Mass-temperature Relation Research Articles

The ClusterMgas‐TXRelation: Evidence for a High Level of Preheating

Recent X-ray observations have been used to demonstrate that the cluster gas mass-temperature relation is steeper than theoretical self-similar predictions drawn from numerical simulations that consider the evolution of the cluster gas through the effects of gravity and shock heating alone. One possible explanation for this is that the gas mass fraction is not constant across clusters of different temperature, as is usually assumed. Observationally, however, there is no compelling evidence for gas mass fraction variation, especially in the case of hot clusters. Seeking an alternative physical explanation for the observed trends, we investigate the role in the cluster gas mass-temperature relation of the preheating of the intracluster medium by some arbitrary source for clusters with emission-weighted mean temperatures of TX 3 keV. Making use of the physically motivated, analytic model developed in 2002 by Babul and coworkers, we find that preheating does, indeed, lead to a steeper relation. This is in agreement with previous theoretical studies on the relation. However, in apparent conflict with these studies, we argue that a level of entropy injection is required to match observations. In particular, an entropy floor of 300 keV cm2 is required. We also present a new test, namely, the study of the relation within different fixed radii. This allows one to indirectly probe the density profiles of clusters, since it samples different fractions of the virial radius for clusters of different temperature. This test also confirms that a high level of preheating is required to match observations.

Modified Entropy Models for the Intracluster Medium

We present a set of cluster models that link the present-day properties of clusters to the processes that govern galaxy formation. These models treat the entropy distribution of the intracluster medium as its most fundamental property. Because convection strives to establish an entropy gradient that rises with radius, the observable properties of a relaxed cluster depend entirely on its dark-matter potential and the entropy distribution of its uncondensed gas. Guided by simulations, we compute the intracluster entropy distribution that arises in the absence of radiative cooling and supernova heating by assuming that the gas-density distribution would be identical to that of the dark matter. The lowest-entropy gas would then fall below a critical entropy threshold at which the cooling time equals a Hubble time. Radiative cooling and whatever feedback is associated with it must modify the entropy of that low-entropy gas, changing the overall entropy distribution function and thereby altering the observable properties of the cluster. Using some phenomenological prescriptions for entropy modification based on the existence of this cooling threshold, we construct a remarkably realistic set of cluster models. The surface-brightness profiles, mass-temperature relation, and luminosity-temperature relation of observed clusters all naturally emerge from these models. By introducing a single adjustable parameter related to the amount of intracluster gas that can cool within a Hubble time, we can also reproduce the observed temperature gradients of clusters and the deviations of cooling-flow clusters from the standard luminosity-temperature relation.

A new measurement of the X-ray temperature function of clusters of galaxies

We present a newly measured X-ray temperature function of galaxy clusters using a complete flux-limited sample of 61 clusters. The sample is constructed with the total survey area of 8.14 steradians and the flux limit of ergs s-1 cm-2 in the 0.1–2.4 keV band. X-ray temperatures and fluxes of the sample clusters were accurately measured with ASCA and ROSAT data. The derived temperature function covers an unprecedentedly wide temperature range of 1.4–11 keV. By fitting these data with theoretically predicted temperature functions given by the Press-Schechter formalism together with a recent formation approximation and the CDM power spectrum, we obtained tight and individual constraints on and . We also employed the Formation-Epoch model in which the distribution in the formation epoch of clusters as well as the temperature evolution are taken into account, showing significantly different results. Systematics caused by the uncertainty in the mass-temperature relation are studied and found to be as large as the statistical errors.

Can simulations reproduce the observed temperaturemass relation for clusters of galaxies?

It has become increasingly apparent that traditional hydrodynamical simulations of galaxy clusters are unable to reproduce the observed properties of galaxy clusters, in particular overpredicting the mass corresponding to a given cluster temperature. Such overestimation may lead to systematic errors in results using galaxy clusters as cosmological probes, such as constraints on the density perturbation normalization σ8. In this paper we demonstrate that inclusion of additional gas physics, namely radiative cooling and a possible pre-heating of gas prior to cluster formation, is able to bring the temperature—mass relation in the innermost parts of clusters into good agreement with recent determinations by Allen, Schmidt & Fabian using Chandra data.

Mass‐Temperature Relation of Galaxy Clusters: A Theoretical Study

Combining conservation of energy throughout the nearly spherical collapse of galaxy clusters with the virial theorem, we derive the mass-temperature relation for X-ray clusters of galaxies, T = CM2/3. The normalization factor C and the scatter of the relation are determined from first principles, with the additional assumption of an initial Gaussian random field. We are also able to reproduce the recently observed break in the M-T relation at T ~ 3 keV, based on the scatter in the underlying density field for a low-density ΛCDM cosmology. Finally, by combining observational data of high-redshift clusters with our theoretical formalism, we find a semiempirical temperature-mass relation that is expected to hold at redshifts up to unity with less than 20% error.

The X-ray virial relations for relaxed lensing clusters observed withChandra

We examine the relations linking mass, X-ray temperature and bolometric luminosity for a sample of luminous, relatively relaxed clusters of galaxies observed with the Chandra Observatory, for which independent confirmation of the mass results is available from gravitational lensing studies. Within radii corresponding to a fixed overdensity Δ = 2500 with respect to the critical density at the redshifts of the clusters, the observed temperature profiles, scaled in units of T2500 and r2500, exhibit an approximately universal form which rises within r ∼ 0.3r2500 and then remains approximately constant out to r2500. We obtain best-fitting slopes for the mass–temperature and temperature–luminosity relations consistent with the predictions from simple scaling arguments i.e. and , respectively. We confirm the presence of a systematic offset of ∼40 per cent between the normalizations of the observed and predicted mass–temperature relations for both SCDM and ΛCDM cosmologies.

Problems for Modified Newtonian Dynamics in Clusters and the Lyα Forest?

The observed dynamics of gas and stars on galactic and larger scales cannot be accounted for by self-gravity, indicating that there are large quantities of unseen matter or that gravity is non-Newtonian in these regimes. Milgrom's modified Newtonian dynamics (MOND) postulates that Newton's laws are modified at very low acceleration, and can account for the rotation curves of galaxies and some other astrophysical observations, without dark matter. Here we apply MOND to two independent physical systems: Lyα absorbers and galaxy clusters. While physically distinct, both are simple hydrodynamical systems with characteristic accelerations in the MOND regime. We find that, because MOND violates the strong equivalence principle, the properties of Lyα absorbers depend strongly on the (unknown) background acceleration field in which they are embedded. If this field is small compared to their internal accelerations, then the absorbers are more dense and about 10 times smaller than in Newtonian gravity with dark matter, in conflict with sizes inferred from quasar pair studies. If, however, the background field is rather large, then the absorbers take on properties similar to those predicted in the cold dark matter picture. In clusters MOND appears to explain the observed (baryonic) mass-temperature relation. However, given observed gas density and enclosed mass profiles and the assumption of hydrostatic equilibrium, MOND predicts radial temperature profiles that disagree badly with observations. We show this explicitly for the Virgo, Abell 2199, and Coma Clusters, but the results are general and seem very difficult to avoid. If this discrepancy is to be resolved by positing additional (presumably baryonic) dark matter, then this dark matter must have ~1-3 times the cluster gas mass within 1 Mpc and about 10 times the gas mass within 200 kpc. This result strongly disfavors MOND as an alternative to dark matter.

The effect of formation redshifts on the cluster mass-temperature relation

I employ an ensemble of hydrodynamical simulations and the xspec mekal emission model to reproduce observable spectral and flux-weighted temperatures for 24 clusters. Each cluster is imaged at 16 points in its history, which allows the investigation of evolutionary effects on the mass—temperature relation. In the zero-redshift scaling relations, I find no evidence for a relationship between cluster temperature and formation epoch for those clusters that acquired 75 per cent of their final mass since a redshift of 0.6. This result holds for both observable and intrinsic intracluster medium temperatures, and implies that halo formation epochs are not an important variable in analysis of observable cluster temperature functions.

Universal gas density and temperature profile

We present an analytic approach to predict gas density and temperature profiles in dark matter haloes. We assume that the gas density profile traces the dark matter density profile in outer parts of the haloes, as suggested by many hydrodynamic simulations. Under this assumption, the hydrostatic equilibrium uniquely fixes the two free parameters in the model, the mass-temperature normalization and the polytropic index, that determine the temperature profile. This enables us to predict a universal gas profile from any universal dark matter profile. Our results show that gas tracing dark matter in the outer parts of the haloes is inconsistent with gas being isothermal; on the contrary, it requires temperature to decrease slowly with radius, in agreement with observations. We compare our predictions for X-ray surface brightness profiles of the haloes and the mass-temperature relation with observations. We find that they are generally in a good agreement. We compare the universal profile with the beta profile and find that, although the beta profile gives a reasonable fit to our predicted profiles, the deviation from it can explain many of the observed trends, once we take into account the observational selection effects. Our model predicts that the mass-temperature relation does not follow the self-similar relation because of the mass-dependent halo concentration. We also predict surface brightness profiles of the Sunyaev-Zel'dovich (SZ) effect. We find that fitted to the beta profile the core radii and beta inferred from the SZ effect are systematically larger than those from the X-ray measurement.

Power-spectrum normalization from the local abundance of rich clusters of galaxies

The number density of rich galaxy clusters still provides the most robust way of normalizing the power spectrum of dark matter perturbations on scales relevant to large-scale structure. We revisit this constraint in light of several recent developments: (1) the availability of well-defined samples of local clusters with relatively accurate X-ray temperatures; (2) new theoretical mass functions for dark matter haloes which provide a good fit to large numerical simulations; (3) more accurate mass-temperature relations from larger catalogs of hydrodynamical simulations; (4) the requirement to consider closed as well as open and flat cosmologies to obtain full multi-parameter likelihood constraints for CMB and SNe studies. We present a new sample of clusters drawn from the literature and use this sample to obtain improved results on sigma_8, the normalization of the matter power spectrum on scales of 8 h^{-1} Mpc, as a function of the matter density and cosmological constant in a Universe with general curvature. We discuss our differences with previous work, and the remaining major sources of uncertainty. Final results on the 68 per cent confidence region, approximately independent of power spectrum shape, can be expressed as constraints on sigma at an appropriate cluster normalization scale R_Cl. We provide fitting formulas for R_Cl and sigma(R_Cl) for general cosmologies, as well as for sigma_8 as a function of cosmology and shape parameter Gamma. For flat models we find approximately sigma_8 \simeq 0.495^{+0.034}_{-0.037}) Omega_M^{-0.60} for Gamma=0.23, where the error bar is dominated by uncertainty in the mass-temperature relation.

Effects of Preheating on X‐Ray Scaling Relations in Galaxy Clusters

The failure of purely gravitational and gasdynamical models of X-ray cluster formation to reproduce basic observed properties of the local cluster population suggests the need for one or more additional physical processes operating on the intracluster medium (ICM). We present results from 84 moderate-resolution gasdynamic simulations designed to investigate systematically the effects of preheating (an early elevated ICM adiabat) on the resultant, local X-ray size-temperature, luminosity-temperature, and ICM mass-temperature relations. Seven sets of 12 simulations are performed for a ΛCDM cosmology, each set characterized by a different initial entropy level Si. The slopes of the observable relations steepen monotonically as Si is increased. Observed slopes for all three relations are reproduced by models with Si ∈ 55-150 keV cm2, levels that compare favorably to empirical determinations of core ICM entropy by Lloyd-Davies, Ponman, & Cannon. The redshift evolution for the case of a locally successful model with Si = 106 keV cm2 is presented. At temperatures kT 3 keV, little or no evolution in physical isophotal sizes or bolometric luminosities is expected to z 1. The ICM and total masses at fixed T are lower at higher z, as expected from the virial theorem. ICM mass fractions show a mild T dependence. Clusters with kT 3 keV contain ICM mass fractions depressed by modest amounts (25%) below the cosmic mean baryon fraction Ωb/Ωm; hot clusters subject to preheating remain good tracers of the cosmic mix of clustered mass components at redshifts z 1.

The temperature-mass relation in magnetized galaxy clusters

We use cosmological, magneto-hydrodynamic simulations of galaxy clusters to quantify the dynamical importance of magnetic fields in these clusters. The set-up of initial magnetic field strengths at high redshifts is chosen such that observed Faraday-rotation measurements in low-redshift clusters are well reproduced in the simulations. We compute the radial profiles of the intracluster gas temperature and of the thermal and magnetic pressure in a set of clusters simulated in the framework of an Einstein-de Sitter and a low-density, spatially-flat CDM cosmological model. We find that, for a realistic range of initial magnetic field strengths, the temperature of the intracluster gas changes by less than $\approx5%$.

Details of the mass-temperature relation for clusters of galaxies

We present results on the total mass and temperature determination using two samples of clusters of galaxies. One sample is constructed with emphasis on the completeness of the sample, while the advantage of the other is the use of the temperature profiles, derived with ASCA. We obtain remarkably similar fits to the M-T relation for both samples, with the normalization and the slope significantly different from both prediction of self-similar collapse and hydrodynamical simulations. We discuss the origin of these discrepancies and also combine the X-ray mass with velocity dispersion measurements to provide a comparison with high-resolution dark matter simulations. Finally, we discuss the importance of a cluster formation epoch in the observed M-T relation.

The Mass‐Temperature Relation of 22 Nearby Clusters

We present a new investigation of the mass-temperature (Mtot-TX) relation of 22 nearby clusters based on the analysis of their ROSAT X-ray surface brightness profiles (SX ) and their ASCA emission-weighted temperatures. Two methods of the cluster mass estimations are employed and their results are compared: (1) the conventional β-model for gas distribution along with the isothermal and hydrostatic equilibrium assumptions, and (2) the NFW profile for dark matter distribution whose characteristic density and length are determined by the observed SX(r). These two models yield essentially the same goodness of fits for SX(r) and the similar Mtot-TX relations, with the latter demonstrating a significant departure from the simple gravitational scaling of Mtot ∝ T. It is also shown that the best-fit Mtot-TX relations could be reconciled with the theoretical expectation if the low-temperature clusters (TX < 3.5 keV) are excluded from the list, which lends support to the scenario that the intracluster medium is preheated in the early phase of cluster formation. Together with the entropy-temperature distribution, the existence of a similarity break at TX = 3-4 keV in the dynamical scaling relations for galaxy clusters has been confirmed.

Cluster Temperature Evolution: The Mass‐Temperature Relation

Evolution of the cluster temperature function is extremely sensitive to the mean matter density of the universe. Current measurements based on cluster temperature surveys indicate that ΩM ≈ 0.3 with a 1 σ statistical error ~0.1, but the systematic errors in this method are of comparable size. Many more high-z cluster temperatures will be arriving from Chandra and XMM in the near future. In preparation for future cluster temperature surveys, this paper analyzes the cluster mass-temperature relation, with the intention of identifying and reducing the systematic errors it introduces into measurements of cosmological parameters. We show that the usual derivation of this relation from spherical top-hat collapse is physically inconsistent and propose a more realistic derivation based on a hierarchical merging model that more faithfully reflects the gradual ceasing of cluster evolution in a low-ΩM universe. We also analyze the effects of current systematic uncertainties in the Mvir-TX relation and show that they introduce a systematic uncertainty of ~0.1 in the best-fitting ΩM. Future improvements in the accuracy of the Mvir-TX relation will most likely come from comparisons of predicted cluster temperature functions with temperature functions derived directly from large-scale structure simulations.

Cosmological Smoothed Particle Hydrodynamic Simulations with Four Million Particles: Statistical Properties of X‐Ray Clusters in a Low‐Density Universe

We present results from a series of cosmological smoothed particle hydrodynamics (SPH) simulations coupled with the particle-particle-particle-mesh solver for the gravitational force. The simulations are designed to predict the statistical properties of X-ray clusters of galaxies as well as to study the formation of galaxies. We have seven simulation runs with different assumptions about the thermal state of the intracluster gas. Following the recent work by Pearce and coworkers, we modify our SPH algorithm so as to phenomenologically incorporate galaxy formation by decoupling the cooled gas particles from the hot gas particles. All the simulations employ 1283 particles both for dark matter and for gas components and thus constitute the largest systematic catalogs of clusters simulated in the SPH method performed so far. These enable us to compare the analytical predictions about statistical properties of X-ray clusters against our direct simulation results in an unbiased manner. We find that the luminosities of the simulated clusters are quite sensitive to the thermal history and also to the numerical resolution of the simulations and thus are not reliable. On the other hand, the mass-temperature relation for the simulated clusters is fairly insensitive to the assumptions of the thermal state of the intracluster gas, is robust against the numerical resolution, and in fact agrees well with the analytic prediction. Therefore, prediction of the X-ray temperature functions of clusters on the basis of the Press-Schechter mass function and the virial equilibrium is fairly reliable.

FORMULA][F]Ω[INF]m[/INF][/F][/FORMULA] from the Temperature-Redshift Distribution of EMSS Clusters of Galaxies

We constrain Ωm through a maximum likelihood analysis of temperatures and redshifts of the high-redshift clusters from the Extended Medium-Sensitivity Survey (EMSS). We simultaneously fit the low-redshift Markevitch sample (an all-sky sample from ROSAT with z = 0.04-0.09), a moderate redshift EMSS sample from Henry (nine clusters with z = 0.3-0.4), and a more distant EMSS sample (five clusters with z = 0.5-0.83 from Donahue et al.) finding best-fit values of Ωm = 0.45 ± 0.1 for an open universe and Ωm = 0.27 ± 0.1 for a flat universe. We individually analyze the effects of our governing assumptions, including the evolution and dispersion of the cluster luminosity-temperature relation, the evolution and dispersion of the cluster mass-temperature relation, the choice of low-redshift cluster sample, and the accuracy of the standard Press-Schechter formalism. We examine whether the existence of the massive distant cluster MS 1054-0321 skews our results, and we find its effect to be small. From our maximum likelihood analysis we conclude that our results are not very sensitive to our assumptions, and bootstrap analysis shows that our results are not sensitive to the current temperature measurement uncertainties. The systematic uncertainties are ~±0.1, and Ωm = 1 universes are ruled out at greater than 99.7% (3 σ) confidence.

The M- TX relation for clusters of galaxies

If clusters of galaxies are self-similar and the intracluster gas is in global quasiequilibrium with the dark matter, a tight relation between mass and X-ray temperature is expected in most cosmological models. We here calibrate this relation using 8 clusters with well-defined global temperatures measured with ASCA and masses inferred from gravitational lensing. The surface lensing masses are deprojected in accordance with N-body simulations and analytic results. The data are well-fitted by the theoretical mass-temperature relation and are consistent with the empirical normalisation found in gasdynamic simulations. As there is no discrepancy between the lensing and X-ray derived masses this approach could lead to a powerful and expedient way of measuring masses of clusters of galaxies. Constraints on N( z) and Λ can also be obtained by studying high-redshift cluster lenses.

The mass--temperature relation for clusters of galaxies

A tight mass–temperature relation, M(r)/r ∝ T TX, is expected in most cosmological models if clusters of galaxies are homologous and the intracluster gas is in global equilibrium with the dark matter. We here calibrate this relation using eight clusters with well-defined global temperatures measured with ASCA and masses inferred from weak and strong gravitational lensing. The surface lensing masses are deprojected in accordance with N-body simulations and analytic results. The data are well-fitted by the mass–temperature relation and are consistent with the empirical normalization found by Evrard et al. (1996) using gas-dynamic simulations. Thus, there is no discrepancy between lensing and X-ray-derived masses using this approach. The dispersion around the relation is 27 per cent, entirely dominated by observational errors. The next generation of X-ray telescopes combined with wide-field HST imaging could provide a sensitive test of the normalization and intrinsic scatter of the relation, resulting in a powerful and expedient way of measuring masses of clusters of galaxies. In addition, as M(r)/r (as derived from lensing) is dependent on the cosmological model at high redshift, the relation represents a new tool for determination of cosmological parameters, notably the cosmological constant Λ.

On the Evolution of the Temperature–Virial Mass Relation for Clusters of Galaxies

X-ray temperature measurements of clusters of galaxies are now reaching to redshifts high enough to constrain ? -->0. A redshift-dependent relation that maps these X-ray temperatures to the virial masses of clusters is an essential ingredient when one is trying to determine cosmological parameters from cluster evolution. Most such relations assume that clusters form from top-hat perturbations that virialized just before the time at which we are observing them. The smaller ? -->0 is, the less accurate these relations become. Here we derive a relation between virial mass and cluster temperature that allows for the fact that clusters form gradually and cease forming when the density of the universe drops well below the critical value. We show how sensitively the expected redshift distribution of clusters depends on the mass-temperature relation used and argue that one needs to use a relation that yields no evolution in the low-? -->0 limit.