The evolution of substructure – III. The outskirts of clusters

We present an investigation of satellite galaxies in the outskirts of galaxy clusters taken from a series of high-resolution N -body simulations. We focus on the so-called backsplash population, i.e. satellite galaxies that once were inside the virial radius of the host but now reside beyond it. We find that this population is significant in number and needs to be appreciated when interpreting the various galaxy morphology environmental relationships and decoupling the degeneracy between nature and nurture. Specifically, we find that approximately half of the galaxies with current cluster-centric distance in the interval 1–2 virial radii of the host are backsplash galaxies that once penetrated deep into the cluster potential, with 90 per cent of these entering to within 50 per cent of the virial radius. These galaxies have undergone significant tidal disruption, losing on average 40 per cent of their mass. This results in a mass function for the backsplash population different from those galaxies infalling for the first time. We further show that these two populations are kinematically distinct and should be observable within existent spectroscopic surveys.     

Testing fundamental physics with distant star clusters: theoretical models for pressure-supported stellar systems

We investigate the mean velocity dispersion and the velocity dispersion profile of stellar systems in modified Newtonian dynamics (MOND), using the N -body code n-mody , which is a particle-mesh-based code with a numerical MOND potential solver developed by Ciotti, Londrillo & Nipoti. We have calculated mean velocity dispersions for stellar systems following Plummer density distributions with masses in the range of 10⁴ to  10⁹ M_⊙  and which are either isolated or immersed in an external field. Our integrations reproduce previous analytic estimates for stellar velocities in systems in the deep MOND regime  ( a _i, a _e≪ a ₀)  , where the motion of stars is either dominated by internal accelerations  ( a _i≫ a _e)  or constant external accelerations  ( a _e≫ a _i)  . In addition, we derive for the first time analytic formulae for the line-of-sight velocity dispersion in the intermediate regime  ( a _i∼ a _e∼ a ₀)  . This allows for a much-improved comparison of MOND with observed velocity dispersions of stellar systems. We finally derive the velocity dispersion of the globular cluster Pal 14 as one of the outer Milky Way halo globular clusters that have recently been proposed as a differentiator between Newtonian and MONDian dynamics.     

Dynamic evolution of nearby galaxy clusters

A study of the evolution of 377 rich ACO clusters with redshift z < 0.2 is presented. The data concerning galaxies in the investigated clusters were obtained using FOCAS packages applied to Digital Sky Survey I. The 377 galaxy clusters constitute a statistically uniform sample to which visual galaxy/star reclassifications were applied. Cluster shape within 2.0 h^–1 Mpc from the adopted cluster centre (the mean and the median of all galaxy coordinates, the position of the brightest and of the third brightest galaxy in the cluster) was determined through its ellipticity calculated using two methods: the covariance ellipse method (hereafter CEM) and the method based on Minkowski functionals (hereafter MFM). We investigated ellipticity dependence on the radius of circular annuli, in which ellipticity was calculated. This was realized by varying the radius from 0.5 to 2 Mpc in steps of 0.25 Mpc. By performing Monte Carlo simulations, we generated clusters to which the two ellipticity methods were applied. We found that the covariance ellipse method works better than the method based on Minkowski functionals. We also found that ellipticity distributions are different for different methods used. Using the ellipticity‐redshift relation, we investigated the possibility of cluster evolution in the low‐redshift Universe. The correlation of cluster ellipticities with redshifts is undoubtly an indicator of structural evolution. Using the t‐Student statistics, we found a statistically significant correlation between ellipticity and redshift at the significance level of α = 0.95. In one of the two shape determination methods we found that ellipticity grew with redshift, while the other method gave opposite results. Monte Carlo simulations showed that only ellipticities calculated at the distance of 1.5 Mpc from cluster centre in the Minkowski functional method are robust enough to be taken into account, but for that radius we did not find any relation between e and z. Since CEM pointed towards the existence of the e (z) relation, we conclude that such an effect is real though rather weak. A detailed study of the e (z) relation showed that the observed relation is nonlinear, and the number of elongated structures grows rapidly for z > 0.14 (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

X-ray clusters of galaxies in conformal gravity

We run adiabatic N -body/hydrodynamical simulations of isolated self-gravitating gas clouds to test whether conformal gravity, an alternative theory to general relativity, is able to explain the properties of X-ray galaxy clusters without resorting to dark matter. We show that the gas clouds rapidly reach equilibrium with a density profile which is well fitted by a β-model whose normalization and slope are in approximate agreement with observations. However, conformal gravity fails to yield the observed thermal properties of the gas cloud: (i) the mean temperature is at least an order of magnitude larger than the observed and (ii) the temperature profiles increase with the square of the distance from the cluster centre, in clear disagreement with real X-ray clusters. These results depend on a gravitational potential whose parameters reproduce the velocity rotation curves of spiral galaxies. However, this parametrization stands on an arbitrarily chosen conformal factor. It remains to be seen whether a different conformal factor, specified by a spontaneous breaking of the conformal symmetry, can reconcile this theory with observations.     

The evolution of the galaxy red sequence in simulated clusters and groups

N -body/hydrodynamical simulations of the formation and evolution of galaxy groups and clusters in a Λ cold dark matter (ΛCDM) cosmology are used in order to follow the building-up of the colour–magnitude relation in two clusters and in 12 groups. We have found that galaxies, starting from the more massive, move to the red sequence (RS) as they get aged over times and eventually set upon a 'dead sequence' (DS) once they have stopped their bulk star formation activity. Fainter galaxies keep having significant star formation out to very recent epochs and lie broader around the RS. Environment plays a role as galaxies in groups and cluster outskirts hold star formation activity longer than the central cluster regions. However, galaxies experiencing infall from the outskirts to the central parts keep star formation on until they settle on to the DS of the core galaxies. Merging contributes to mass assembly until z ∼ 1, after which major events only involve the brightest cluster galaxies.
The emerging scenario is that the evolution of the colour–magnitude properties of galaxies within the hierarchical framework is mainly driven by star formation activity during dark matter haloes assembly. Galaxies progressively quenching their star formation settle to a very sharp 'red and dead' sequence, which turns out to be universal, its slope and scatter being almost independent of the redshift (since at least z ∼ 1.5) and environment.
Differently from the DS, the operatively defined RS evolves more evidently with z , the epoch when it changes its slope being closely corresponding to that at which the passive galaxies population takes over the star-forming one: this goes from z ≃ 1 in clusters down to 0.4 in normal groups.     

Can simulations reproduce the observed temperature–mass relation for clusters of galaxies?

It has become increasingly apparent that traditional hydrodynamical simulations of galaxy clusters are unable to reproduce the observed properties of galaxy clusters, in particular overpredicting the mass corresponding to a given cluster temperature. Such overestimation may lead to systematic errors in results using galaxy clusters as cosmological probes, such as constraints on the density perturbation normalization σ ₈. In this paper we demonstrate that inclusion of additional gas physics, namely radiative cooling and a possible pre-heating of gas prior to cluster formation, is able to bring the temperature–mass relation in the innermost parts of clusters into good agreement with recent determinations by Allen, Schmidt & Fabian using Chandra data.     

Ram pressure stripping the hot gaseous haloes of galaxies in groups and clusters

We use a large suite of carefully controlled full hydrodynamic simulations to study the ram pressure stripping of the hot gaseous haloes of galaxies as they fall into massive groups and clusters. The sensitivity of the results to the orbit, total galaxy mass, and galaxy structural properties is explored. For typical structural and orbital parameters, we find that ∼30 per cent of the initial hot galactic halo gas can remain in place after 10 Gyr. We propose a physically simple analytic model that describes the stripping seen in the simulations remarkably well. The model is analogous to the original formulation of Gunn & Gott, except that it is appropriate for the case of a spherical (hot) gas distribution (as opposed to a face-on cold disc) and takes into account that stripping is not instantaneous but occurs on a characteristic time-scale. The model reproduces the results of the simulations to within ≈10 per cent at almost all times for all the orbits, mass ratios, and galaxy structural properties we have explored. The one exception involves unlikely systems where the orbit of the galaxy is highly non-radial and its mass exceeds about 10 per cent of the group or cluster into which it is falling (in which case the model underpredicts the stripping following pericentric passage). The proposed model has several interesting applications, including modelling the ram pressure stripping of both observed and cosmologically simulated galaxies and as a way to improve present semi-analytic models of galaxy formation. One immediate consequence is that the colours and morphologies of satellite galaxies in groups and clusters will differ significantly from those predicted with the standard assumption of complete stripping of the hot coronae.     

Star clusters with primordial binaries – I. Dynamical evolution of isolated models

In order to interpret the results of complex realistic star cluster simulations, which rely on many simplifying approximations and assumptions, it is essential to study the behaviour of even more idealized models, which can highlight the essential physical effects and are amenable to more exact methods. With this aim, we present the results of N -body calculations of the evolution of equal-mass models, starting with primordial binary fractions of 0–100 per cent, with values of N ranging from 256 to 16 384. This allows us to extrapolate the main features of the evolution to systems comparable in particle number with globular clusters.
In this range, we find that the steady-state 'deuterium main sequence' is characterized by a ratio of the core radius to half-mass radius that follows qualitatively the analytical estimate by Vesperini & Chernoff, although the N dependence is steeper than expected. Interestingly, for an initial binary fraction f greater than 10 per cent, the binary heating in the core during the post-collapse phase almost saturates (becoming nearly independent of f ), and so little variation in the structural properties is observed. Thus, although we observe a significantly lower binary abundance in the core with respect to the Fokker–Planck simulations by Gao et al., this is of little dynamical consequence.
At variance with the study of Gao et al., we see no sign of gravothermal oscillations before 150 half-mass relaxation times. At later times, however, oscillations become prominent. We demonstrate the gravothermal nature of these oscillations.     

On the trapping of stars by a newborn stellar supercluster

Numerical experiments conducted by Fellhauer et al. suggest that a supercluster may capture up to about 40 per cent of its mass from the galaxy where it belongs. Nevertheless, in those experiments the cluster was created making appear its mass out of nothing, rather than from mass already present in the galaxy. Here, we use a thought experiment, plus a few simple computations, to show that the difference between the dynamical effects of these two scenarios (i.e. mass creation versus mass concentration) is actually very important. We also present the results of new numerical experiments, simulating the formation of the cluster through mass concentration, that show that trapping depends critically on the process of cluster formation and that the amounts of gained mass are substantially smaller than those obtained from mass creation. Besides, the criterion used by Fellhauer et al. to decide the membership to the supercluster is not adequate, and the use of a more sensible criterion, based on Jacobi's integral, renders a number of captures at least an order of magnitude smaller. All things considered, the captures cannot exceed, at most, a few per cent of the mass of the cluster.     

Effects of external tidal field on the evolution of the outer regions of multi-mass star clusters

We present N -body simulations (including an initial mass function) of globular clusters in the Galaxy in order to study effects of the tidal field systematically on the properties of the outer parts of globular clusters. Using nbody6 , which correctly takes into account the two-body relaxation, we investigate the development of tidal tails of globular clusters in the Galactic tidal field. For simplicity, we have employed only the spherical components (bulge and halo) of the Galaxy, and ignored the effects of stellar evolution which could have been important in the very early phase of the cluster evolution. The total number of stars in our simulations is about 20 000, which is much smaller than the realistic number of stars. All simulations had been done for several orbital periods in order to understand the development of the tidal tails. In our scaled-down models, the relaxation time is sufficiently short to show the mass segregation effect, but we did not go far enough to see the core collapse, and the fraction of stars lost from the cluster at the end of the simulations is only ∼10 per cent. The radial distribution of extra-tidal stars can be described by a power law with a slope around −3 in surface density. The directions of tidal tails are determined by the orbits and locations of the clusters. We find that the length of tidal tails increases towards the apogalacticon and decreases towards the perigalacticon. This is an anti-correlation with the strength of the tidal field, caused by the fact that the time-scale for the stars to respond to the potential is similar to the orbital time-scale of the cluster. The escape of stars in the tidal tails towards the pericentre could be another reason for the decrease of the length of tidal tails. We find that the rotational angular velocity of tidally induced clusters shows quite different behaviour from that of initially rotating clusters.