Mass profiles and anisotropies of early-type galaxies

We discuss the problem of using stellar kinematics of early-type galaxies to constrain the orbital anisotropies and radial mass profiles of galaxies. We demonstrate that compressing the light distribution of a galaxy along the line of sight produces approximately the same signature in the line-of-sight velocity profiles as radial anisotropy. In particular, fitting spherically symmetric dynamical models to apparently round, isotropic face-on flattened galaxies leads to a spurious bias towards radial orbits in the models, especially if the galaxy has a weak face-on stellar disc. Such face-on stellar discs could plausibly be the cause of the radial anisotropy found in spherical models of intermediate luminosity ellipticals such as NGC 2434, 3379 and 6703.
In the light of this result, we use simple dynamical models to constrain the outer mass profiles of a sample of 18 round, early-type galaxies. The galaxies follow a Tully–Fisher relation parallel to that for spiral galaxies, but fainter by at least 0.8 mag ( I -band) for a given mass. The most luminous galaxies show clear evidence for the presence of a massive dark halo, but the case for dark haloes in fainter galaxies is more ambiguous. We discuss the observations that would be required to resolve this ambiguity.     

Galaxies in clusters: the observational characteristics of bow shocks, wakes and tails

The dynamical signatures of the interaction between galaxies in clusters and the intracluster medium (ICM) can potentially yield significant information about the structure and dynamical history of clusters. To develop our understanding of this phenomenon we present results from numerical modelling of the galaxy–ICM interaction, as the galaxy moves through the cluster. The simulations have been performed for a broad range of ICM temperatures ( kT _cl=1, 4 and 8 keV), representative of poor clusters or groups through to rich clusters.
There are several dynamical features that can be identified in these simulations. For supersonic galaxy motion, a leading bow shock is present, and also a weak gravitationally focused wake or tail behind the galaxy (analogous to Bondi–Hoyle accretion). For galaxies with higher mass replenishment rates and a denser interstellar medium (ISM), the dominant feature is a dense ram-pressure stripped tail. In line with other simulations, we find that the ICM/galaxy–ISM interaction can result in complex time-dependent dynamics, with ram-pressure stripping occurring in an episodic manner.
In order to facilitate this comparison between the observational consequences of dynamical studies and X-ray observations we have calculated synthetic X-ray flux and hardness maps from these simulations. These calculations predict that the ram-pressure stripped tail will usually be the most visible feature, though in nearby galaxies the bow shock preceding the galaxy should also be apparent in deeper X-ray observations. We briefly discuss these results and compare them with X-ray observations of galaxies where there is evidence of such interactions.     

Properties of spherical galaxies and clusters with an NFW density profile

Using the standard dynamical theory of spherical systems, we calculate the properties of spherical galaxies and clusters whose density profiles obey the universal form first obtained in high-resolution cosmological N -body simulations by Navarro, Frenk & White (NFW). We adopt three models for the internal kinematics: isotropic velocities, constant anisotropy and increasingly radial OsipkovMerritt anisotropy. Analytical solutions are found for the radial dependence of the mass, gravitational potential, velocity dispersion, energy and virial ratio and we test their variability with the concentration parameter describing the density profile and amount of velocity anisotropy. We also compute structural parameters, such as half-mass radius, effective radius and various measures of concentration. Finally, we derive projected quantities, the surface mass density and line-of-sight as well as aperture-velocity dispersion, all of which can be directly applied in observational tests of current scenarios of structure formation. On the mass scales of galaxies, if constant mass-to-light is assumed, the NFW surface density profile is found to fit HubbleReynolds laws well. It is also well fitted by Sérsic R ^{1/ m} laws, for     but in a much narrower range of m and with much larger effective radii than are observed. Assuming in turn reasonable values of the effective radius, the mass density profiles imply a mass-to-light ratio that increases outwards at all radii.     

The importance of interloper removal in galaxy clusters: saving more objects for the Jeans analysis

We study the effect of contamination by interlopers in kinematic samples of galaxy clusters. We demonstrate that without the proper removal of interlopers the inferred parameters of the mass distribution in the cluster are strongly biased towards higher mass and lower concentration. The interlopers are removed using two procedures previously shown to work most efficiently on simulated data. One is based on using the virial mass estimator and calculating the maximum velocity available to cluster members and the other relies on the ratio of the virial and projected mass estimators. We illustrate the performance of the methods in detail using the example of A576, a cluster with a strong uniform background contamination, and compare the case of A576 to 15 other clusters with different degree of contamination. We model the velocity dispersion and kurtosis profiles obtained for the cleaned data samples of these clusters solving the Jeans equations to estimate the mass, concentration and anisotropy parameter. We present the mass–concentration relation for the total sample of 22 clusters.     

Are 'Bondi–Hoyle wakes' detectable in clusters of galaxies?

In clusters of galaxies, the reaction of the intracluster medium (ICM) to the motion of the co-existing galaxies in the cluster triggers the formation of unique features, which trace their position and motion. Galactic wakes, for example, are an apparent result of the ICM/galaxy interactions, and they constitute an important tool for deciphering the motion of the cluster galaxies.
In this paper we investigate whether Bondi–Hoyle accretion can create galactic wakes by focusing the ICM behind moving galaxies. The solution of the equations that describe this physical problem provides us with observable quantities along the wake at any time of its lifetime. We also investigate which are the best environmental conditions for the detectability of such structures in the X-ray images of clusters of galaxies.
We find that significant Bondi–Hoyle wakes can only be formed in low-temperature clusters, and that they are more pronounced behind slow-moving, relatively massive galaxies. The scalelength of these elongated structures is not very large: in the most favourable conditions a Bondi–Hoyle wake in a cluster at the redshift of z =0.05 is 12 arcsec long. However, the X-ray emission of the wake is noticeably strong: the X-ray flux can reach ∼30 times the flux of the surrounding medium. Such features will be easily detectable in the X-ray images of nearby, relatively poor clusters of galaxies by the Chandra and XMM-Newton satellites.     

Richness dependence of the recent evolution of clusters of galaxies

We revisit the issue of the recent dynamical evolution of clusters of galaxies using a sample of Abell, Corwin & Olowin (ACO) clusters with   z < 0.14  , which has been selected such that it does not contain clusters with multiple velocity components nor strongly merging or interacting clusters, as revealed in X-rays. We use as proxies of the cluster dynamical state the projected cluster ellipticity, velocity dispersion and X-ray luminosity. We find indications for a recent dynamical evolution of this cluster population, which however strongly depends on the cluster richness. Poor clusters appear to be undergoing their primary phase of virialization, with their ellipticity increasing with redshift with a rate  dε/d z ≃ 2.5 ± 0.4  , while the richest clusters show an ellipticity evolution in the opposite direction (with  dε/d z ≃−1.2 ± 0.1  ), which could be due to secondary infall. When taking into account sampling effects due to the magnitude-limited nature of the ACO cluster catalogue we find no significant evolution of the cluster X-ray luminosity, while the velocity dispersion increases with decreasing redshift, independent of the cluster richness, at a rate  dσ _v /d z ≃−1700 ± 400 km s⁻¹  .     

From kinematics to dynamics in thin galactic discs

We present a method for recovering the distribution functions of edge-on thin axisymmetric discs directly from their observable kinematic properties. The most generally observable properties of such a stellar system are the line-of-sight velocity distributions of the stars at different projected radii along the galaxy. If the gravitational potential is known, then the general two-integral distribution function can be reconstructed using the shapes of the high-velocity tails of these line-of-sight distributions. If the wrong gravitational potential is adopted, then a distribution function can still be constructed using this technique, but the low-velocity parts of the observed velocity distributions will not be reproduced by the derived dynamical model. Thus, the gravitational potential is also tightly constrained by the observed kinematics.     

Mass distribution in nearby Abell clusters

We study the mass distribution in six nearby  ( z < 0.06)  relaxed Abell clusters of galaxies A0262, A0496, A1060, A2199, A3158 and A3558. Given the dominance of dark matter in galaxy clusters, we approximate their total density distribution by the Navarro, Frenk & White (NFW) formula characterized by virial mass and concentration. We also assume that the anisotropy of galactic orbits is reasonably well described by a constant and that galaxy distribution traces that of the total density. Using the velocity and position data for 120–420 galaxies per cluster we calculate, after removal of interlopers, the profiles of the lowest order even velocity moments, dispersion and kurtosis. We then reproduce the velocity moments by jointly fitting the moments to the solutions of the Jeans equations. Including the kurtosis in the analysis allows us to break the degeneracy between the mass distribution and anisotropy and constrain the anisotropy as well as the virial mass and concentration. The method is tested in detail on mock data extracted from the N -body simulations of dark matter haloes. We find that the best-fitting Galactic orbits are remarkably close to isotropic in most clusters. Using the fitted pairs of mass and concentration parameters for the six clusters, we conclude that the trend of decreasing concentration for higher masses found in the cosmological N -body simulations is consistent with the data. By scaling the individual cluster data by mass, we combine them to create a composite cluster with 1465 galaxies and perform a similar analysis on such sample. The estimated concentration parameter then lies in the range  1.5 < c < 14  and the anisotropy parameter in the range  −1.1 < β < 0.5  at the 95 per cent confidence level.     

Dynamical Substructures of Galaxy Cluster Abell 85

Abell 85 is a cD cluster of galaxies with the redshift of 0.055 in the southern hemisphere. Based on the spectroscopic data obtained by predecessors and the data of the SDSS (Sloan Digital Sky Survey), 370 member galaxies of the cluster are sieved by means of the 3σ method and their dynamical states are analyzed. From the spatial distribution and the local line-of-sight velocity distribution of these member galaxies it is found that this cluster of galaxies contains 4 clear substructures and they are just in the process of pairwise coalescence. This shows that the cluster Abell 85 is in the actively dynamical state, far from reaching the dynamical equilibrium.     

The flattening and the orbital structure of early-type galaxies and collisionless N-body binary disc mergers

We use oblate axisymmetric dynamical models including dark haloes to determine the orbital structure of intermediate mass to massive early-type galaxies in the Coma galaxy cluster. We find a large variety of orbital compositions. Averaged over all sample galaxies the unordered stellar kinetic energy in the azimuthal and the radial direction are of the same order, but they can differ by up to 40 per cent in individual systems. In contrast, both for rotating and non-rotating galaxies the vertical kinetic energy is on average smaller than in the other two directions. This implies that even most of the rotating ellipticals are flattened by an anisotropy in the stellar velocity dispersions. Using three-integral axisymmetric toy models, we show that flattening by stellar anisotropy maximizes the entropy for a given density distribution. Collisionless disc merger remnants are radially anisotropic. The apparent lack of strong radial anisotropy in observed early-type galaxies implies that they may not have formed from mergers of discs unless the influence of dissipational processes was significant.     

Galaxy cluster masses without non-baryonic dark matter

We apply the modified acceleration law obtained from Einstein gravity coupled to a massive skew symmetric field,   F _μνλ  , to the problem of explaining X-ray galaxy cluster masses without exotic dark matter. Utilizing X-ray observations to fit the gas mass profile and temperature profile of the hot intracluster medium (ICM) with King 'β-models', we show that the dynamical masses of the galaxy clusters resulting from our modified acceleration law fit the cluster gas masses for our sample of 106 clusters without the need of introducing a non-baryonic dark matter component. We are further able to show for our sample of 106 clusters that the distribution of gas in the ICM as a function of radial distance is well fitted by the dynamical mass distribution arising from our modified acceleration law without any additional dark matter component. In a previous work, we applied this theory to galaxy rotation curves and demonstrated good fits to our sample of 101 low surface brightness, high surface brightness and dwarf galaxies including 58 galaxies that were fitted photometrically with the single-parameter mass-to-light ratio ( M / L )_stars. The results obtained there were qualitatively similar to those obtained using Milgrom's phenomenological Modified Newtonian Dynamics (MOND) model, although the determined galaxy masses were quantitatively different, and MOND does not show a return to Keplerian behaviour at extragalactic distances. The results obtained here are compared to those obtained using Milgrom's phenomenological MOND model which does not fit the X-ray galaxy cluster masses unless an auxiliary dark matter component is included.     

Velocity dispersions of dwarf spheroidal galaxies: dark matter versus MOND

We present predictions for the line-of-sight velocity dispersion profiles of dwarf spheroidal galaxies and compare them to observations in the case of the Fornax dwarf. The predictions are made in the framework of standard dynamical theory of spherical systems with different velocity distributions. The stars are assumed to be distributed according to Sérsic laws with parameters fitted to observations. We compare predictions obtained assuming the presence of dark matter haloes (with density profiles adopted from N -body simulations) with those resulting from Modified Newtonian Dynamics (MOND). If the anisotropy of velocity distribution is treated as a free parameter, observational data for Fornax are reproduced equally well by models with dark matter and with MOND. If stellar mass-to-light ratio of 1 M_⊙/L_⊙ is assumed, the required mass of the dark halo is     , two orders of magnitude larger than the mass in stars. The derived MOND acceleration scale is     . In both cases a certain amount of tangential anisotropy in the velocity distribution is needed to reproduce the shape of the velocity dispersion profile in Fornax.     

LoCuSS: the connection between brightest cluster galaxy activity, gas cooling and dynamical disturbance of X-ray cluster cores

We study the distribution of projected offsets between the cluster X-ray centroid and the brightest cluster galaxy (BCG) for 65 X-ray-selected clusters from the Local Cluster Substructure Survey, with a median redshift of   z = 0.23  . We find a clear correlation between X-ray/BCG projected offset and the logarithmic slope of the cluster gas density profile at  0.04 r ₅₀₀(α  ), implying that more dynamically disturbed clusters have weaker cool cores. Furthermore, there is a close correspondence between the activity of the BCG, in terms of detected Hα and radio emission, and the X-ray/BCG offset, with the line-emitting galaxies all residing in clusters with X-ray/BCG offsets of ≤15 kpc. Of the BCGs with  α < −0.85  and an offset <0.02 r ₅₀₀, 96 per cent (23/24) have optical emission and 88 per cent (21/24) are radio active, while none has optical emission outside these criteria. We also study the cluster gas fraction ( f _gas) within r ₅₀₀ and find a significant correlation with X-ray/BCG projected offset. The mean f _gas of the 'small offset' clusters (<0.02 r ₅₀₀) is  0.106 ± 0.005 (σ= 0.03  ) compared to  0.145 ± 0.009 (σ= 0.04  ) for those with an offset >0.02 r ₅₀₀, indicating that the total mass may be systematically underestimated in clusters with larger X-ray/BCG offsets. Our results imply a link between cool core strength and cluster dynamical state consistent with the view that cluster mergers can significantly perturb cool cores, and set new constraints on models of the evolution of the intracluster medium.     

A catalogue and analysis of local galaxy ages and metallicities

We have assembled a catalogue of relative ages, metallicities and abundance ratios for about 150 local galaxies in field, group and cluster environments. The galaxies span morphological types from cD and ellipticals, to late-type spirals. Ages and metallicities were estimated from high-quality published spectral line indices using Worthey & Ottaviani (1997) single stellar population evolutionary models.
The identification of galaxy age as a fourth parameter in the fundamental plane ( Forbes, Ponman & Brown 1998 ) is confirmed by our larger sample of ages. We investigate trends between age and metallicity, and with other physical parameters of the galaxies, such as ellipticity, luminosity and kinematic anisotropy. We demonstrate the existence of a galaxy age–metallicity relation similar to that seen for local galactic disc stars, whereby young galaxies have high metallicity, while old galaxies span a large range in metallicities.
We also investigate the influence of environment and morphology on the galaxy age and metallicity, especially the predictions made by semi-analytic hierarchical clustering models (HCM). We confirm that non-cluster ellipticals are indeed younger on average than cluster ellipticals as predicted by the HCM models. However we also find a trend for the more luminous galaxies to have a higher [Mg/Fe] ratio than the lower luminosity galaxies, which is opposite to the expectation from HCM models.     

X-ray and strong lensing mass estimate of MS2137.3–2353

We present new mass estimates of the cluster of galaxies MS2137.3–2353, inferred from X-ray and strong lensing analyses. This cluster exhibits an outstanding strong lensing configuration and indicates a well-relaxed dynamical state, being most suitable for a mass reconstruction which combines both techniques. Despite this, several previous studies have claimed a significant discrepancy between the X-ray and the strong lensing mass estimates. The primary aim of this paper is to address and explain this mismatch. For this purpose, we have analysed Chandra observations to recover the profiles of the intracluster medium properties and, assuming a functional form for the matter density, the total mass distribution. The notable strong-lensing features of MS2137.3 allow us to reconstruct its projected mass in the central regions with good accuracy, by taking advantage of the lensing inversion code lenstool . We compare the results obtained for both methods. Our mass estimates for MS2137.3 are in agreement within errors, leading to a mean, extrapolated value of   M ₂₀₀≃ 4.4 ± 0.3 × 10¹⁴ M_⊙  , under the assumption of the Navarro–Frenk–White (NFW) mass profile. However, the strong lensing mass estimate is affected by the details of the brightest cluster galaxy mass modelling, since the radial arc is a very sensitive probe of the total mass derivative in the central region. In particular, we do not find evidence for a high concentration for the NFW density profile, as reported in some earlier works.     

A comparison of different cluster mass estimates: consistency or discrepancy?

Rich and massive clusters of galaxies at intermediate redshift are capable of magnifying and distorting the images of background galaxies. A comparison of different mass estimators among these clusters can provide useful information about the distribution and composition of cluster matter and its dynamical evolution. Using the hitherto largest sample of lensing clusters drawn from the literature, we compare the gravitating masses of clusters derived from the strong/weak gravitational lensing phenomena, from the X-ray measurements based on the assumption of hydrostatic equilibrium, and from the conventional isothermal sphere model for the dark matter profile characterized by the velocity dispersion and core radius of galaxy distributions in clusters. While there is excellent agreement between the weak lensing, X-ray and isothermal sphere model-determined cluster masses, these methods are likely to underestimate the gravitating masses enclosed within the central cores of clusters by a factor of 2–4 as compared with the strong lensing results. Such a mass discrepancy has probably arisen from the inappropriate applications of the weak lensing technique and the hydrostatic equilibrium hypothesis to the central regions of clusters, as well as from assuming an unreasonably large core radius for both luminous and dark matter profiles. Nevertheless, it is pointed out that these cluster mass estimators may be safely applied on scales greater than the core sizes. Namely, the overall clusters of galaxies at intermediate redshift can still be regarded as the dynamically relaxed systems, in which the velocity dispersion of galaxies and the temperature of X-ray emitting gas are good indicators of the underlying gravitational potentials of clusters.     

A maximum-entropy method for reconstructing the projected mass distribution of gravitational lenses

The maximum-entropy method is applied to the problem of reconstructing the projected mass density of a galaxy cluster using its gravitational lensing effects on background galaxies. We demonstrate the method by reconstructing the mass distribution in a model cluster using simulated shear and magnification data to which Gaussian noise is added. The mass distribution is reconstructed directly and the inversion is regularized using the entropic prior for this positive additive distribution. For realistic noise levels, we find that the method faithfully reproduces the main features of the cluster mass distribution not only within the observed field but also slightly beyond it. We estimate the uncertainties in the reconstruction by calculating an analytic approximation to the covariance matrix of the reconstruction values of each pixel. This result is compared with error estimates derived from Monte Carlo simulations for different noise realizations and found to be in good agreement.     

The dynamical state of RX J1347.5−1145 from a combined strong lensing and X-ray analysis

We perform a combined X-ray and strong lensing analysis of RX J1347.5−1145, one of the most luminous galaxy clusters at X-ray wavelengths. We show that evidence from strong lensing alone, based on published Very Large Telescope (VLT) and new Hubble Space Telescope ( HST ) data, strongly argues in favour of a complex structure. The analysis takes into account arc positions, shapes and orientations, and is done thoroughly in the image plane. The cluster inner regions are well fitted by a bimodal mass distribution, with a total projected mass of   M _tot= (9.9 ± 0.3) × 10¹⁴ M_⊙  h ⁻¹  within a radius of 360 kpc  h ⁻¹ (1.5 arcmin). Such a complex structure could be a signature of a recent major merger as further supported by X-ray data. A temperature map of the cluster, based on deep Chandra observations, reveals a hot front located between the first main component and an X-ray emitting south-eastern subclump. The map also unveils a filament of cold gas in the innermost regions of the cluster, most probably a cooling wake caused by the motion of the cD inside the cool core region. A merger scenario in the plane of the sky between two dark matter subclumps is consistent with both our lensing and X-ray analyses, and can explain previous discrepancies with mass estimates based on the virial theorem.     

The nature of the dwarf population in Abell 868

We present the results of a study of the morphology of the dwarf galaxy population in Abell 868, a rich, intermediate-redshift     cluster which has a galaxy luminosity function (LF) with a steep faint-end slope     . A statistical background subtraction method is employed to study the     colour distribution of the cluster galaxies. This distribution suggests that the galaxies contributing to the faint-end of the measured cluster LF can be split into three populations: dwarf irregular galaxies (dIrrs) with     dwarf elliptical galaxies (dEs) with     and contaminating background giant ellipticals (gEs) with     . The removal of the contribution of the background gEs from the counts only marginally lessens the faint-end slope     . However, the removal of the contribution of the dIrrs from the counts produces a flat LF     . The dEs and the dIrrs have similar spatial distributions within the cluster, except that the dIrrs appear to be totally absent within a central projected radius of about 0.2 Mpc     . The number densities of both dEs and dIrrs appear to fall off beyond a projected radius of ≃ 0.35 Mpc. We suggest that the dE and dIrr populations of A868 have been associated with the cluster for similar time-scales, but evolutionary processes such as 'galaxy harassment' tend to fade the dIrr galaxies while having a much smaller effect on the dE galaxies. The harassment would be expected to have the greatest effect on dwarfs residing in the central parts of the cluster.     

The dynamics of S0 galaxies and their Tully–Fisher relation

This paper investigates the detailed dynamical properties of a relatively homogeneous sample of disc-dominated S0 galaxies, with a view to understanding their formation, evolution and structure. By using high signal-to-noise ratio long-slit spectra of edge-on systems, we have been able to reconstruct the complete line-of-sight velocity distributions of stars along the major axes of the galaxies. From these data, we have derived both model distribution functions (the phase density of their stars) and the approximate form of their gravitational potentials.
The derived distribution functions are all consistent with these galaxies being simple disc systems, with no evidence for a complex formation history. Essentially no correlation is found between the characteristic mass scalelengths and the photometric scalelengths in these galaxies, suggesting that they are dark-matter dominated even in their inner parts. Similarly, no correlation is found between the mass scalelengths and asymptotic rotation speed, implying a wide range of dark matter halo properties.
By comparing their asymptotic rotation speeds with their absolute magnitudes, we find that these S0 galaxies are systematically offset from the Tully–Fisher relation for later-type galaxies. The offset in luminosity is what one would expect if star formation had been suddenly switched off a few Gyr ago, consistent with a simple picture in which these S0s were created from ordinary later-type spirals which were stripped of their star-forming interstellar medium when they encountered a dense cluster environment.