Supersonic motions of galaxies in clusters

We study motions of galaxies in galaxy clusters formed in the concordance Λ cold dark matter cosmology. We use high-resolution cosmological simulations that follow the dynamics of dark matter and gas and include various physical processes critical for galaxy formation: gas cooling, heating and star formation. Analysing the motions of galaxies and the properties of intracluster gas in a sample of eight simulated clusters at z = 0, we study the velocity dispersion profiles of the dark matter, gas and galaxies. We measure the mean velocity of galaxy motions and gas sound speed as a function of radius and calculate the average Mach number of galaxy motions. The simulations show that galaxies, on average, move supersonically with the average Mach number of ≈1.4, approximately independent of the cluster-centric radius. The supersonic motions of galaxies may potentially provide an important source of heating for the intracluster gas by driving weak shocks and via dynamical friction, although these heating processes appear to be inefficient in our simulations. We also find that galaxies move slightly faster than the dark matter particles. The magnitude of the velocity bias,   b _v ≈ 1.1  , is, however, smaller than the bias estimated for subhaloes in dissipationless simulations. Interestingly, we find velocity bias in the tangential component of the velocity dispersion, but not in the radial component. Finally, we find significant random bulk motions of gas. The typical gas velocities are of order ≈20–30 per cent of the gas sound speed. These random motions provide about 10 per cent of the total pressure support in our simulated clusters. The non-thermal pressure support, if neglected, will bias measurements of the total mass in the hydrostatic analyses of the X-ray cluster observations.     

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.     

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.     

Dark matter influence on velocity dispersion profiles of clusters of galaxies

We have performed a series ofN-body experiments including the effects of a massive dominant background which follows Schuster's density law in order to simulate clusters of galaxies in which a smoothly distributed dark component is present. The existence of this background is inferred from the weak luminosity segregation observed in clusters which, however, show several characteristics of well-relaxed systems. The comparison of the velocity dispersion profiles of three clusters of galaxies (Coma, Perseus, and Virgo) with those obtained in the numerical experiments allows us to place some constraints on both the distribution and amount of distributed dark material in these clusters. The profiles are rather insensitive to variations in the ratio of the background mass to the mass attached to galaxies (M _b/M_g), but exhibit a strong dependence on their relative concentration. We conclude that highly concentrated background models are not consistent with observations. We find a maximum value for the ratio of the gravitational radius of the galaxies and the background (R _g/R_b) (approximately 0.6) and using previous results (Navarroet al., 1986) we conclude that virial theorem masses underestimate the total mass (M _b+M _g) of the clusters. As a final result, we derive a minimum value for theM _b/M_g ratio. All these conclusions could apply in general if Coma, Perseus, and Virgo constitute a fair sample of the rich clusters of galaxies in the Universe.     

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.     

Optical and X-ray structures of galaxy clusters. I

The differences between optical and X-ray structures of galaxy clusters are discussed. We analyse in detail 7 Abell clusters. There is an increasing number of arguments in favour of different distributions of galaxies, gas, and dark matter in many clusters. We argue that most clusters present sub-structures at least in the gaseous and galactic components and, moreover, the subclustering of different components does not always coincide. Such arguments strongly support the idea that most galaxy clusters are by far more complex systems than accepted until now and are usually not in an hydrostatic isothermal equilibrium.     

Evolutionary approach to the missing mass problem of clusters of galaxies

In a gravitationally bound and stable cluster of galaxies the amount and distribution of matter determine both the velocity dispersion of the members and the type of evolution of the system. The use of the first of these physical connections — the application of virial theorem — led to the idea of missing mass in clusters, that of the second one seems to support this idea by an independent “rediscovery” and “redistribution” of missing mass. On the basis of this “evolutionary approach” to the missing mass problem — that is free from the uncertainties of measuring and interpreting red shifts — evidences are obtained for the existence of large amounts of discretely distributed dark circumgalactic or intragalactic matter in rich clusters of galaxies.     

A primordial feature at the scale of superclusters of galaxies

We investigate a spatially flat cold dark matter model (with the matter density parameter     with a primordial feature in the initial power spectrum. We assume that there is a bump in the power spectrum of density fluctuations at wavelengths     , which corresponds to the scale of superclusters of galaxies . There are indications for such a feature in the power spectra derived from redshift surveys and also in the power spectra derived from peculiar velocities of galaxies. We study the mass function of clusters of galaxies, the power spectrum of the cosmic microwave background (CMB) temperature fluctuations, the rms bulk velocity and the rms peculiar velocity of clusters of galaxies. The baryon density is assumed to be consistent with the big bang nucleosynthesis value. We show that with an appropriately chosen feature in the power spectrum of density fluctuations at the scale of superclusters, the mass function of clusters, the CMB power spectrum, the rms bulk velocity and the rms peculiar velocity of clusters are in good agreement with the observed data.     

The dark matter environment of the Abell 901/902 supercluster: a weak lensing analysis of the HST STAGES survey

We present a high-resolution dark matter reconstruction of the   z = 0.165  Abell 901/902 supercluster from a weak lensing analysis of the Hubble Space Telescope STAGES survey. We detect the four main structures of the supercluster at high significance, resolving substructure within and between the clusters. We find that the distribution of dark matter is well traced by the cluster galaxies, with the brightest cluster galaxies marking out the strongest peaks in the dark matter distribution. We also find a significant extension of the dark matter distribution of Abell 901a in the direction of an infalling X-ray group Abell 901α. We present mass, mass-to-light and mass-to-stellar mass ratio measurements of the structures and substructures that we detect. We find no evidence for variation of the mass-to-light and mass-to-stellar mass ratio between the different clusters. We compare our space-based lensing analysis with an earlier ground-based lensing analysis of the supercluster to demonstrate the importance of space-based imaging for future weak lensing dark matter 'observations'.     

Neutrinos as cluster dark matter

The dynamical mass of clusters of galaxies, calculated in terms of MOdified Newtonian Dynamics (MOND), is a factor of 2 or 3 times smaller than the Newtonian dynamical mass but remains significantly larger than the observed baryonic mass in the form of hot gas and stars in galaxies. Here I consider further the suggestion that the undetected matter might be in the form of cosmological neutrinos with mass of the order of 2 eV. If the neutrinos and baryons have comparable velocity dispersions and if the two components maintain their cosmological density ratio, then the electron density in the cores of clusters should be proportional to T ^3/2, as appears to be true in non-cooling flow clusters. This is equivalent to the 'entropy floor' proposed to explain the steepness of the observed luminosity–temperature relation, but here preheating of the medium is not required. Two-fluid (neutrino–baryon) hydrostatic models of clusters, in the context of MOND, reproduce the observed luminosity–temperature relation of clusters. If the β law is imposed on the gas density distribution, then the self-consistent models predict the general form of the observed temperature profile in both cooling and non-cooling flow clusters.     

Completely dark galaxies: their existence, properties and strategies for finding them

There are a number of theoretical and observational hints that large numbers of low-mass galaxies composed entirely of dark matter exist in the field. The theoretical considerations follow from the prediction of cold dark matter theory that there exist many low-mass galaxies for every massive one. The observational considerations follow from the observed paucity of these low-mass galaxies in the field but not in dense clusters of galaxies; this suggests that the lack of small galaxies in the field is due to the inhibition of star formation in the galaxies as opposed to the fact that their small dark matter haloes do not exist. In this work we outline the likely properties of low-mass dark galaxies, and describe observational strategies for finding them, and where in the sky to search. The results are presented as a function of the global properties of dark matter, in particular the presence or absence of a substantial baryonic dark matter component. If the dark matter is purely cold and has a Navarro, Frenk & White density profile, directly detecting dark galaxies will only be feasible with present technology if the galaxy has a maximum velocity dispersion in excess of 70 km s⁻¹, in which case the dark galaxies could strongly lens background objects. This is much higher than the maximum velocity dispersions in most dwarf galaxies. If the dark matter in galaxy haloes has a baryonic component close to the cosmic ratio, the possibility of directly detecting dark galaxies is much more realistic; the optimal method of detection will depend on the nature of the dark matter. A number of more indirect methods are also discussed.     

Dark matter distribution in dwarf spheroidal galaxies

We study the distribution of dark matter in dwarf spheroidal galaxies by modelling the moments of their line-of-sight velocity distributions. We discuss different dark matter density profiles, both cuspy and possessing flat density cores. The predictions are made in the framework of standard dynamical theory of two-component (stars and dark matter) spherical systems with different velocity distributions. We compare the predicted velocity dispersion profiles to observations in the case of Fornax and Draco dwarfs. For isotropic models the dark haloes with cores are found to fit the data better than those with cusps. Anisotropic models are studied by fitting two parameters, dark mass and velocity anisotropy, to the data. In this case all profiles yield good fits, but the steeper the cusp of the profile, the more tangential is the velocity distribution required to fit the data. To resolve this well-known degeneracy of density profile versus velocity anisotropy, we obtain predictions for the kurtosis of the line-of-sight velocity distribution for models found to provide best fits to the velocity dispersion profiles. It turns out that profiles with cores typically yield higher values of kurtosis which decrease more steeply with distance than the cuspy profiles, which will allow us to discriminate between the profiles once the kurtosis measurements become available. We also show that with present quality of the data the alternative explanation of velocity dispersions in terms of Modified Newtonian Dynamics cannot yet be ruled out.     

Measuring the distribution of galaxies between haloes

We develop a method to measure the probability, P ( N;   M ), of finding N galaxies in a dark matter halo of mass M from the theoretically determined clustering properties of dark matter haloes and the observationally measured clustering properties of galaxies. Knowledge of this function and the distribution of the dark matter completely specifies all clustering properties of galaxies on scales larger than the size of dark matter haloes. Furthermore, P ( N;   M ) provides strong constraints on models of galaxy formation, since it depends upon the merger history of dark matter haloes and the galaxy–galaxy merger rate within haloes. We show that measurements from a combination of the Two Micron All Sky Survey and Sloan Digital Sky Survey or Two-degree Field Galaxy Redshift Survey data sets will allow P ( N;   M ) averaged over haloes occupied by bright galaxies to be accurately measured for N =0–2 .     

Observational constraints of sterile neutrinos in galaxies

We study a model in which degenerate sterile neutrinos account for galactic dark matter. We fit the rotation curves of 5 dwarf galaxies with the degenerate sterile neutrinos in hydrostatic equilibrium. Also we estimate the range of sterile neutrino mass by calculating the upper and lower bounds of the mass densities of sterile neutrino halos in the outermost regions of 21 normal galaxies. The observed rotation curves of 5 dwarf galaxies and 21 normal galaxies are consistent with having sterile neutrinos with mass (26–30) eV, and the similarity of the rotation curves of different galaxies emerges naturally in our model.     

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.     

Satellite kinematics – II. The halo mass–luminosity relation of central galaxies in SDSS

The kinematics of satellite galaxies reflect the masses of the extended dark matter haloes in which they orbit, and thus shed light on the mass–luminosity relation (MLR) of their corresponding central galaxies. In this paper, we select a large sample of centrals and satellites from the Sloan Digital Sky Survey and measure the kinematics (velocity dispersions) of the satellite galaxies as a function of the r -band luminosity of the central galaxies. Using the analytical framework presented in More, van den Bosch & Cacciato, we use these data to infer both the mean and the scatter of the MLR of central galaxies, carefully taking account of selection effects and biases introduced by the stacking procedure. As expected, brighter centrals on average reside in more massive haloes. In addition, we find that the scatter in halo masses for centrals of a given luminosity,  σ_{log  M}   , also increases with increasing luminosity. As we demonstrate, this is consistent with  σ_{log  L}   , which reflects the scatter in the conditional probability function   P ( L _c| M )  , being independent of halo mass. Our analysis of the satellite kinematics yields  σ_{log  L} = 0.16  ±  0.04  , in excellent agreement with constraints from clustering and group catalogues, and with predictions from a semi-analytical model of galaxy formation. We thus conclude that the amount of stochasticity in galaxy formation, which is characterized by  σ_{log  L}   , is well constrained, independent of halo mass and in a good agreement with current models of galaxy formation.     

Gravitational stability of dark energy in galaxies and clusters of galaxies

We analyze the behavior of the scalar field as dark energy of the Universe in a static world of galaxies and clusters of galaxies. We find the analytical solutions of evolution equations of the density and velocity perturbations of dark matter and dark energy, which interact only gravitationally, along with the perturbations of metric in a static world with background Minkowski metric. It was shown that quintessential and phantom dark energy in the static world of galaxies and clusters of galaxies is gravitationally stable and can only oscillate by the influence of self-gravity. In the gravitational field of dark matter perturbations, it is able to condense monotonically, but the amplitude of density and velocity perturbations on all scales remains small. It was also illustrated that the “accretion” of phantom dark energy in the region of dark matter overdensities causes formation of dark energy underdensities-the regions with negative amplitude of density perturbations of dark energy.     

The kinematics of lopsided galaxies

Lopsidedness is a common feature in galaxies, both in the distribution of light and in the kinematics. We investigate the kinematics of a model for lopsided galaxies that consists of a disc lying off-centre in a dark halo, and circling around the halo centre. We search for families of stable, closed, non-crossing orbits, and assume that gas in our galaxies moves on these orbits. Several of our models show strong lopsided gas kinematics, especially those in which the disc spins around its axis in a retrograde sense compared with its motion around the halo centre. We are able to reproduce the H  i velocity map of the kinematically lopsided galaxy NGC 4395.
The lopsidedness in our models is most pronounced in the models where the halo provides a relatively large fraction of the total mass at small radii. This may explain why the gas shows lopsidedness more frequently in late-type galaxies, which are dominated by dark matter. Surfaces of section show large regions of irregular orbits in the models where the halo density is low. This may indicate that these models are unstable.     

Clusters of galaxies with modified Newtonian dynamics

I consider X-ray emitting clusters of galaxies in the context of modified Newtonian dynamics (MOND). Self-gravitating isothermal gas spheres are not good representations of rich clusters; the X-ray luminosity at a given temperature is typically an order of magnitude larger than observed, and the predicted X-ray surface brightness distribution is not well-matched by the standard 'β-model' fits to the observations. Pure gas spheres with a density distribution described by a β-model also fail because, with MOND, these objects are far from isothermal and again overluminous. These problems may be resolved by adding an additional dark mass component in the central regions, here modelled by a constant density sphere contained within two core radii and having a mass typically of one to two times the total cluster mass in the gas. With this additional component, the observed luminosity–temperature relation for clusters of galaxies is reproduced, and the typical mass discrepancy in actual clusters is three to four times smaller than implied by Newtonian dynamics. Thus, while MOND significantly reduces the mass of the dark component in clusters it does not remove it completely. I speculate on the nature of the dark component and argue that neutrinos, with mass near the experimental upper limit are a possible candidate.     

The effect of dwarf galaxy disruption in semi-analytic models

We present results for a galaxy formation model that includes a simple treatment for the disruption of dwarf galaxies by gravitational forces and galaxy encounters within galaxy clusters. This is implemented a posteriori in a semi-analytic model by considering the stability of cluster dark matter subhaloes at   z = 0  . We assume that a galaxy whose dark matter substructure has been disrupted will itself disperse, while its stars become part of the population of intracluster stars responsible for the observed intracluster light. Despite the simplicity of this assumption, our results show a substantial improvement over previous models and indicate that the inclusion of galaxy disruption is indeed a necessary ingredient of galaxy formation models. We find that galaxy disruption suppresses the number density of dwarf galaxies by about a factor of 2. This makes the slope of the faint end of the galaxy luminosity function shallower, in agreement with observations. In particular, the abundance of faint, red galaxies is strongly suppressed. As a result, the luminosity function of red galaxies and the distinction between the red and the blue galaxy populations in colour–magnitude relationships are correctly predicted. Finally, we estimate a fraction of intracluster light comparable to that found in clusters of galaxies.