Cosmological perturbation theory and the spherical collapse model — III. The velocity divergence field and the Ω dependence

Cosmological perturbation theory (PT) is a useful tool to study the cumulants of the density and velocity fields in the large-scale structure of the Universe. In Papers I and II of this series we saw that the spherical collapse (SC) model provides the exact solution to PT at tree-level and gives a good approximation to the loop corrections (next-to-leading orders), indicating negligible tidal effects. Here, we derive predictions for the (smoothed) cumulants of the velocity divergence field θ ≡ ▽ ⊙  v for an irrotational fluid in the SC model. By comparing these with the exact analytic results of Scoccimarro &38; Frieman, it is shown that, at least for the unsmoothed case, the loop corrections to the cumulants of θ are dominated by tidal effects. However, most of the tidal contribution seems to cancel out when computing the hierarchical ratios, T _J  = 〈θ ^J 〉 / 〈θ²〉  ^{J −1}. We also extend the work presented in Papers I and II to give predictions for the cumulants of the density and velocity divergence fields in non-flat spaces. In particular, we show the equivalence between the spherically symmetric solution to the equations of motion in the SC model (given in terms of the density) and that of the Lagrangian PT approach (given in terms of the displacement field). It is shown that the Ω dependence is very weak for both cosmic fields even at one loop (a 10 per cent effect at most), except for the overall factor f (Ω) that couples to the velocity divergence.     

The non-linear redshift-space power spectrum of galaxies

We study the power spectrum of galaxies in redshift space, with third-order perturbation theory to include corrections that are absent in linear theory. We assume a local bias for the galaxies: i.e., the galaxy density is sampled from some local function of the underlying mass distribution. We find that the effect of the non-linear bias in real space is to introduce two new features: first, there is a contribution to the power which is constant with wavenumber, whose nature we reveal as essentially a shot-noise term. In principle this contribution can mask the primordial power spectrum, and could limit the accuracy with which the latter might be measured on very large scales. Secondly, the effect of second- and third-order bias is to modify the effective bias (defined as the square root of the ratio of galaxy power spectrum to matter power spectrum). The effective bias is almost scale-independent over a wide range of scales. These general conclusions also hold in redshift space. In addition, we have investigated the distortion of the power spectrum by peculiar velocities, which may be used to constrain the density of the Universe. We look at the quadrupole-to-monopole ratio, and find that higher order terms can mimic linear theory bias, but the bias implied is neither the linear bias, nor the effective bias referred to above. We test the theory with biased N -body simulations, and find excellent agreement in both real and redshift space, providing the local biasing is applied on a scale whose fractional rms density fluctuations are < 0.5.     

Cluster–subcluster mergers and the formation of narrow-angle tailed radio sources

We examine the ROSAT PSPC X-ray properties of a sample of 15 Abell clusters containing 23 narrow-angle tailed (NAT) radio galaxies. We find that clusters with NATs show a significantly higher level of substructure than a similar sample of radio-quiet clusters, indicating that NAT radio sources are preferentially located in dynamically complex systems. Also, the velocity distribution of the NAT galaxies is similar to that of other cluster members; these velocities are inadequate for producing the ram pressure necessary to bend the radio jets. We therefore propose a new model for NAT formation, in which NATs are associated with dynamically complex clusters undergoing merger events. The U -shaped NAT morphology is produced in part by the merger-induced bulk motion of the ICM bending the jets.     

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.     

Stellar models for very low-mass main-sequence stars: the role of model atmospheres

We present very low-mass stellar models as computed using non-grey model atmospheres for selected assumptions about the stellar metallicities. The role of atmospheres is discussed and the models are compared with models based on the Eddington approximation, and with similar models that have appeared in the recent literature. Theoretical predictions concerning both the HR diagram location and the mass–luminosity relation are presented and discussed in terms of expectations in selected photometric bands. Comparison with available observational data concerning both galactic globular clusters and dwarfs in the solar neighbourhood reveals a satisfactory agreement together with the existence of some residual mismatches.     

Mass segregation in young stellar clusters

We investigate the evolutionary effect of dynamical mass segregation in young stellar clusters. Dynamical mass segregation acts on a time-scale of order the relaxation time of a cluster. Although some degree of mass segregation occurs earlier, the position of massive stars in rich young clusters generally reflects the cluster's initial conditions. In particular, the positions of the massive stars in the Trapezium cluster in Orion cannot be due to dynamical mass segregation, but indicate that they formed in, or near, the centre of the cluster. Implications of this for cluster formation and for the formation of high-mass stars are discussed.     

TRIFFID Photometry of Globular Cluster Cores — I. Photometric Techniques and Variable Stars in M15

The Galway/DIAS Image Sharpening Camera, TRIFFID, has been used to make observations in two colours of the centre of the post-core-collapse globular cluster M15. We present here our analysis of the photometry in B over two seasons. We have combined the complementary qualities of the HST 's high astrometric precision and TRIFFID's extended coverage and photometric precision, to perform crowded-field photometry in the innermost region of M15. Our technique virtually eliminates the problem of extreme crowding which has hitherto hampered studies of the variable star populations in globular cluster cores, and thereby provides an extension of the HST 's capability. Candidate variables detected with the HST have been confirmed and monitored over longer periods. We show that most of these are RR Lyrae stars, and that one is a short-period Type II Cepheid (the third to be discovered in M15). Our photometric study also produced evidence of a similar number of new variables. These also appear to be RR Lyrae stars, except for a possible eclipsing system. Further data from an upgraded version of TRIFFID have recently been obtained to help to refine the light curves of all these objects.