ensemble of simulated clusters to argue that the observed, intrinsic variance in the temperature--luminosity relation is directly indicative of mass--luminosity variance, and derive $sigm se 0.43 pm 0.06$ from HIFLUGCS data. Adding this to the likelihood analysis results in best-fit estimates $p se 1.59 pm 0.05$, $lnlf se 1.34 pm 0.09$, and $sigm se 0.37 pm 0.05$ for self-similar redshift evolution in a concordance ($Omega_m se 0.3$, $Omega_Lambda se 0.7$, $sigma_8 se0.9$) universe. We show that the present-epoch intercept is very sensitive to power spectrum normalization, $lnlf spropto sigate^{-4}$, and the slope is weakly sensitive to the matter density, $p spropto Omega_m^{1/2}$. The intercept derived here is dimmer by a factor 2, and slope slightly steeper, than the L-M relation published using hydrostatic mass estimates of the HIFLUGCS sample. We show that this discrepancy is largely due to Malmquist bias of the xray flux-limited sample. In light of new WMAP constraints, we discuss the interplay between parameters and sources of systematic error, and offer a compromise model with $Omega_m se 0.24$, $sigma_8 se 0.85$, and somewhat lower scatter $sigm se 0.25$, in which hydrostatic mass estimates remain accurate to $ssim 15%$. We stress the need for independent calibration of the L-M relation via weak gravitational lensing.
The main uncertainty in current determinations of the power spectrum normalization, sigma_8, from abundances of X-ray luminous galaxy clusters arises from the calibration of the mass-temperature relation. We use our weak lensing mass determinations of 30 clusters from the hitherto largest sample of clusters with lensing masses, combined with X-ray temperature data from the literature, to calibrate the normalization of this relation at a temperature of 8 keV, M_{500c,8 keV}=(8.7 +/- 1.6) h^{-1} 10^{14} M_sun. This normalization is consistent with previous lensing-based results based on smaller cluster samples, and with some predictions from numerical simulations, but higher than most normalizations based on X-ray derived cluster masses. Assuming the theoretically expected slope alpha=3/2 of the mass-temperature relation, we derive sigma_8 = 0.88 +/-0.09 for a spatially-flat LambdaCDM universe with Omega_m = 0.3. The main systematic errors on the lensing masses result from extrapolating the cluster masses beyond the field-of-view used for the gravitational lensing measurements, and from the separation of cluster/background galaxies, contributing each with a scatter of 20%. Taking this into account, there is still significant intrinsic scatter in the mass-temperature relation indicating that this relation may not be very tight, at least at the high mass end. Furthermore, we find that dynamically relaxed clusters are 75 +/-40% hotter than non-relaxed clusters.
We present the K-band luminosity-halo mass relation, $L_{K,500}-M_{500,WL}$, for a subsample of 20 of the 100 brightest clusters in the XXL Survey observed with WIRCam at the Canada-France-Hawaii Telescope (CFHT). For the first time, we have measured this relation via weak-lensing analysis down to $M_{500,WL} =3.5 times 10^{13},M_odot$. This allows us to investigate whether the slope of the $L_K-M$ relation is different for groups and clusters, as seen in other works. The clusters in our sample span a wide range in mass, $M_{500,WL} =0.35-12.10 times 10^{14},M_odot$, at $0<z<0.6$. The K-band luminosity scales as $log_{10}(L_{K,500}/10^{12}L_odot) propto beta log_{10}(M_{500,WL}/10^{14}M_odot)$ with $beta = 0.85^{+0.35}_{-0.27}$ and an intrinsic scatter of $sigma_{lnL_K|M} =0.37^{+0.19}_{-0.17}$. Combining our sample with some clusters in the Local Cluster Substructure Survey (LoCuSS) present in the literature, we obtain a slope of $1.05^{+0.16}_{-0.14}$ and an intrinsic scatter of $0.14^{+0.09}_{-0.07}$. The flattening in the $L_K-M$ seen in previous works is not seen here and might be a result of a bias in the mass measurement due to assumptions on the dynamical state of the systems. We also study the richness-mass relation and find that group-sized halos have more galaxies per unit halo mass than massive clusters. However, the brightest cluster galaxy (BCG) in low-mass systems contributes a greater fraction to the total cluster light than BCGs do in massive clusters; the luminosity gap between the two brightest galaxies is more prominent for group-sized halos. This result is a natural outcome of the hierarchical growth of structures, where massive galaxies form and gain mass within low-mass groups and are ultimately accreted into more massive clusters to become either part of the BCG or one of the brighter galaxies. [Abridged]
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