Hydrostatic Mass Estimates Research Articles

Scaling relations and mass bias in hydrodynamical f (R) gravity simulations of galaxy clusters

We investigate the impact of chameleon-type f(R) gravity models on the properties of galaxy clusters and groups. Our f(R) simulations follow for the first time also the hydrodynamics of the intracluster and intragroup medium. This allows us to assess how f(R) gravity alters the X-ray scaling relations of clusters and how hydrostatic and dynamical mass estimates are biased when modifications of gravity are ignored in their determination. We find that velocity dispersions and intracluster medium temperatures are both increased by up to 1/3 in f(R) gravity in low-mass halos, while the difference disappears in massive objects. The mass scale of the transition depends on the background value f_R0 of the scalar degree of freedom. These changes in temperature and velocity dispersion alter the mass-temperature and X-ray luminosity-temperature scaling relations and bias dynamical and hydrostatic mass estimates that do not explicitly account for modified gravity towards higher values. Recently, a relative enhancement of X-ray compared to weak lensing masses was found by the Planck Collaboration (2013). We demonstrate that an explanation for this offset may be provided by modified gravity and the associated bias effects, which interestingly are of the required size. Finally, we find that the abundance of subhalos at fixed cluster mass is only weakly affected by f(R) gravity.

WEIGHING GALAXY CLUSTERS WITH GAS. II. ON THE ORIGIN OF HYDROSTATIC MASS BIAS IN ΛCDM GALAXY CLUSTERS

The use of galaxy clusters as cosmological probes hinges on our ability to measure their masses accurately and with high precision. Hydrostatic mass is one of the most common methods for estimating the masses of individual galaxy clusters, which suffer from biases due to departures from hydrostatic equilibrium. Using a large, mass-limited sample of massive galaxy clusters from a high-resolution hydrodynamical cosmological simulation, in this work we show that in addition to turbulent and bulk gas velocities, acceleration of gas introduces biases in the hydrostatic mass estimate of galaxy clusters. In unrelaxed clusters, the acceleration bias is comparable to the bias due to non-thermal pressure associated with merger-induced turbulent and bulk gas motions. In relaxed clusters, the mean mass bias due to acceleration is small (<3%), but the scatter in the mass bias can be reduced by accounting for gas acceleration. Additionally, this acceleration bias is greater in the outskirts of higher redshift clusters where mergers are more frequent and clusters are accreting more rapidly. Since gas acceleration cannot be observed directly, it introduces an irreducible bias for hydrostatic mass estimates. This acceleration bias places limits on how well we can recover cluster masses from future X-ray and microwave observations. We discuss implications for cluster mass estimates based on X-ray, Sunyaev-Zeldovich effect, and gravitational lensing observations and their impact on cluster cosmology.

What sets temperature gradients in galaxy clusters? Implications for non-thermal pressure support and mass-observable scaling relations

We present a spherically symmetric model for the origin and evolution of the temperature profiles in the hot plasma filling galaxy groups and clusters. We find that the gas in clusters is generically not isothermal, and that the temperature declines with radius at large distances from the cluster center (outside the core- and scale radii). This temperature profile is determined by the accretion history of the halo, and is not quantitatively well-described by a polytropic model. We explain quantitatively how the large-scale temperature gradient persists in spite of thermal conduction and convection. These results are a consequence of the cosmological assembly of clusters and cannot be reproduced with non-cosmological simulations of isolated halos. We show that the variation in halo assembly histories produces a ~10% scatter in temperature at fixed mass. On top of this scatter, conduction decreases the temperature of the gas near the scale radius in massive clusters, which may bias hydrostatic mass estimates inferred from x-ray and SZ observations. As an example application of our model profiles, we use mixing-length theory to estimate the turbulent pressure support created by the magnetothermal instability (MTI): in agreement with our earlier MHD simulations, we find that the convection produced by the MTI can provide ~5% non-thermal pressure support near r_500. The magnitude of this turbulent pressure support is likely to be non-monotonic in halo mass, peaking in ~10^14.5 M_sun halos.

Probing cluster dynamics in RXC J1504.1-0248 via radial and two-dimensional gas and galaxy properties

We studied one of the most X-ray luminous cluster of galaxies in the REFLEX survey, RXC J1504.1-0248 (hereafter R1504; z=0.2153), using XMM-Newton X-ray imaging spectroscopy, VLT/VIMOS optical spectroscopy, and WFI optical imaging. The mass distributions were determined using both the so-called hydrostatic method with X-ray imaging spectroscopy and the dynamical method with optical spectroscopy, respectively, which yield M^{H.E.}_{500}=(5.81+/-0.49)*1.e14Msun and M^{caustic}_{500}=(4.17+/-0.42)*1e14Msun. According to recent calibrations, the richness derived mass estimates closely agree with the hydrostatic and dynamical mass estimates. The line-of-sight velocities of spectroscopic members reveal a group of galaxies with high-velocities (>1000 km/s) at a projected distance of about r^{H.E.}_{500}=(1.18+/-0.03) Mpc south-east of the cluster centroid, which is also indicated in the X-ray two-dimensional (2-D) temperature, density, entropy, and pressure maps. The dynamical mass estimate is 80% of the hydrostatic mass estimate at r^{H.E.}_{500}. It can be partially explained by the ~20% scatter in the 2-D pressure map that can be propagated into the hydrostatic mass estimate. The uncertainty in the dynamical mass estimate caused by the substructure of the high velocity group is ~14%. The dynamical mass estimate using blue members is 1.23 times that using red members. The global properties of R1504 obey the observed scaling relations of nearby clusters, although its stellar-mass fraction is rather low.

EVOLUTION OF THE MERGER-INDUCED HYDROSTATIC MASS BIAS IN GALAXY CLUSTERS

In this work, we examine the effects of mergers on the hydrostatic mass estimate of galaxy clusters using high-resolution Eulerian cosmological simulations. We utilize merger trees to isolate the last merger for each cluster in our sample and follow the time evolution of the hydrostatic mass bias as the systems relax. We find that during a merger, a shock propagates outward from the parent cluster, resulting in an overestimate in the hydrostatic mass bias. After the merger, as a cluster relaxes, the bias in hydrostatic mass estimate decreases but remains at a level of -5-10% with 15-20% scatter within r500. We also investigate the post-merger evolution of the pressure support from bulk motions, a dominant cause of this residual mass bias. At r500, the contribution from random motions peaks at 30% of the total pressure during the merger and quickly decays to \sim 10-15% as a cluster relaxes. Additionally, we use a measure of the random motion pressure to correct the hydrostatic mass estimate. We discover that 4 Gyr after mergers, the direct effects of the merger event on the hydrostatic mass bias have become negligible. Thereafter, the mass bias is primarily due to residual bulk motions in the gas which are not accounted for in the hydrostatic equilibrium equation. We present a hydrostatic mass bias correction method that can recover the unbiased cluster mass for relaxed clusters with 9% scatter at r500 and 11% scatter in the outskirts, within r200.

THE DARK MATTER DISTRIBUTION IN A383: EVIDENCE FOR A SHALLOW DENSITY CUSP FROM IMPROVED LENSING, STELLAR KINEMATIC, AND X-RAY DATA

We extend our analyses of the dark matter (DM) distribution in relaxed clusters to the case of Abell 383, a luminous X-ray cluster at z=0.189 with a dominant central galaxy and numerous strongly-lensed features. Following our earlier papers, we combine strong and weak lensing constraints secured with Hubble Space Telescope and Subaru imaging with the radial profile of the stellar velocity dispersion of the central galaxy, essential for separating the baryonic mass distribution in the cluster core. Hydrostatic mass estimates from Chandra X-ray observations further constrain the solution. These combined datasets provide nearly continuous constraints extending from 2 kpc to 1.5 Mpc in radius, allowing stringent tests of results from recent numerical simulations. Two key improvements in our data and its analysis make this the most robust case yet for a shallow slope \beta of the DM density profile \rho_DM ~ r^-\beta on small scales. First, following deep Keck spectroscopy, we have secured the stellar velocity dispersion profile to a radius of 26 kpc for the first time in a lensing cluster. Secondly, we improve our previous analysis by adopting a triaxial DM distribution and axisymmetric dynamical models. We demonstate that in this remarkably well-constrained system, the logarithmic slope of the DM density at small radii is \beta < 1.0 (95% confidence). An improved treatment of baryonic physics is necessary, but possibly insufficient, to reconcile our observations with the recent results of high-resolution simulations.

LoCuSS: A COMPARISON OF CLUSTER MASS MEASUREMENTS FROMXMM-NEWTONAND SUBARU—TESTING DEVIATION FROM HYDROSTATIC EQUILIBRIUM AND NON-THERMAL PRESSURE SUPPORT

We compare X-ray hydrostatic and weak-lensing mass estimates for a sample of 12 clusters that have been observed with both XMM-Newton and Subaru. At an over-density of \Delta=500, we obtain 1-M^{X}/M^{WL}=0.01+/-0.07 for the whole sample. We also divided the sample into undisturbed and disturbed sub-samples based on quantitative X-ray morphologies using asymmetry and fluctuation parameters, obtaining 1-M^{X}/M^{WL}=0.09+/-0.06 and -0.06+/-0.12 for the undisturbed and disturbed clusters, respectively. In addition to non-thermal pressure support, there may be a competing effect associated with adiabatic compression and/or shock heating which leads to overestimate of X-ray hydrostatic masses for disturbed clusters, for example, in the famous merging cluster A1914. Despite the modest statistical significance of the mass discrepancy, on average, in the undisturbed clusters, we detect a clear trend of improving agreement between M^{X} and M^{WL} as a function of increasing over-density, M^{X}/M^{WL}=(0.908+/-0.004)+(0.187+/-0.010) \log_{10}(\Delta /500). We also examine the gas mass fractions, f_{gas}=M^{gas}/M^{WL}, finding that they are an increasing function of cluster radius, with no dependence on dynamical state, in agreement with predictions from numerical simulations. Overall, our results demonstrate that XMM-Newton and Subaru are a powerful combination for calibrating systematic uncertainties in cluster mass measurements.

A LINE-OF-SIGHT GALAXY CLUSTER COLLISION: SIMULATED X-RAY OBSERVATIONS

Several lines of evidence have suggested that the the galaxy cluster Cl 0024+17, an apparently relaxed system, is actually a collision of two clusters, the interaction occurring along our line of sight. In this paper we present a high-resolution N-body/hydrodynamics simulation of such a collision. We have created mock X-ray observations of our simulated system using MARX, a program that simulates the on-orbit performance of the Chandra X-ray Observatory. We analyze these simulated data to generate radial profiles of the surface brightness and temperature. At later times, t = 2.0 3.0 Gyr after the collision, the simulated surface brightness profiles are better fit by a superposition of two β-model profiles than a single profile, in agreement with the observations of Cl 0024+17. In general, due to projection effects, much of the post-collision density and temperature structure of the clusters is not seen in the observations. In particular, the observed temperatures from spectral fitting are much lower than the temperature of the hottest gas. We determine from our fitted profiles that if the system is modeled as a single cluster, the hydrostatic mass estimate is a factor �2-3 less than the actual mass, but if the system is modeled as two galaxy clusters in superposition, a hydrostatic mass estimation can be made which is accurate to within �10%. We examine some implications of these results for galaxy cluster X-ray surveys. Subject headings: galaxies: clusters: general — galaxies: clusters: individual (Cl 0024+17)— methods: N-body simulations — X-rays: galaxies: clusters

The LX—M relation of clusters of galaxies

Abstract We present a new measurement of the scaling relation between X-ray luminosity and total mass for 17 000 galaxy clusters in the maxBCG cluster sample. Stacking subsamples within fixed ranges of optical richness, N200, we measure the mean 0.1–2.4 keV X-ray luminosity, 〈LX〉 , from the ROSAT All-Sky Survey. The mean mass, 〈M200〉, is measured from weak gravitational lensing of SDSS background galaxies. For 9 ⩽ N200 &amp;lt; 200, the data are well fitted by a power law, 〈LX〉/1042h−2 erg s−1=[12.6+1.4−1.3 (stat) ± 1.6 (sys)](〈M200〉/1014h−1 M⊙)1.65±0.13. The slope agrees to within 10 per cent with previous estimates based on X-ray selected catalogues, implying that the covariance in LX and N200 at a fixed halo mass is not large. The luminosity intercept is 30 per cent, or 2σ, lower than that determined from the X-ray flux-limited sample of Reiprich &amp; Böhringer, assuming hydrostatic equilibrium. This slight difference could arise from a combination of Malmquist bias and/or systematic error in hydrostatic mass estimates, both of which are expected. The intercept agrees with that derived by Stanek et al. using a model for the statistical correspondence between clusters and haloes in a WMAP3 cosmology with power spectrum normalization s8= 0.85. Similar exercises applied to future data sets will allow constraints on the covariance among optical and hot gas properties of clusters at a fixed mass.

Cluster Structure in Cosmological Simulations. I. Correlation to Observables, Mass Estimates, and Evolution

We use Enzo, a hybrid Eulerian AMR/N-body code including non-gravitational heating and cooling, to explore the morphology of the X-ray gas in clusters of galaxies and its evolution in current generation cosmological simulations. We employ and compare two observationally motivated structure measures: power ratios and centroid shift. Overall, the structure of our simulated clusters compares remarkably well to low-redshift observations, although some differences remain that may point to incomplete gas physics. We find no dependence on cluster structure in the mass-observable scaling relations, T_X-M and Y_X-M, when using the true cluster masses. However, estimates of the total mass based on the assumption of hydrostatic equilibrium, as assumed in observational studies, are systematically low. We show that the hydrostatic mass bias strongly correlates with cluster structure and, more weakly, with cluster mass. When the hydrostatic masses are used, the mass-observable scaling relations and gas mass fractions depend significantly on cluster morphology, and the true relations are not recovered even if the most relaxed clusters are used. We show that cluster structure, via the power ratios, can be used to effectively correct the hydrostatic mass estimates and mass-scaling relations, suggesting that we can calibrate for this systematic effect in cosmological studies. Similar to observational studies, we find that cluster structure, particularly centroid shift, evolves with redshift. This evolution is mild but will lead to additional errors at high redshift. Projection along the line of sight leads to significant uncertainty in the structure of individual clusters: less than 50% of clusters which appear relaxed in projection based on our structure measures are truly relaxed.

Effects of Galaxy Formation on Thermodynamics of the Intracluster Medium

We present detailed comparisons of the intracluster medium (ICM) in cosmological Eulerian cluster simulations with deep Chandra observations of nearby relaxed clusters. To assess the impact of galaxy formation, we compare two sets of simulations, one performed in the non-radiative regime and another with radiative cooling and several physical processes critical to various aspects of galaxy formation: star formation, metal enrichment and stellar feedback. We show that the observed ICM properties outside cluster cores are well-reproduced in the simulations that include cooling and star formation, while the non-radiative simulations predict an overall shape of the ICM profiles inconsistent with observations. In particular, we find that the ICM entropy in our runs with cooling is enhanced to the observed levels at radii as large as half of the virial radius. We also find that outside cluster cores entropy scaling with the mean ICM temperature in both simulations and Chandra observations is consistent with being self-similar within current error bars. We find that the pressure profiles of simulated clusters are also close to self-similar and exhibit little cluster-to-cluster scatter. The X-ray observable-total mass relations for our simulated sample agree with the Chandra measurements to \~10%-20% in normalization. We show that this systematic difference could be caused by the subsonic gas motions, unaccounted for in X-ray hydrostatic mass estimates. The much improved agreement of simulations and observations in the ICM profiles and scaling relations is encouraging and the existence of tight relations of X-ray observables, such as Yx, and total cluster mass and the simple redshift evolution of these relations hold promise for the use of clusters as cosmological probes.

The X‐Ray Luminosity–Mass Relation for Local Clusters of Galaxies

We investigate the relationship between soft 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, $L \spropto M^p\rhoc^s(z)$. 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.

ChandraSample of Nearby Relaxed Galaxy Clusters: Mass, Gas Fraction, and Mass‐Temperature Relation

We present gas and total mass profiles for 13 low-redshift, relaxed clusters spanning a temperature range 0.7-9 keV, derived from all available Chandra data of sufficient quality. In all clusters, gas temperature profiles are measured to large radii (Vikhlinin et al.) so that direct hydrostatic mass estimates are possible to nearly r_500 or beyond. The gas density was accurately traced to larger radii; its profile is not described well by a beta-model, showing continuous steepening with radius. The derived rho_tot profiles and their scaling with mass generally follow the Navarro-Frenk-White model with concentration expected for dark matter halos in LambdaCDM cosmology. In the inner region (r<0.1r_500), the gas density and temperature profiles exhibit significant scatter and trends with mass, but they become nearly self-similar at larger radii. Correspondingly, we find that the slope of the mass-temperature relation for these relaxed clusters is in good agreement with the simple self-similar behavior, M_500 ~ T^alpha, where alpha=(1.5-1.6)+-0.1, if the gas temperatures are measured excluding the central cool cores. The normalization of this M-T relation is significantly, by =~ 30%, higher than most previous X-ray determinations. We derive accurate gas mass fraction profiles, which show increase both with radius and cluster mass. The enclosed f_gas profiles within r_2500 =~ 0.4 r_500 have not yet reached any asymptotic value and are still far (by a factor of 1.5-2) from the Universal baryon fraction according to the CMB observations. The f_gas trends become weaker and its values closer to Universal at larger radii, in particular, in spherical shells r_2500<r<r_500.

ITAL]Chandra[/ITAL] Estimate of the Magnetic Field Strength near the Cold Front in A3667

We use the Chandra observation of the cold front in the intracluster gas of A3667 to estimate the magnetic field strength near the front. The front is seen in the Chandra data as a sharp discontinuity in the gas density that delineates a large body of dense cool gas moving with near-sonic velocity through the less dense, hotter gas. Without a magnetic field, the front should be quickly disturbed by the Kelvin-Helmholtz instability arising from tangential motion of gas layers. However, the Chandra image shows that the front is stable within a ±30° sector in the direction of the cloud motion, beyond which it gradually disappears. We suggest that the Kelvin-Helmholtz instability within the ±30° sector is suppressed by the surface tension of the magnetic field whose field lines are parallel to the front. The required field strength is B ~ 10 μG. The magnetic field near the front is expected to be stronger and to have a very different structure compared with the bulk of the intergalactic medium because the field lines are stretched by the tangential gas motions. Such a magnetic configuration, once formed, would effectively stop the plasma diffusion and heat conduction across the front and may inhibit gas mixing during the subcluster merger. We note that even the increased magnetic field near the front contributes only 10%-20% to the total gas pressure, and therefore magnetic pressure is unimportant for hydrostatic cluster mass estimates.