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.     

X-ray binary unified analysis: pulse/RV application to Vela X1: GP Velorum

A procedure for simultaneous analysis of multiple kinds of observations is developed for binaries that contain X-ray pulsars. A wide variety of observation types might be included, although we consider only velocity: pulse and light: velocity: pulse cases at present. The model operates with equipotentials and can accommodate non-synchronous rotation and eccentric orbits. The duration condition imposed by observed X-ray eclipses is incorporated as an embedded constraint, so that only solutions consistent with the eclipse duration are found. Relations needed for the method of differential corrections in least-squares solutions are specified, and we apply the Marquardt scheme for improvement of solution convergence. Parameters of Vela X1: GP Velorum are obtained from seven combinations of pulse and radial velocity data. The estimated masses are thereby put into some perspective, especially for the neutron star. The mass of the supergiant ( m  sin³  i ) now ranges only ±5 per cent from the mean of seven results, although the uncertainty in i makes the actual mass range larger. We discuss the determinacy of certain parameters and their historical consistency. For example, the systemic radial velocity differs among spectroscopic data sets by more than 20 km s⁻¹. We show that, contrary to published assertions, the orbital inclinations of high-mass X-ray binaries are essentially indeterminable by the usual methods, although lower limits to inclination may be meaningful for some examples.     

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.     

Studies of ultracompact H ii regions — II. High-resolution radio continuum and methanol maser survey

High spatial resolution radio continuum and 6.67-GHz methanol spectral line data are presented for methanol masers previously detected by Walsh et al. (1997). Methanol maser and/or radio continuum emission is found in 364 cases towards IRAS -selected regions. For those sources with methanol maser emission, relative positions have been obtained to an accuracy of typically 0.05 arcsec, with absolute positions accurate to around 1 arcsec. Maps of selected sources are provided. The intensity of the maser emission does not seem to depend on the presence of a continuum source. The coincidence of water and methanol maser positions in some regions suggests there is overlap in the requirements for methanol and water maser emission to be observable. However, there is a striking difference between the general proximity of methanol and water masers to both cometary and irregularly shaped ultracompact (UC) H  ii regions, indicating that, in other cases, there must be differing environments conducive to stimulating their emission. We show that the methanol maser is most likely present before an observable UC H  ii region is formed around a massive star and is quickly destroyed as the UC H  ii region evolves. There are 36 out of 97 maser sites that are linearly extended. The hypothesis that the maser emission is found in a circumstellar disc is not inconsistent with these 36 maser sites, but is unlikely. It cannot, however, account for all other maser sites. An alternative model which uses shocks to create the masing spots can more readily reproduce the maser spot distributions.     

The destructive effects of binary encounters on red giants in the Galactic Centre

We consider the destructive effects of encounters between binaries and red giant stars in the Galactic Centre. Such encounters may explain the observed depletion of luminous red giants within the central 0.2 pc of the galaxy. We consider encounters involving 2- and 8-M⊙ red giants, and thus span the range of stellar masses contributing to the most luminous red giants observed in the Galactic Centre. To explore the phase space of encounters thoroughly, we simulate 18 × 10³ encounters using a modified four-body code in which the red giant core and components of the binary are treated as point masses, and where the envelope configuration is assumed to remain static throughout the encounter. We then rerun a small number of encounters with a smoothed particle hydrodynamics (SPH) code to confirm the reliability of conclusions drawn from the four-body runs. We see two possible pathways to red giant destruction. A large fraction of encounters lead to the formation of common-envelope systems, where two compact objects (drawn from the red giant core and the components of the original binary) form a binary within a common gaseous envelope, whilst the third body is ejected. The destruction of the red giant will then follow when the envelope is ejected as the binary hardens. In a smaller number of encounters, the intruding binary passes through the star and ejects the red giant core from the envelope. The red giant envelope will then disperse on short time-scales. We compute the time-scales for both of these processes to occur in the Galactic Centre for a variety of binary populations.     

Optical and near-infrared imaging of faint Gigahertz Peaked Spectrum sources

A sample of 47 faint Gigahertz Peaked Spectrum (GPS) radio sources selected from the Westerbork Northern Sky Survey (WENSS) has been imaged in the optical and near-infrared, resulting in an identification fraction of 87 per cent. The R  −  I R  −  K colours of the faint optical counterparts are as expected for passively evolving elliptical galaxies, assuming that they follow the R -band Hubble diagram as determined for radio-bright GPS galaxies. We find evidence that the radio spectral properties of the GPS quasars are different from those of GPS galaxies. The observed distribution of radio spectral peak frequencies for GPS sources optically identified with bright stellar objects (presumably quasars) is shifted compared with GPS sources identified with faint or extended optical objects (presumably galaxies), in the sense that a GPS quasar is likely to have a higher peak frequency than a GPS galaxy. This means that the true peak frequency distribution is different for the GPS galaxies and quasars, because the sample selection effects are independent of optical identification. The correlation between peak frequency and redshift that has been suggested for bright sources has not been found in this sample; no correlation exists between R magnitude (and therefore redshift) and peak frequency for the GPS galaxies. We therefore believe that the claimed correlation is actually caused by the dependence of the peak frequency on optical host, because the GPS galaxies are generally at lower redshifts than the quasars. The difference in the peak frequency distributions of the GPS galaxies and quasars is further evidence against the hypothesis that they form a single class of object.     

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.