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Register a new userThe physics inside the scaling relations for X-ray galaxy clusters: gas clumpiness, gas mass fraction and slope of the pressure profile
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S. Ettori
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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.
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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.
(Abridged) We examine the radial entropy distribution and its scaling using 31 nearby galaxy clusters from the Representative XMM-Newton Cluster Structure Survey (REXCESS). The entropy profiles are robustly measured at least out to R_1000 in all systems and out to R_500 in 13 systems. Compared to theoretical expectations, the observed distributions show a radial and mass-dependent excess entropy that is greater and extends to larger radii in lower mass systems. At R_500, the mass dependence and entropy excess are both negligible within the uncertainties. Mirroring this behaviour, the scaling of gas entropy is shallower than self-similar in the inner regions, but steepens with radius, becoming consistent with self-similar at R_500. The dispersion in scaled entropy in the inner regions is linked to the presence of cool cores and dynamical activity; at larger radii the dispersion decreases by a factor of two and the dichotomy between subsamples disappears. Parameterising the profiles with a power law plus constant model, there are two peaks in central entropy K_0; however, we cannot distinguish between a bimodal or a left-skewed distribution. The outer slopes are correlated with system temperature; their distribution is unimodal with a median value of 0.98. Renormalising the dimensionless entropy profiles by the gas mass fraction profile f_gas(< R), leads to a remarkable reduction in the scatter, implying that gas mass fraction variations with radius and mass are the cause of the observed entropy properties. We discuss a tentative scenario to explain the behaviour of the entropy and gas mass fraction in the REXCESS sample, in which extra heating and merger mixing maintains an elevated central entropy level in the majority of the population, and a smaller fraction of systems develops a cool core.
Magnetic fields have been observed in galaxy clusters with strengths of the order of $sim mu$G. The non-thermal pressure exerted by magnetic fields also contributes to the total pressure in galaxy clusters and can in turn affect the estimates of the gas mass fraction, $f_{gas}$. In this paper, we have considered a central magnetic field strength of $5mu$G, motivated by observations and simulations of galaxy clusters. The profile of the magnetic field has also been taken from the results obtained from simulations and observations. The role of magnetic field has been taken into account in inferring the gas density distribution through the hydrostatic equilibrium condition (HSE) by including the magnetic pressure. We have found that the resultant gas mass fraction is smaller with magnetic field as compared to that without magnetic field. However, this decrease is dependent on the strength and the profile of the magnetic field. We have also determined the total mass using the NFW profile to check for the dependency of $f_{gas}$ estimates on total mass estimators. From our analysis, we conclude that for the magnetic field strength that galaxy clusters seem to possess, the non-thermal pressure from magnetic fields has an impact of $approx 1~%$ on the gas mass fraction of galaxy clusters. However, with upcoming facilities like Square Kilometre Array (SKA), it can be further expected to improve with more precise observations of the magnetic field strength and profile in galaxy clusters, particularly in the interior region.
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.
(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.
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