Non-parametric reconstruction of cluster mass distribution from strong lensing: modelling Abell 370

We describe a new non-parametric technique for reconstructing the mass distribution in galaxy clusters with strong lensing, i.e. from multiple images of background galaxies. The observed positions and redshifts of the images are considered as rigid constraints, and through the lens (ray-trace) equation they provide us with linear constraint equations. These constraints confine the mass distribution to some allowed region, which is then found by linear programming. Within this allowed region we study in detail the mass distribution with minimum mass-to-light variation, and also some other distributions, such as the smoothest mass distribution.
The method is applied to the extensively studied cluster Abell 370, which hosts a giant luminous arc and several other multiply imaged background galaxies. Our mass maps are constrained by the observed positions and redshifts (spectroscopic or model-inferred by previous authors) of the giant arc and multiple-image systems. The reconstructed maps obtained for Abell 370 reveal a detailed mass distribution, with substructure quite different from the light distribution. The method predicts the bimodal nature of the cluster, and that the projected mass distribution is indeed elongated along the axis defined by the two dominant cD galaxies. However, the peaks in the mass distribution appear to be offset from the centres of the cDs.
We also present an estimate for the total mass of the central region of the cluster. This is in good agreement with previous mass determinations. The total mass of the central region is M =(2.0–2.7)×10¹⁴ M⊙ h ⁻¹₅₀, depending on the solution chosen.     

Constraining the Mass Distribution of Cluster Galaxies by Weak Lensing

Analysing the weak lensing distortions of the images of faint background galaxies provides a means to constrain the average mass distribution of cluster galaxies and potentially to test the extent of their dark matter haloes as a function of the density of their environment. The observable image distortions are a consequence of the interplay between the effects of a global cluster mass distribution and the perturbations resulting from individual cluster galaxies. Starting from a reconstruction of the cluster mass distribution with conventional techniques, we apply a maximum likelihood method to infer the average properties of an ensemble of cluster galaxies. From simulations this approach is found to be reliable as long as the galaxies including their dark matter haloes only contribute a small fraction to the total mass of the system. If their haloes are extended, the galaxies contain a substantial mass fraction. In this case our method is still applicable in the outer regions of clusters, where the surface mass density is low, but yields biased estimates of the parameters describing the mass profiles of the cluster galaxies in the central part of the cluster. In that case it will be necessary to resort to more sophisticated strategies by modelling cluster galaxies and an underlying global mass distribution simultaneously. We conclude that galaxy–galaxy lensing in clusters provides a unique means to probe the presence and extent of dark haloes of cluster galaxies.     

Mass estimation in the outer regions of galaxy clusters

We present a technique for estimating the mass in the outskirts of galaxy clusters where the usual assumption of dynamical equilibrium is not valid. The method assumes that clusters form through hierarchical clustering and requires only galaxy redshifts and positions on the sky. We apply the method to dissipationless cosmological N -body simulations where galaxies form and evolve according to semi-analytic modelling. The method recovers the actual cluster mass profile within a factor of 2 to several megaparsecs from the cluster centre. This error originates from projection effects, sparse sampling, and contamination by foreground and background galaxies. In the absence of velocity biases, this method can provide an estimate of the mass-to-light ratio on scales ∼1–10  h ⁻¹ Mpc where this quantity is still poorly known.     

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.     

Tracing the nature of dark energy with galaxy distribution

Dynamical dark energy (DE) is a viable alternative to the cosmological constant. Constructing tests to discriminate between Λ and dynamical DE models is difficult, however, because the differences are not large. In this paper we explore tests based on the galaxy mass function, the void probability function (VPF), and the number of galaxy clusters. At high z , the number density of clusters shows large differences between DE models, but geometrical factors reduce the differences substantially. We find that detecting a model dependence in the cluster redshift distribution is a significant challenge. We show that the galaxy redshift distribution is potentially a more sensitive characteristic. We do this by populating dark matter haloes in N -body simulations with galaxies using well-tested halo occupation distributions. We also estimate the VPF and find that samples with the same angular surface density of galaxies, in different models, exhibition almost model-independent VPF which therefore cannot be used as a test for DE. Once again, geometry and cosmic evolution compensate each other. By comparing VPFs for samples with fixed galaxy mass limits, we find measurable differences.     

A new method to derive star formation histories of galaxies from their star cluster distributions

Star formation happens in a clustered way which is why the star cluster population of a particular galaxy is closely related to the star formation history of this galaxy. From the probabilistic nature of a mass function follows that the mass of the most massive cluster of a complete population, M _max, has a distribution with the total mass of the population as a parameter. The total mass of the population is connected to the star formation rate (SFR) by the length of a formation epoch.
Since due to evolutionary effects only massive star clusters are observable up to high ages, it is convenient to use this M _max(SFR) relation for the reconstruction of a star formation history. The age distribution of the most massive clusters can therefore be used to constrain the star formation history of a galaxy. The method, including an assessment of the inherent uncertainties, is introduced with this contribution, while following papers will apply this method to a number of galaxies.     

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.     

Ram-pressure histories of cluster galaxies

Ram-pressure stripping can remove significant amounts of gas from galaxies that orbit in clusters and massive groups, and thus has a large impact on the evolution of cluster galaxies. In this paper, we reconstruct the present-day distribution of ram pressure and the ram-pressure histories of cluster galaxies. To this aim, we combine the Millennium Simulation and an associated semi-analytic model of galaxy evolution with analytic models for the gas distribution in clusters. We find that about one quarter of galaxies in massive clusters are subject to strong ram pressures that are likely to cause an expedient loss of all gas. Strong ram pressures occur predominantly in the inner core of the cluster, where both the gas density and the galaxy velocity are higher. Since their accretion on to a massive system, more than 64 per cent of galaxies that reside in a cluster today have experienced strong ram pressures of  >10⁻¹¹ dyn cm⁻²  which most likely led to a substantial loss of the gas.     

The apparent and intrinsic shape of the APM galaxy clusters

We estimate the distribution of intrinsic shapes of APM galaxy clusters from the distribution of their apparent shapes. We measure the projected cluster ellipticities using two alternative methods. The first method is based on moments of the discrete galaxy distribution while the second is based on moments of the smoothed galaxy distribution. We study the performance of both methods using Monte Carlo cluster simulations covering the range of APM cluster distances and including a random distribution of background galaxies. We find that the first method suffers from severe systematic biases, whereas the second is more reliable. After excluding clusters dominated by substructure and quantifying the systematic biases in our estimated shape parameters, we recover a corrected distribution of projected ellipticities. We use the non-parametric kernel method to estimate the smooth apparent ellipticity distribution, and numerically invert a set of integral equations to recover the corresponding distribution of intrinsic ellipticities under the assumption that the clusters are either oblate or prolate spheroids. The prolate spheroidal model fits the APM cluster data best.     

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.     

Searching for tidal tails – investigating galaxy harassment

Galaxy harassment has been proposed as a physical process that morphologically transforms low surface density disc galaxies into dwarf elliptical galaxies in clusters. It has been used to link the observed very different morphology of distant cluster galaxies (relatively more blue galaxies with 'disturbed' morphologies) with the relatively large numbers of dwarf elliptical galaxies found in nearby clusters. One prediction of the harassment model is that the remnant galaxies should lie on low surface brightness tidal streams or arcs. We demonstrate in this paper that we have an analysis method that is sensitive to the detection of arcs down to a surface brightness of 29 B μ and we then use this method to search for arcs around 46 Virgo cluster dwarf elliptical galaxies. We find no evidence for tidal streams or arcs and consequently no evidence for galaxy harassment as a viable explanation for the relatively large numbers of dwarf galaxies found in the Virgo cluster.     

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.     

星系际弥散恒星成分研究进展

对于星系际弥散恒星的研究是分别从观测、数值模拟和半解析模型这三个方面进行的.现在已经在邻近星系团及中低红移处观测到弥散恒星,甚至在Virgo及Coma星系团中观测到了单个的弥散恒星.观测数据的积累使得人们能够从统计上了解星系际弥散恒星的性质.研究表明星系际弥散恒星围绕着星系团势阱中心呈椭球状对称分布,其在星系团恒星总质...     

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.     

Effects of cluster galaxies on arc statistics

We present the results of a set of numerical simulations evaluating the effect of cluster galaxies on arc statistics.
We perform a first set of gravitational lensing simulations using three independent projections for each of nine different galaxy clusters obtained from N -body simulations. The simulated clusters consist of dark matter only. We add a population of galaxies to each cluster, mimicking the observed luminosity function and the spatial galaxy distribution, and repeat the lensing simulations including the effects of cluster galaxies, which themselves act as individual lenses. Each galaxy is represented by a spherical Navarro, Frenk & White density profile.
We consider the statistical distributions of the properties of the gravitational arcs produced by our clusters with and without galaxies. We find that the cluster galaxies do not introduce perturbations strong enough to significantly change the number of arcs and the distributions of lengths, widths, curvature radii and length-to-width ratios of long arcs. We find some changes to the distribution of short-arc properties in the presence of cluster galaxies. The differences appear in the distribution of curvature radii for arc lengths smaller than 12 arcsec, while the distributions of lengths, widths and length-to-width ratios are significantly changed only for arcs shorter than 4 arcsec.     

-ray wakes as probes of galaxy cluster dynamics

If a galaxy resides in a cluster, then its passage through the pervasive intracluster medium will produce a detectable signature in the X-ray emission from the cluster. Such features have now been detected in a number of systems. The simplest kinematic information that can be extracted from this signature is the galaxy's direction of motion on the plane of the sky. This paper explores the constraints on cluster dynamics that could be derived from such information. In particular, we show that it is possible to define a projected anisotropy parameter, B ( r ), which is directly analogous to the usual orbital anisotropy parameter. We describe an estimator for this quantity, ( R ), which can be derived in a robust and straightforward manner. We present a simple dynamical model for a cluster consisting of a Michie distribution function of galaxies orbiting in a truncated singular isothermal sphere potential. Using this model, we demonstrate the ambiguity between the distribution of mass and the distribution of galaxy orbits when interpreting the traditional measures of cluster kinematics (the projected density of galaxies and their line-of-sight velocity dispersion). As an example, we show how two very different dynamical models can fit the kinematic properties of the Coma cluster. We demonstrate that the measurement of using a relatively small sample of wake directions ( N _wake≈50) would provide an effective mechanism for lifting this degeneracy. Thus, by combining X-ray measurements of wake directions with number counts and line-of-sight velocities derived from optical data, it will prove possible to measure both the orbit distribution and the form of the gravitational potential in clusters of galaxies. The requisite X-ray observations lie within reach of the soon-to-be-launched AXAF satellite.     

Galaxy cluster mass profiles

Accurate measurements of the mass distribution in galaxy and cluster haloes are essential to test the cold dark matter (CDM) paradigm. The cosmological model predicts a universal shape for the density profile in all haloes, independent of halo mass. Its profile has a 'cuspy' centre, with no evidence for the constant density core. In this paper, we carry out a careful analysis of 12 galaxy clusters, using Chandra data to compute the mass distribution in each system under the assumption of hydrostatic equilibrium. Due to their low concentration, clusters provide ideal objects for studying the central cusps in dark matter haloes. The majority of the systems are consistent with the CDM model, but four objects exhibit flat inner density profiles. We suggest that the flat inner profile found for these clusters is due to an underestimation of the mass in the cluster centre (rather than any problem with the CDM model), since these objects also have a centrally peaked gas mass fraction. We discuss possible causes for erroneously low-mass measurements in the cores of some systems.     

The mass of the Andromeda galaxy

This paper argues that the Milky Way galaxy is probably the largest member of the Local Group. The evidence comes from estimates of the total mass of the Andromeda galaxy (M31) derived from the three-dimensional positions and radial velocities of its satellite galaxies, as well as the projected positions and radial velocities of its distant globular clusters and planetary nebulae. The available data set comprises 10 satellite galaxies, 17 distant globular clusters and nine halo planetary nebulae with radial velocities. We find that the halo of Andromeda has a mass of together with a scalelength of 90 kpc and a predominantly isotropic velocity distribution. For comparison, our earlier estimate for the Milky Way halo is Although the error bars are admittedly large, this suggests that the total mass of M31 is probably less than that of the Milky Way . We verify the robustness of our results to changes in the modelling assumptions and to errors caused by the small size and incompleteness of the data set.
Our surprising claim can be checked in several ways in the near future. The numbers of satellite galaxies, planetary nebulae and globular clusters with radial velocities can be increased by ground-based spectroscopy, while the proper motions of the companion galaxies and the unresolved cores of the globular clusters can be measured using the astrometric satellites Space Interferometry Mission ( SIM ) and Global Astrometric Interferometer for Astrophysics ( GAIA ). Using 100 globular clusters at projected radii 20 R 50 kpc with both radial velocities and proper motions, it will be possible to estimate the mass within 50 kpc to an accuracy of 20 per cent. Measuring the proper motions of the companion galaxies with SIM and GAIA will reduce the uncertainty in the total mass caused by the small size of the data set to 22 per cent.     

Warped discs and the directional stability of jets in active galactic nuclei

The radial distribution of globular clusters in galaxies is always less peaked to the centre than that of the halo stars. Extending previous work to a sample of Hubble Space Telescope globular cluster systems in ellipticals, we evaluate the number of clusters potentially lost to the galactic centre as the integrals of the difference between the observed globular cluster system distribution and the underlying halo light profile. In the sample of galaxies examined it is found that the initial populations of globular clusters may have been ∼30 per cent to 50 per cent richer than now. If these 'missing' globular clusters have decayed and have been partly destroyed in the very central galactic zones, they have carried there a significant quantity of mass that, plausibly, contributed to the formation and feeding of a massive object therein. It is relevant to note that the observed correlation between the core radius of the globular cluster system and the parent galaxy luminosity can be interpreted as a result of evolution.