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Register a new userThe generalized scaling relations for X-ray galaxy clusters: the most powerful mass proxy
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S. Ettori
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The application to observational data of the generalized scaling relations (gSR) presented in Ettori et al. (2012) is here discussed. We extend further the formalism of the gSR in the self-similar model for X-ray galaxy clusters, showing that for a generic relation M_tot ~ L^a M_g^b T^c, where L, M_g and T are the gas luminosity, mass and temperature, respectively, the values of the slopes lay in the plane 4*a+3*b+2*c=3. Using published dataset, we show that some projections of the gSR are the most efficient relations, holding among observed physical X-ray quantities, to recover the cluster mass. This conclusion is based on the evidence that they provide the lowest chi^2, the lowest total scatter and the lowest intrinsic scatter among the studied scaling laws on both galaxy group and cluster mass scales. By the application of the gSR, the intrinsic scatter is reduced in all the cases down to a relative error on M_tot below 16 per cent. The best-fit relations are: M_tot ~ M_g^a T^{1.5-1.5a}, with a~0.4, and M_tot ~ L^a T^{1.5-2a}, with a~0.15. As a by product of this study, we provide the estimates of the gravitating mass at Delta=500 for 120 objects (50 from the Mahdavi et al. 2013 sample, 16 from Maughan 2012; 31 from Pratt et al. 2009; 23 from Sun et al. 2009), 114 of which are unique entries. The typical relative error in the mass provided from the gSR only (i.e. not propagating any uncertainty associated with the observed quantities) ranges between 3-5 per cent on cluster scale and is about 10 per cent for galaxy groups. With respect to the hydrostatic values used to calibrate the gSR, the masses are recovered with deviations in the order of 10 per cent due to the different mix of relaxed/disturbed objects present in the considered samples. In the extreme case of a gSR calibrated with relaxed systems, the hydrostatic mass in disturbed objects is over-estimated by about 20 per cent.
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(Abridged) This is the second in a series of papers in which we derive simultaneous constraints on cosmology and X-ray scaling relations using observations of massive, X-ray flux-selected galaxy clusters. The data set consists of 238 clusters drawn from the ROSAT All-Sky Survey with 0.1-2.4 keV luminosities >2.5e44 erg/second, and incorporates extensive follow-up observations using the Chandra X-ray Observatory. Our analysis accounts self-consistently for all selection effects, covariances and systematic uncertainties. Here we describe the reduction of the follow-up X-ray observations, present results on the cluster scaling relations, and discuss their implications. Our constraints on the luminosity-mass and temperature-mass relations, measured within r_500, lead to three important results. First, the data support the conclusion that excess heating of the intracluster medium has altered its thermodynamic state from that expected in a simple, gravitationally dominated system; however, this excess heating is primarily limited to the central regions of clusters (r<0.15r_500). Second, the intrinsic scatter in the center-excised luminosity-mass relation is remarkably small, being undetected at the <10% level in current data; for the hot, massive clusters under investigation, this scatter is smaller than in either the temperature-mass or Y_X-mass relations (10-15%). Third, the evolution with redshift of the scaling relations is consistent with the predictions of simple, self-similar models of gravitational collapse, indicating that the mechanism responsible for heating the central regions of clusters was in operation before redshift 0.5 (the limit of our data) and that its effects on global cluster properties have not evolved strongly since then.
We present the X-ray properties and scaling relations of a large sample of clusters extracted from the Marenostrum MUltidark SImulations of galaxy Clusters (MUSIC) dataset. We focus on a sub-sample of 179 clusters at redshift z~0.11, with 3.2e14M_sun/h<M_vir<2e15Msun/h, complete in mass. We employed the X-ray photon simulator PHOX to obtain synthetic Chandra Observations and derive observable-like global properties of the intracluster medium (ICM), as X-ray temperature (T_X) and luminosity (L_X). T_X is found to slightly under-estimate the true mass-weighted temperature, although tracing fairly well the cluster total mass. We also study the effects of T_X on scaling relations with cluster intrinsic properties: total (M_500) and gas (M_g500) mass; integrated Compton parameter (Y_SZ) of the Sunyaev-Zeldovich (SZ) thermal effect; Y_X=M_g500 T_X. We confirm that Y_X is a very good mass proxy, with a scatter on M_500-Y_X and Y_SZ-Y_X lower than 5%. The study of scaling relations among X-ray, intrinsic and SZ properties indicates that MUSIC clusters reasonably resemble the self-similar prediction, especially for correlations involving T_X. The observational approach also allows for a more direct comparison with real clusters, from which we find deviations mainly due to the physical description of the ICM, affecting T_X and, particularly, L_X.
We use numerical simulations to investigate, for the first time, the joint effect of feedback from supernovae (SNe) and active galactic nuclei (AGN) on the evolution of galaxy cluster X-ray scaling relations. Our simulations are drawn from the Millennium Gas Project and are some of the largest hydrodynamical N-body simulations ever carried out. Feedback is implemented using a hybrid scheme, where the energy input into intracluster gas by SNe and AGN is taken from a semi-analytic model of galaxy formation. This ensures that the source of feedback is a population of galaxies that closely resembles that found in the real universe. We show that our feedback model is capable of reproducing observed local X-ray scaling laws, at least for non-cool core clusters, but that almost identical results can be obtained with a simplistic preheating model. However, we demonstrate that the two models predict opposing evolutionary behaviour. We have examined whether the evolution predicted by our feedback model is compatible with observations of high-redshift clusters. Broadly speaking, we find that the data seems to favour the feedback model for z<0.5, and the preheating model at higher redshift. However, a statistically meaningful comparison with observations is impossible, because the large samples of high-redshift clusters currently available are prone to strong selection biases. As the observational picture becomes clearer in the near future, it should be possible to place tight constraints on the evolution of the scaling laws, providing us with an invaluable probe of the physical processes operating in galaxy clusters.
In galaxy clusters, the relations between observables in X-ray and millimeter wave bands and the total mass have normalizations, slopes and redshift evolutions that are simple to estimate in a self-similar scenario. We study these scaling relations and show that they can be efficiently expressed, in a more coherent picture, by fixing the normalizations and slopes to the self-similar predictions, and advocating, as responsible of the observed deviations, only three physical mass-dependent quantities: the gas clumpiness $C$, the gas mass fraction $f_g$ and the logarithmic slope of the thermal pressure profile $beta_P$. We use samples of the observed gas masses, temperature, luminosities, and Compton parameters in local clusters to constrain normalization and mass dependence of these 3 physical quantities, and measure: $C^{0.5} f_g = 0.110 (pm 0.002 pm 0.002) left( E_z M / 5 times 10^{14} M_{odot} right)^{0.198 (pm 0.025 pm 0.04)}$ and $beta_P = -d ln P/d ln r = 3.14 (pm 0.04 pm 0.02) left( E_z M / 5 times 10^{14} M_{odot} right)^{0.071 (pm 0.012 pm 0.004)}$, where both a statistical and systematic error (the latter mainly due to the cross-calibration uncertainties affecting the cxo and xmm results used in the present analysis) are quoted. The degeneracy between $C$ and $f_g$ is broken by using the estimates of the Compton parameters. Together with the self-similar predictions, these estimates on $C$, $f_g$ and $beta_P$ define an inter-correlated internally-consistent set of scaling relations that reproduces the mass estimates with the lowest residuals.
All-sky data from the Planck survey and the Meta-Catalogue of X-ray detected Clusters of galaxies (MCXC) are combined to investigate the relationship between the thermal Sunyaev-Zeldovich (SZ) signal and X-ray luminosity. The sample comprises ~ 1600 X-ray clusters with redshifts up to ~ 1 and spans a wide range in X-ray luminosity. The SZ signal is extracted for each object individually, and the statistical significance of the measurement is maximised by averaging the SZ signal in bins of X-ray luminosity, total mass, or redshift. The SZ signal is detected at very high significance over more than two decades in X-ray luminosity (10^43 erg/s < L_500 E(z)^-7/3 < 2 X 10^45 erg/s). The relation between intrinsic SZ signal and X-ray luminosity is investigated and the measured SZ signal is compared to values predicted from X-ray data. Planck measurements and X-ray based predictions are found to be in excellent agreement over the whole explored luminosity range. No significant deviation from standard evolution of the scaling relations is detected. For the first time the intrinsic scatter in the scaling relation between SZ signal and X-ray luminosity is measured and found to be consistent with the one in the luminosity -- mass relation from X-ray studies. There is no evidence of any deficit in SZ signal strength in Planck data relative to expectations from the X-ray properties of clusters, underlining the robustness and consistency of our overall view of intra-cluster medium properties.
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