X-ray Surface Brightness Profiles Research Articles

An Unusual Discontinuity in the X‐Ray Surface Brightness Profile of NGC 507: Evidence of an Abundance Gradient?

We present results from a 45 ks Chandra ACIS-I observation of the nearby (z = 0.01646) NGC 507 group. The X-ray surface brightness profile of the outer region of the group is well described by an isothermal β-profile consistent with earlier ROSAT observations. We find a sharp edge or discontinuity in the radial surface brightness profile 55 kpc east and southeast of NGC 507 covering an ~125° arc. At the sharpest part of the discontinuity, the surface brightness declines by a factor of ~2 over a distance of 6.9 kpc (~15''). The inner and outer gas temperatures across the discontinuity differ by only about 0.2 keV (interior and exterior gas temperatures are 1.2 and 1.4 keV, respectively). Spectral analysis indicates that there is a gradient in the elemental abundance across the discontinuity, and comparison with the low-resolution NRAO VLA Sky Survey radio maps suggests that the discontinuity is aligned with a low surface brightness radio lobe. We conclude that the appearance of this discontinuity may be the result of two phenomena: the transonic (ℳ ~ 0.75-1) expansion/inflation of the radio lobe close to our line of sight and the transport of high-abundance material from the center of the galaxy due to this expansion.

The X-ray surface brightness profiles of hot galaxy clusters up to $\vec z$ ~ 0.8: Evidence for self-similarity and constraints on $\Omega_\mathsf{0}$

We study the surface brightness profiles of a sample of 25 distant hot clusters, observed with ROSAT, with published temperatures from ASCA. For both open and flat cosmological models, the derived emission measure profiles are scaled according to the self-similar model of cluster formation. We use the standard scaling relations of cluster properties with redshift and temperature, with the empirical slope of the relation derived by Neumann & Arnaud ([CITE]). Using a test, we perform a quantitative comparison of the scaled emission measure profiles of distant clusters with a local reference profile derived from the sample of 15 hot nearby clusters compiled by Neumann & Arnaud (1999), which were found to obey self-similarity. This comparison allows us to both check the validity of the self-similar model across the redshift range , and to constrain the cosmological parameters. For a low-density flat universe, the scaled distant cluster data were found to be consistent, both in shape and normalisation, with the local reference profile. It indicates that hot clusters constitute a homologous family up to high redshifts, and gives support to the standard picture of structure formation for the dark matter component. Because of the intrinsic regularity in the hot cluster population, the scaled profiles can be used as distance indicators, the correct cosmology being the one for which the various profiles at different redshifts coincide. The intrinsic limitations of the method, in particular possible systematic errors and biases related to the model uncertainties, are discussed. Using the standard evolution model, the present data allow us to put a tight constraint on for a flat Universe: at 90% confidence level (statistical errors only). The critical model () was excluded at the 98% confidence level. Consistently, the observed evolution of the normalisation of the relation was found to comply with the self-similar model for , . The constraint derived on is in remarkable agreement with the constraint obtained from luminosity distances to SNI or from combined analysis of the power spectrum of the 2dF galaxy redshift Survey and the Cosmic Microwave Background anisotropies.

DeepROSATHRI Observations of the NGC 1399/NGC 1404 Region: Morphology and Structure of the X‐Ray Halo

We present the analysis of a deep (167 ks) ROSAT HRI observation of the cD galaxy NGC 1399 in the Fornax Cluster, comparing it with previous work on this galaxy and with recent Chandra data. We find, in agreement with previous observations, an extended and asymmetric gaseous halo with a luminosity (in the 0.1-2.4 keV energy band) of LX = (5.50 ± 0.04) × 1041 ergs s-1 within 46 kpc (assuming a distance of D = 19 Mpc). Using both HRI and, at larger radii, archival PSPC data, we find that the radial behavior of the X-ray surface brightness profile is not consistent with a simple β-model and suggests instead three distinct components. We use a multicomponent bidimensional model to study in detail these three components, which we identify respectively with the cooling flow region, the galactic halo, and the cluster halo. From these data we derive a binding mass distribution in agreement with that suggested by optical dynamical indicators, with an inner core dominated by luminous matter and an extended dark halo differently distributed on galactic and cluster scales. The HRI data and a preliminary analysis of Chandra public data allow us to detect significant density fluctuations in the halo. We discuss possible nonequilibrium scenarios to explain the hot halo structure, including tidal interactions with neighboring galaxies, ram stripping from the intracluster medium, and merging events. In the innermost region of NGC 1399, the comparison between the X-ray and radio emission suggests that the radio-emitting plasma is displacing and producing shocks in the hot X-ray-emitting gas. We do not detect the nuclear source in X-rays, and we pose an upper limit of ~4 × 1039 ergs s-1 (0.1-2.4 keV) to its X-ray luminosity. We found that the NGC 1404 halo is well represented by a single symmetric β-model and follows the stellar light profile within the inner 8 kpc. The mass distribution is similar to the "central" component of the NGC 1399 halo. At larger radii, ram pressure stripping from the intracluster gas produces strong asymmetries in the galactic halo. Finally, we discuss the properties of the point-source population, finding evidence of correlation between the source excess and NGC 1399.

Reexamination of the Galaxy Formation–regulated Gas Evolution Model in Groups and Clusters

As an alternative explanation of the entropy excess and the steepening of the X-ray luminosity-temperature relation in groups and clusters, the galaxy formation-regulated gas evolution (GG) model proposed recently by Bryan makes an attempt to incorporate the formation of galaxies into the evolution of gas without additional heating by nongravitational processes. This seems to provide a unified scheme for our understanding of the structures and evolution of both galaxies and gas in groups and clusters. In this paper, we present an extensive comparison of the X-ray properties of groups and clusters predicted by the GG model and those revealed by current X-ray observations, using various large data sources in the literature and also taking the observational selection effects into account. These include an independent check of the fundamental working hypothesis of the GG model, i.e., galaxy formation was less efficient in rich clusters than in groups, a new test of the radial gas distributions revealed by both the gas mass fraction and the X-ray surface brightness profiles, and an reexamination of the X-ray luminosity-temperature and entropy-temperature relations. In particular, it shows that the overall X-ray surface brightness profiles predicted by the GG model are very similar in shape, insensitive to the X-ray temperature, and the shallower X-ray surface brightness profiles seen at low-temperature systems may arise from the current observational selection effect. This can be used as the simplest approach to distinguishing between the GG model and the preheating scenario. The latter yields an intrinsically shallower gas distribution in groups than in rich clusters.

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.

Galaxy Morphological Segregation in Clusters: Local versus Global Conditions

We study the relative fraction of galaxy morphological types in clusters, as a function of the projected local galaxy density and different global parameters: cluster projected gas density, cluster projected total mass density , and reduced clustercentric distance. Since local and global densities are correlated, we have considered different tests to search for the parameters to which segregation show the strongest dependence. Also, we have explored the results of our analysis applied to the central regions of the clusters and their outskirts. We consider a sample of clusters of galaxies with temperature estimates to derive the projected mass density profile and the 500 density contrast radius ($r_{500}$) using the NFW model and the scaling relation respectively. The X-ray surface brightness profiles are used to obtain the projected gas density assuming the hydrostatic equilibrium model. Our results suggest that the morphological segregation in clusters is controlled by the local galaxy density in the outskirts. On the other hand, the global projected mass density, shows the strongest correlation with the fraction of morphological types in the central high density region, with a marginal dependence on the local galaxy density.

Testing the Universality of the TIS Model on Cluster Scales from the X-ray Surface Brightness Profiles

The truncated isothermal sphere (TIS) model has been recently suggested as an alternative for virialized dark halos (Shapiro et al. 1999). Both its profound theoretical motivation and its successful explanations for the galactic rotation curves and the gravitational scaling laws of clusters indicate that the TIS model is a promising candidate among other prevailing models such as the NFW profile and the Burkert profile. This promotes us to re-examine the universality of the TIS model on cluster scales from a different angle. Using an ensemble of X-ray surface brightness profiles of 45 clusters, we test the goodness of fit of the TIS predicted gas distributions to the X-ray data under the assumption of isothermal, hydrostatic equilibrium. Unlike the conventional β model or the NFW/Burkert profile, for which about half of the clusters have the reduced χ 2 ν values smaller than 2, ν the TIS model fails in the fitting of the X-ray surface brightness profiles of clusters in the sense that 38 out of the 45 clusters show χ 2 ν > 2. This may constitute a challenge for the universality of the TIS model unless the present analysis is seriously contaminated by other uncertainties including the negligence of non-gravitational heating processes and the unconventional sampling of the X-ray data.

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.

On the Radial Density Profile of Intracluster Gas Tracing the Isothermal Dark Halo with a Finite Core

The cusped NFW universal density profile suggested by typical CDM models has been challenged in recent years by the discoveries of the soft cores for a broad range of masses from dwarf galaxies to clusters of galaxies. It is thus desirable that a new, analytic model would instead become available for virialized dark halos. One promising candidate is probably the empirical density profile proposed by Burkert, which resembles an isothermal profile with a constant core in the inner region and matches the NFW profile at large radii. Meanwhile, such a revised dark halo (RDH) profile has turned out a great success on galactic scales. This stimulates us to apply the RDH profile to more massive systems like clusters of galaxies. In this paper we have made an attempt to derive the radial density profile of intracluster gas from the RDH profile, and compare it with those revealed by X-ray observations and inferred from the NFW profile. It is shown that the RDH predicted gas density can be well represented by the conventional beta model with a typical beta parameter of 0.7-0.9. Fitting the theoretically predicted X-ray surface brightness profile to an ensemble of 45 X-ray clusters, we find that the RDH and NFW profiles become to be almost indistinguishable. Yet, the RDH profile allows us to work out straightforwardly the central dark matter density of clusters from X-ray measurements. Using the 45 clusters, we find that the central densities of clusters have an average value of ~0.01 solar mass pc^{-3}, in agreement with the result estimated on galactic scales, which reinforces the claim for the presence of the soft halo cores over the entire mass range.

The Effects of Gasdynamics, Cooling, Star Formation, and Numerical Resolution in Simulations of Cluster Formation

We present the analysis of a suite of simulations of a Virgo-mass galaxy cluster. Undertaken within the framework of standard cold dark matter cosmology, these simulations were performed at differing resolutions and with increasingly complex physical processes, with the goal of identifying the effects of each on the evolution of the cluster. We focus on the cluster at the present epoch and examine properties including the radial distributions of density, temperature, entropy, and velocity. We also map observable projected properties such as the surface mass density, X-ray surface brightness, and Sunyaev-Zeldovich signature. We identify significant differences between the simulations, which highlights the need for caution when comparing numerical simulations to observations of galaxy clusters. While resolution affects the inner density profile in dark matter simulations, the addition of a gaseous component, especially one that cools and forms stars, affects the entire cluster. For example, in simulations with gasdynamics but no cooling, improving the gravitational force resolution from 200 to 14 kpc increases the X-ray luminosity and emission-weighted temperature by factors of 2.9 and 1.6, respectively, and it changes the form of the X-ray surface brightness and temperature profiles. At the higher resolution, a simulation that includes cooling and star formation converts 30% of the cluster baryons into stars and produces a massive central galaxy that substantially alters the cluster potential well. This cluster has 20% higher X-ray luminosity and 30% higher emission-weighted temperature than the corresponding cluster in the no-cooling simulation. Its properties are reasonably close to those of observed X-ray dominant (XD) clusters, with conversion of cooled gas into stars greatly reducing the observational conflicts found by Suginohara & Ostriker in simulations with cooling but no star formation. We conclude that both resolution and included physical processes play important roles in simulating the formation and evolution of galaxy clusters. Therefore, physical inferences drawn from simulations that do not include gaseous components that can cool and form stars present a poor representation of reality.

Properties of the doubleβmodel for intracluster gas

We present an extensive study of the double β model for the X-ray surface brightness profiles of clusters, and derive analytically the gas density and total masses of clusters under the hydrostatic equilibrium hypothesis. It is shown that the employment of the double β model instead of the conventional single β model can significantly improve the goodness-of-fit to the observed X-ray surface brightness profiles of clusters, which will in turn lead to a better determination of the gas and total mass distributions in clusters. In particular, the observationally fitted β parameter for the extended component in a double β model may become larger. This opens a new possibility of resolving the long-standing β discrepancy for clusters. Using an ensemble of 33 ROSAT PSPC observed clusters drawn from the Mohr, Mathiesen & Evrard sample, we find that the asymptotic value of βfit is 0.83±0.33 at large radii, consistent with both the average spectroscopic parameter βspec=0.78±0.37 and the result given by numerical simulations.

The Butcher-Oemler Effect at Moderate Redshift

We present the results of Butcher-Oemler–style analysis of three moderate-redshift (0.1 < z < 0.2) clusters that have bimodal X-ray surface brightness profiles. We find that at least two of these clusters exhibit unusually high fractions of blue galaxies (fb's) as compared with clusters at comparable redshifts studied by Butcher & Oemler. This implies that star formation is occurring in a high fraction of the galaxies in the two clusters. Our results are consistent with hierarchical clustering models in which subcluster-subcluster mergers create shocks in the intracluster medium. The shocks, in turn, induce simultaneous starbursts in a large fraction of cluster galaxies. Our study therefore lends weight to the hypothesis that the Butcher-Oemler effect is an environmental, as well as evolutionary, phenomenon.

The entropy and energy of intergalactic gas in galaxy clusters

Studies of the X-ray surface brightness profiles of clusters, coupled with theoretical considerations, suggest that the breaking of self-similarity in the hot gas results from an `entropy floor', established by some heating process, which affects the structure of the intracluster gas strongly in lower mass systems. Fitting analytical models for the radial variation in gas density and temperature to X-ray spectral images from the ROSAT PSPC and ASCA GIS, we derive gas entropy profiles for 20 galaxy clusters and groups. Scaling these profiles to coincide in the self-similar case, the lowest mass systems are found to have higher scaled entropy profiles than more massive systems. This appears to be due to a baseline entropy of 70-140 h50^-1/3 keV cm^2, depending on the extent to which shocks have been suppressed in low mass systems. The extra entropy may be present in all systems, but is detectable only in poor clusters, compared to the entropy generated by gravitational collapse. This excess entropy appears to be distributed uniformly with radius outside the central cooling regions. We determine the energy associated with this entropy floor, by studying the net reduction in binding energy of the gas in low mass systems, and find that it corresponds to a preheating temperature of ~0.3 keV. Since the relationship between entropy and energy injection depends upon gas density, we can combine the excesses of 70-140 keV cm^2 and 0.3 keV to derive the typical electron density of the gas into which the energy was injected. The resulting value of 1-3x10^-4 h50^1/2 cm-3, implies that the heating must have happened prior to cluster collapse but after a redshift z~7-10. The energy requirement is well matched to the energy from supernova explosions responsible for the metals which now pollute the intracluster gas.

Constraints on the asymptotic baryon fractions of galaxy clusters at large radii

While X-ray measurements have so far revealed an increase in the volume-averaged baryon fractions $f_b(r)$ of galaxy clusters with cluster radii $r$, $f_b(r)$ should asymptotically reach a universal value $f_b(\infty)=f_b$, provided that clusters are representative of the Universe. In the framework of hydrostatic equilibrium for intracluster gas, we have derived the necessary conditions for $f_b(\infty)=f_b$: The X-ray surface brightness profile described by the $\beta$ model and the temperature profile approximated by the polytropic model should satisfy $\gamma\approx2(1-1/3\beta)$ and $\gamma\approx1+1/3\beta$ for $\beta 1$, respectively, which sets a stringent limit to the polytropic index: $\gamma 2/3$ breaks down at rather large radii ($\ga30r_c$) where hydrostatic equilibrium has probably become inapplicable. We further explore how to obtain the asymptotic value $f_b(\infty)$ of baryon fraction from the X-ray measurement made primarily over the finite central region of a cluster. We demonstrate our method using a sample of 19 strong lensing clusters, which enables us to place a useful constraint on $f_b(\infty)$: $0.094\pm0.035 \leq f_b(\infty) \leq 0.41\pm0.18$. An optimal estimate of $f_b(\infty)$ based on three cooling flow clusters with $\beta = 0.142\pm0.007$ or $\Omega_M = 0.35\pm0.09$.

Note on a polytropic -model to fit the X-ray surface brightness of clusters of galaxies

I suggest that the β-model used to fit the X-ray surface brightness profiles of extended sources, like groups and clusters of galaxies, has to be corrected when the counts are collected in a wide energy band comparable to the mean temperature of the source, and a significant gradient in the gas temperature is observed. I present a revised version of the β-model for the X-ray brightness that applies to an intracluster gas with temperature and density related by a polytropic equation and extends the standard version that is strictly valid for an isothermal gas. Given a temperature gradient observed through an energy window of 1–10 keV typical for the new generation of X-ray observatories, the β parameter can change systematically by up to 20 per cent from the value obtained under isothermal assumption, i.e. by an amount larger than any statistical uncertainty obtained from the present data. Within the virial regions of typical clusters of galaxies, these systematic corrections affect the total gravitating mass estimate by 5–10 per cent, the gas mass by 10–30 per cent and the gas fraction value up to 50 per cent, when compared with the measurements obtained under the isothermal assumption.

X‐Ray Properties of the Abell 644 Cluster of Galaxies

We use new ASCA observations and archival ROSAT Position Sensitive Proportional Counter (PSPC) data to determine the X-ray spectral properties of the intracluster gas in Abell 644. From the overall spectrum, we determine the average gas temperature to be 8.64 (+0.67,-0.56) keV, and an abundance of 0.32 (+/-0.04) $Z_{\odot}$. The global ASCA and ROSAT spectra imply a cooling rate of 214 (+100,-91) $M_{\odot}$ yr$^{-1}$. The PSPC X-ray surface brightness profile and the ASCA data suggest a somewhat higher cooling rate. We determine the gravitational mass and gas mass as a function of radius. The total gravitating mass within 1.2 Mpc is $6.2\times10^{14}$ $M_{\odot}$, of which 20% is in the form of hot gas. There is a region of elevated temperature 1.5-5 arcmin to the west of the cluster center. The south-southwest region of the cluster also shows excess emission in the ROSAT PSPC X-ray image, aligned with the major axis of the optical cD galaxy in the center of the cluster. We argue that the cluster is undergoing or has recently undergone a minor merger. The combination of a fairly strong cooling flow and evidence for a merger make this cluster an interesting case to test the disruption of cooling flow in mergers.

X‐Ray Mass Estimates atz∼ 0.3 for the Canadian Network for Observational Cosmology Cluster Sample

Results are presented from the analysis of ROSAT High-Resolution Imager (HRI) and Position-Sensitive Proportional Counter (PSPC) observations of the Canadian Network for Observational Cosmology (CNOC) subsample of the Extended Medium-Sensitivity Survey (EMSS) high-redshift galaxy clusters. X-ray surface brightness profiles of 14 clusters with 0.17 < z < 0.55 are constructed and fit to isothermal β models. Where possible, we use both the HRI and PSPC data to constrain the fit. Under the assumptions of isothermality, hydrostatic equilibrium, and spherical symmetry, we derive total X-ray masses within a range of radii from 141 to 526 h-1100 kpc. These masses are compared with both the dynamical masses obtained from galaxy velocities and the projected masses from published gravitational lensing studies. We find no systematic bias between X-ray and dynamical methods across the sample, with an average MDyn/MX=1.04 ± 0.07, although individual clusters exhibit mass discrepancies up to a factor of 2. We estimate that the systematic effects due to cooling flows, nonequilibrium systems, and temperature gradients affect the average mass ratio by no more than 15%-20%. Weak gravitational lensing masses appear to be systematically higher than X-ray results by factors of ~50%, while strong-lensing estimates show larger discrepancies (factors of ~2.5). However, these comparisons are complicated by the need to extrapolate the X-ray data to larger or smaller radii. We calculate X-ray-derived cluster gas masses, from which we obtain a cluster baryon fraction of ~5% h-3/2100, yielding Ω0~0.3 h-1/2100.

Is the Butcher‐Oemler Effect a Function of the Cluster Redshift?

Using PSPC ROSAT data, we measure the X-ray surface brightness profiles, size, and luminosity of the Butcher-Oemler (BO) sample of clusters of galaxies. The cluster X-ray size, as measured by the Petrosian rη = 2 radius, does not change with redshift and is independent of X-ray luminosity. On the other hand, the X-ray luminosity increases with redshift. Considering that fair samples show no evolution, or negative luminosity evolution, we conclude that the BO sample is not formed from the same class of objects observed at different look-back times. This is in conflict with the usual interpretation of the Butcher-Oemler as an evolutionary (or redshift dependent) effect, based on the assumption that we are comparing the same class of objects at different redshifts. Other trends present in the BO sample reflect selection criteria rather than differences in look-back time, as independently confirmed by the fact that trends lose strength when we enlarge the sample with an X-ray-selected sample of clusters. The variety of optical sizes and shapes of the clusters in the Butcher-Oemler sample and the Malmquist-like bias are the reasons for these selection effects that mimic the trends usually interpreted as changes due to evolution.

Einstein ObservatoryImages of Clusters of Galaxies

We present the X-ray characteristics of a sample of 368 clusters of galaxies with redshifts less than 0.2 observed with the Einstein Imaging Proportional Counter. For each cluster, we measure the 0.5-4.5 keV counting rate and compute the 0.5-4.5 keV source luminosity, as well as the bolometric luminosity within fixed metric radii. We detect 85% of Abell clusters with z<0.1, demonstrating that the large majority of these optically selected clusters are not the results of chance superpositions. For 163 clusters, we measure their X-ray surface brightness profiles and determine their core radii. For ~230 clusters, we then use either our measured core radii and β values, or mean values derived for this sample, to measure central gas densities and gas masses. We use estimated or measured cluster gas temperatures, along with the derived gas-density profiles, to estimate total cluster masses, under the assumptions that the gas is isothermal and in hydrostatic equilibrium. We also present contour plots of the X-ray emission, which we use to classify the cluster morphology. We find the percentage of clusters with substructure in their X-ray images is about 40%, with no significant change in this percentage as a function of X-ray luminosity. This implies that a large fraction of all present epoch clusters are still undergoing subcluster mergers. Based on our analysis of surface brightness profiles, we find that most clusters have core radii in the range from 0.1 to 0.3 Mpc (for H0=50 km s-1 Mpc-1), with more massive single clusters having larger core radii. The β values determined from the slope of the surface brightness profiles fall in the narrow range from 0.4 to 0.8, with β values increasing with cluster gas temperatures. No change in the value of β is found in the surface brightness profiles for individual clusters as a function of distance from the cluster center. We compare the β values derived from the surface brightness profiles with the corresponding β values calculated from the gas temperatures and cluster velocity dispersions. We argue that much of the discrepancy between the values of β derived from these two methods results from overestimates of the cluster velocity dispersion due to cluster substructure. Finally, we compare the gas mass to the cluster virial mass and find, for an isothermal gas, that, within a fixed metric radius of 1 Mpc, the gas mass fraction increases as a function of X-ray luminosity from 10% to 20% of the total cluster mass.

Cluster Mass Estimate and a Cusp of the Mass‐Density Distribution in Clusters of Galaxies

We study density cusps in the center of clusters of galaxies in order to reconcile X-ray mass estimates with gravitational lensing masses. For various mass-density models with cusps, we compute X-ray surface brightness distributions and fit them to observations to measure the range of parameters in the density models. The Einstein radii estimated from these density models are compared with Einstein radii derived from the observed arcs for Abell 2163, Abell 2218, and RX J1347.5-1145. The X-ray masses and lensing masses corresponding to these Einstein radii are also compared. While steeper cusps give smaller ratios of lensing mass to X-ray mass, the X-ray surface brightnesses estimated from flatter cusps are better fits to the observations. For Abell 2163 and Abell 2218, although the isothermal sphere with a finite core cannot produce giant arc images, a density model with a central cusp can produce a finite Einstein radius that is smaller than the observed radii. We find that a total mass-density profile that declines as ~r-1.4 produces the largest radius in models that are consistent with the X-ray surface brightness profile. As a result, the extremely large ratio of the lensing mass to the X-ray mass is improved from 2.2 to 1.4 for Abell 2163 and from 3 to 2.4 for Abell 2218. For RX J1347.5-1145, which is a cooling flow cluster, we cannot reduce the mass discrepancy.