Pointing to the minimum scatter: the generalized scaling relations for galaxy clusters

We introduce a generalized scaling law, M_tot = 10^K A^a B^b, to look for the minimum scatter in reconstructing the total mass of hydrodynamically simulated X-ray galaxy clusters, given gas mass M_gas, luminosity L and temperature T. We find a locus in the plane of the logarithmic slopes $a$ and $b$ of the scaling relations where the scatter in mass is minimized. This locus corresponds to b_M = -3/2 a_M +3/2 and b_L = -2 a_L +3/2 for A=M_gas and L, respectively, and B=T. Along these axes, all the known scaling relations can be identified (at different levels of scatter), plus a new one defined as M_tot ~ (LT)^(1/2). Simple formula to evaluate the expected evolution with redshift in the self-similar scenario are provided. In this scenario, no evolution of the scaling relations is predicted for the cases (b_M=0, a_M=1) and (b_L=7/2, a_L=-1), respectively. Once the single quantities are normalized to the average values of the sample under considerations, the normalizations K corresponding to the region with minimum scatter are very close to zero. The combination of these relations allows to reduce the number of free parameters of the fitting function that relates X-ray observables to the total mass and includes the self-similar redshift evolution.Comment: 6 pages, 3 figures. MNRAS in pres

Weighing simulated galaxy clusters using lensing and X-ray

We aim at investigating potential biases in lensing and X-ray methods to measure the cluster mass profiles. We do so by performing realistic simulations of lensing and X-ray observations that are subsequently analyzed using observational techniques. The resulting mass estimates are compared among them and with the input models. Three clusters obtained from state-of-the-art hydrodynamical simulations, each of which has been projected along three independent lines-of-sight, are used for this analysis. We find that strong lensing models can be trusted over a limited region around the cluster core. Extrapolating the strong lensing mass models to outside the Einstein ring can lead to significant biases in the mass estimates, if the BCG is not modeled properly for example. Weak lensing mass measurements can be largely affected by substructures, depending on the method implemented to convert the shear into a mass estimate. Using non-parametric methods which combine weak and strong lensing data, the projected masses within R200 can be constrained with a precision of ~10%. De-projection of lensing masses increases the scatter around the true masses by more than a factor of two due to cluster triaxiality. X-ray mass measurements have much smaller scatter (about a factor of two smaller than the lensing masses) but they are generally biased low by 5-20%. This bias is ascribable to bulk motions in the gas of our simulated clusters. Using the lensing and the X-ray masses as proxies for the true and the hydrostatic equilibrium masses of the simulated clusters and averaging over the cluster sample we are able to measure the lack of hydrostatic equilibrium in the systems we have investigated.Comment: 27 pages, 21 figures, accepted for publication on A&A. Version with full resolution images can be found at http://pico.bo.astro.it/~massimo/Public/Papers/massComp.pd

Cool Core Clusters from Cosmological Simulations

We present results obtained from a set of cosmological hydrodynamic simulations of galaxy clusters, aimed at comparing predictions with observational data on the diversity between cool-core (CC) and non-cool-core (NCC) clusters. Our simulations include the effects of stellar and AGN feedback and are based on an improved version of the smoothed particle hydrodynamics code GADGET-3, which ameliorates gas mixing and better captures gas-dynamical instabilities by including a suitable artificial thermal diffusion. In this Letter, we focus our analysis on the entropy profiles, the primary diagnostic we used to classify the degree of cool-coreness of clusters, and on the iron profiles. In keeping with observations, our simulated clusters display a variety of behaviors in entropy profiles: they range from steadily decreasing profiles at small radii, characteristic of cool-core systems, to nearly flat core isentropic profiles, characteristic of non-cool-core systems. Using observational criteria to distinguish between the two classes of objects, we find that they occur in similar proportions in both simulations and in observations. Furthermore, we also find that simulated cool-core clusters have profiles of iron abundance that are steeper than those of NCC clusters, which is also in agreement with observational results. We show that the capability of our simulations to generate a realistic cool-core structure in the cluster population is due to AGN feedback and artificial thermal diffusion: their combined action allows us to naturally distribute the energy extracted from super-massive black holes and to compensate for the radiative losses of low-entropy gas with short cooling time residing in the cluster core.Comment: 6 pages, 4 figures, accepted in ApJL, v2 contains some modifications on the text (results unchanged

Measuring the dark matter velocity anisotropy in galaxy clusters

The Universe contains approximately 6 times more dark matter than normal baryonic matter, and a directly observed fundamental difference between dark matter and baryons would both be significant for our understanding of dark matter structures and provide us with information about the basic characteristics of the dark matter particle. We discuss one distinctive feature of dark matter structures in equilibrium, namely the property that a local dark matter temperature may depend on direction. This is in stark contrast to baryonic gases. We used X-ray observations of two nearby, relaxed galaxy clusters, under the assumptions of hydrostatic equilibrium and identical dark matter and gas temperatures in the outer cluster region, to measure this dark matter temperature anisotropy beta_dm, with non-parametric Monte Carlo methods. We find that beta_dm is greater than the value predicted for baryonic gases, beta_gas=0, at more than 3 sigma confidence. The observed value of the temperature anisotropy is in fair agreement with the results of cosmological N-body simulations and shows that the equilibration of the dark matter particles is not governed by local point-like interactions in contrast to baryonic gases.Comment: 5 pages, 3 figures, extended discussions, matches accepted versio

Thermal Conduction in Simulated Galaxy Clusters

We study the formation of clusters of galaxies using high-resolution hydrodynamic cosmological simulations that include the effect of thermal conduction with an effective isotropic conductivity of 1/3 the classical Spitzer value. We find that, both for a hot ($T_{\rm ew}\simeq 12$ keV) and several cold ($T_{\rm ew}\simeq 2$ keV) galaxy clusters, the baryonic fraction converted into stars does not change significantly when thermal conduction is included. However, the temperature profiles are modified, particularly in our simulated hot system, where an extended isothermal core is readily formed. As a consequence of heat flowing from the inner regions of the cluster both to its outer parts and into its innermost resolved regions, the entropy profile is altered as well. This effect is almost negligible for the cold cluster, as expected based on the strong temperature dependence of the conductivity. Our results demonstrate that while thermal conduction can have a significant influence on the properties of the intra--cluster medium of rich galaxy clusters, it appears unlikely to provide by itself a solution for the overcooling problem in clusters, or to explain the current discrepancies between the observed and simulated properties of the intra--cluster medium.Comment: 4 Pages, 3 Figures, Submitted to ApJ-Letter

Spectroscopic-Like Temperature of Clusters of Galaxies and Cosmological Implications

The thermal properties of hydrodynamical simulations of galaxy clusters are usually compared to observations by relying on the emission-weighted temperature T_ew, instead of on the spectroscopic X-ray temperature T_spec, which is obtained by actual observational data. Here we show that, if the intra-cluster medium is thermally complex, T_ew fails at reproducing T_spec. We propose a new formula, the spectroscopic-like temperature, T_sl, which approximates T_spec better than a few per cent. By analyzing a set of hydrodynamical simulations of galaxy clusters, we also find that T_sl is lower than T_ew by 20-30 per cent. As a consequence, the normalization of the M-T relation from the simulations is larger than the observed one by about 50 per cent. If masses in simulated clusters are estimated by following the same assumptions of hydrostatic equilibrium and beta-model gas density profile, as often done for observed clusters, then the M-T relation decreases by about 40 per cent, and significantly reduces its scatter. Based on this result, we conclude that using the observed M-T relation to infer the amplitude of the power spectrum from the X--ray temperature function could bias low sigma_8 by 10-20 per cent. This may alleviate the tension between the value of sigma_8 inferred from the cluster number density and those from cosmic microwave background and large scale structure.Comment: 6 pages, 3 figures, to appear in the proceedings of the Rencontres du Vietnam "New Views on the Universe

Cosmological hydrodynamical simulations of galaxy clusters: X-ray scaling relations and their evolution

We analyse cosmological hydrodynamical simulations of galaxy clusters to study the X-ray scaling relations between total masses and observable quantities such as X-ray luminosity, gas mass, X-ray temperature, and $Y_{X}$. Three sets of simulations are performed with an improved version of the smoothed particle hydrodynamics GADGET-3 code. These consider the following: non-radiative gas, star formation and stellar feedback, and the addition of feedback by active galactic nuclei (AGN). We select clusters with $M_{500} > 10^{14} M_{\odot} E(z)^{-1}$, mimicking the typical selection of Sunyaev-Zeldovich samples. This permits to have a mass range large enough to enable robust fitting of the relations even at $z \sim 2$. The results of the analysis show a general agreement with observations. The values of the slope of the mass-gas mass and mass-temperature relations at $z=2$ are 10 per cent lower with respect to $z=0$ due to the applied mass selection, in the former case, and to the effect of early merger in the latter. We investigate the impact of the slope variation on the study of the evolution of the normalization. We conclude that cosmological studies through scaling relations should be limited to the redshift range $z=0-1$, where we find that the slope, the scatter, and the covariance matrix of the relations are stable. The scaling between mass and $Y_X$ is confirmed to be the most robust relation, being almost independent of the gas physics. At higher redshifts, the scaling relations are sensitive to the inclusion of AGNs which influences low-mass systems. The detailed study of these objects will be crucial to evaluate the AGN effect on the ICM.Comment: 24 pages, 11 figures, 5 tables, replaced to match accepted versio

On the Baryon Fractions in Clusters and Groups of Galaxies

We present the baryon fractions of 2MASS groups and clusters as a function of cluster richness using total and gas masses measured from stacked ROSAT X-ray data and stellar masses estimated from the infrared galaxy catalogs. We detect X-ray emission even in the outskirts of clusters, beyond r_200 for richness classes with X-ray temperatures above 1 keV. This enables us to more accurately determine the total gas mass in these groups and clusters. We find that the optically selected groups and clusters have flatter temperature profiles and higher stellar-to-gas mass ratios than the individually studied, X-ray bright clusters. We also find that the stellar mass in poor groups with temperatures below 1 keV is comparable to the gas mass in these systems. Combining these results with individual measurements for clusters, groups, and galaxies from the literature, we find a break in the baryon fraction at ~1 keV. Above this temperature, the baryon fraction scales with temperature as f_b \propto T^0.20\pm0.03. We see significantly smaller baryon fractions below this temperature, and the baryon fraction of poor groups joins smoothly onto that of systems with still shallower potential wells such as normal and dwarf galaxies where the baryon fraction scales with the inferred velocity dispersion as f_b \propto \sigma^1.6. The small scatter in the baryon fraction at any given potential well depth favors a universal baryon loss mechanism and a preheating model for the baryon loss. The scatter is, however, larger for less massive systems. Finally, we note that although the broken power-law relation can be inferred from data points in the literature alone, the consistency between the baryon fractions for poor groups and massive galaxies inspires us to fit the two categories of objects (galaxies and clusters) with one relation.Comment: 21 pages, 5 figures, ApJ in pres

Substructures in hydrodynamical cluster simulations

The abundance and structure of dark matter subhalos has been analyzed extensively in recent studies of dark matter-only simulations, but comparatively little is known about the impact of baryonic physics on halo substructures. We here extend the SUBFIND algorithm for substructure identification such that it can be reliably applied to dissipative hydrodynamical simulations that include star formation. This allows, in particular, the identification of galaxies as substructures in simulations of clusters of galaxies, and a determination of their content of gravitationally bound stars, dark matter, and hot and cold gas. Using a large set of cosmological cluster simulations, we present a detailed analysis of halo substructures in hydrodynamical simulations of galaxy clusters, focusing in particular on the influence both of radiative and non-radiative gas physics, and of non-standard physics such as thermal conduction and feedback by galactic outflows. We also examine the impact of numerical nuisance parameters such as artificial viscosity parameterizations. We find that diffuse hot gas is efficiently stripped from subhalos when they enter the highly pressurized cluster atmosphere. This has the effect of decreasing the subhalo mass function relative to a corresponding dark matter-only simulation. These effects are mitigated in radiative runs, where baryons condense in the central subhalo regions and form compact stellar cores. However, in all cases, only a very small fraction, of the order of one percent, of subhalos within the cluster virial radii preserve a gravitationally bound hot gaseous atmosphere. (abridged)Comment: improved manuscript, to appear in MNRA