Gravitational lensing effects on high-redshift Type II supernova studies with the Next Generation Space Telescope

We derive the expected Type II supernova (SN) differential number counts, N ( m ), and Hubble diagram for SCDM and LCDM cosmological models, taking into account the effects of gravitational lensing (GL) produced by the intervening cosmological mass. The mass distribution of dark matter haloes (i.e. the lenses) is obtained by means of a Monte Carlo method applied to the PressSchechter mass function. The haloes are assumed to have a Navarro, Frenk & White (NFW) density profile, in agreement with recent simulations of hierarchical cosmological models. Up to z =15, the (SCDM, LCDM) models predict a total number of (857, 3656) SNII yr¹ in 100 surveyed 44 arcmin² fields of the Next Generation Space Telescope ( NGST ). NGST will be able to reach the peak of the N ( m ) curve, located at AB 30(31) for SCDM (LCDM) in J and K wavelength bands, and detect (75 per cent, 51 per cent) of the above SN events. This will allow a detailed study of the early cosmic star formation history, as traced by SNIIe. N ( m ) is only very mildly affected by the inclusion of lensing effects. In addition, GL introduces a moderate uncertainty in the determination of cosmological parameters from Hubble diagrams, when these are pushed to higher z . For example, for a 'true' LCDM with (_M=0.4, =0.6), without proper account of GL, one would instead derive We briefly compare our results with previous similar work and discuss the limitations of the model.     

The transparency of the Universe limited by Lyα clouds

The brightnesses of supernovae are commonly understood to indicate that cosmological expansion is accelerating due to dark energy. However the entire discussion presumes a perfectly transparent universe because no effects of reddening associated with the interstellar extinction law are seen. We note that with two kinds of dark matter (baryonic and nonbaryonic) strongly dominating the known mass of the universe, it is seriously premature to assume that these dark matter components have not reduced the transmission of the universe for cosmological sources. We show that the long‐known Lyα clouds, if nucleated by the population of baryonic dark matter primordial planetoids indicated by quasar microlensing, would act as spherical lenses and achromatically fade cosmologically distant sources. We attempt to estimate the amount of this cosmological fading, but ultimately the calculation is limited by lack of a satisfactory model for the tenuous outer parts of a primordial planetoid. We also consider the effects of such cosmological fading on the light of quasars. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Using galaxy redshift surveys to detect gravitationally lensed quasars

Gravitationally lensed quasars can be discovered as a by-product of galaxy redshift surveys. Lenses discovered spectroscopically in this way should require less observational effort per event than those found in dedicated lens surveys. Further, the lens galaxies should be relatively nearby, facilitating a number of detailed observations that are impossible for the more common high-redshift lenses. This is epitomized by the wide range of results that have been obtained from Q 2237+0305, which was discovered as part of the Center for Astrophysics redshift survey, and remains the only quasar lens discovered in this way. The likelihood of this survey yielding a lens is calculated to be ∼0.03, which is an order of magnitude larger than previous estimates due to two effects. First, the quasar images themselves increase the observed flux of the lens, so that lens galaxies up to a magnitude fainter than the nominal survey limit must be included in the calculation. Secondly, it is possible for lensed quasars with extremely faint deflectors to enter the survey due to the extended morphology of the multiple images. Extrapolating these results to future surveys, the 2 degree Field galaxy redshift survey should contain between 10 and 50 lenses and the Sloan Digital Sky Survey should yield between 50 and 300 lenses, depending on the cosmological model and the observing conditions.     

The formation and evolution of clusters of galaxies in different cosmogonies

The formation of galaxy clusters in hierarchically clustering universes is investigated by means of high-resolution N -body simulations. The simulations are performed using a newly developed multimass scheme which combines a PM code with a high-resolution N -body code. Numerical effects resulting from time-stepping and gravitational softening are investigated, as well as the influence of the simulation box size and of the assumed boundary conditions. Special emphasis is laid on the formation process and the influence of various cosmological parameters. Cosmogonies with massive neutrinos are also considered. Differences between clusters in the same cosmological model seem to dominate over differences caused by differing background cosmogony. The cosmological model can alter the time evolution of cluster collapse, but the merging pattern remains fairly similar, e.g. the number of mergers and the mass ratio of mergers. The gross properties of a halo, such as its size and total angular momentum, also evolve in a similar manner for all cosmogonies, and can be described using analytical models. It is shown that the density distribution of a halo shows a characteristic radial dependence which follows a power law with a slope of =1 at small radii and =3 at large radii, independent of the background cosmogony or the considered redshift. The shape of the density profiles follows the generic form proposed by Navarro et al. for all hierarchically clustering scenarios, and retains very little information about the formation process or the cosmological model. Only the central matter concentration of a halo is correlated with the formation time and therefore the corresponding cosmogony. We emphasize the role of non-radial motions of the halo particles in the evolution of the density profile.     

The alignment of clusters using large-scale simulations

The alignment of clusters of galaxies with their nearest neighbours and between clusters within a supercluster is investigated using simulations of 512³ dark matter particles for ΛCDM and τ CDM cosmological models. Strongly significant alignments are found for separations of up to 15  h ⁻¹ Mpc in both cosmologies, but for the ΛCDM model the alignments extend up to separations of 30  h ⁻¹ Mpc. The effect is strongest for nearest neighbours, but is not significant enough to be useful as an observational discriminant between cosmologies. As a check of whether this difference in alignments is present in other cosmologies, smaller simulations with 256³ particles are investigated for four different cosmological models. Because of poor number statistics, only the standard CDM model shows indications of having different alignments from the other models.     

Testing Bekenstein's relativistic Modified Newtonian Dynamics with lensing data

We propose to use multiple-imaged gravitational lenses to set limits on gravity theories without dark matter, specifically tensor–vector–scalar (TeVeS) theory, a theory which is consistent with fundamental relativistic principles and the phenomenology of Modified Newtonian Dynamics (MOND) theory. After setting the framework for lensing and cosmology, we analytically derive the deflection angle for the point lens and the Hernquist galaxy profile, and study their patterns in convergence, shear and amplification. Applying our analytical lensing models, we fit galaxy-quasar lenses in the CfA-Arizona Space Telescope Lens Survey (CASTLES) sample. We do this with three methods, fitting the observed Einstein ring sizes, the image positions, or the flux ratios. In all the cases, we consistently find that stars in galaxies in MOND/TeVeS provide adequate lensing. Bekenstein's toy μ function provides more efficient lensing than the standard MOND μ function. But for a handful of lenses, a good fit would require a lens mass orders of magnitude larger/smaller than the stellar mass derived from luminosity unless the modification function μ and modification scale a ₀ for the universal gravity were allowed to be very different from what spiral galaxy rotation curves normally imply. We discuss the limitation of present data and summarize constraints on the MOND μ function. We also show that the simplest TeVeS 'minimal-matter' cosmology, a baryonic universe with a cosmological constant, can fit the distance–redshift relation from the supernova data, but underpredicts the sound horizon size at the last scattering. We conclude that lensing is a promising approach to differentiate laws of gravity.     

Designing weak lensing surveys: a generalized eigenmode analysis

We study the estimators of various second-order weak lensing statistics such as the shear correlation functions  ξ_±  and the aperture mass dispersion  〈 M ²_ap〉  which can directly be constructed from weak lensing shear maps. We compare the efficiency with which these estimators can be used to constrain cosmological parameters. To this end we introduce the Karhunen–Loève (KL) eigenmode analysis techniques for weak lensing surveys. These tools are shown to be very effective as a diagnostics for optimizing survey strategies. The usefulness of these tools to study the effect of angular binning, the depth and width of the survey and noise contributions due to intrinsic ellipticities and number density of source galaxies on the estimation of cosmological parameters is demonstrated. Results from independent analysis of various parameters and joint estimations are compared. We also study how degeneracies among various cosmological and survey parameters affect the eigenmodes associated with these parameters.     

The Δθ–zs relation for gravitational lenses as a cosmological test

Recently, Park &38; Gott claimed that there is a statistically significant, strong, negative correlation between the image separation Δθ and source redshift z _s for gravitational lenses. This is somewhat puzzling if one believes in a flat ( k  = 0) universe, since in this case the typical image separation is expected to be independent of the source redshift, while one expects a negative correlation in a k  = −1 universe and a positive one in a k  = +1 universe. Park &38; Gott explored several effects that could cause the observed correlation, but no combination of these can explain the observations with a realistic scenario. Here, I explore this test further in three ways. First, I show that in an inhomogeneous universe a negative correlation is expected regardless of the value of k . Secondly, I test whether the Δθ– z _s relation can be used as a test to determine λ₀ and Ω₀, rather than just the sign of k . Thirdly, I compare the results of the test from the Park &38; Gott sample with those using other samples of gravitational lenses, which can illuminate (unknown) selection effects and probe the usefulness of the Δθ– z _s relation as a cosmological test.     

Determination of cosmology and evolution from K-band magnitude–redshift and number count observations

We determine cosmological and evolutionary parameters from the 3CR K -band Hubble diagram and K -band number counts, assuming that the galaxies in question undergo pure luminosity evolution. Separately the two data sets are highly degenerate with respect to choice of cosmological and evolutionary parameters, but in combination the degeneracy is resolved. Of models that either are flat or have  Ω_Λ=0  , the preferred ones are close to the canonical case  Ω_{cold  matter}=1  ,  Ω_Λ=0  , with luminosity evolution amounting to 1 mag brighter at   z =1  .     

Modelling the number counts of early-type galaxies by pure luminosity evolution

In this paper, we explore the plausible luminosity evolution of early-type galaxies in different cosmological models by constructing a set of pure luminosity evolution (PLE) models via the choices of the star-formation rate (SFR) parameters and formation redshift z _f of galaxies, with the observational constraints derived from the Hubble Space Telescope ( HST  ) morphological number counts for elliptical and S0 galaxies of the Medium Deep Survey (MDS) and the Hubble Deep Field (HDF). We find that the number counts of early-type galaxies can be explained by the pure luminosity evolution models, without invoking exotic scenarios such as merging or introducing an additional population, but the evolution should be nearly passive, with a high z _f assumed. The conclusion is valid in all of the three cosmological models we adopt in this paper. We also present the redshift distributions for three bins of observed magnitudes in the F814w passband, to show the redshift at which the objects that dominate the counts at a given magnitude may be found. The predictions of the redshift distribution of 22.5 <  b _j  < 24.0 are also presented for comparison with future data.     

Linear perturbations in a universe with a cosmological constant

There is now evidence that the cosmological constant Λ has a non-zero positive value. Alternative scenarios to a pure cosmological constant model are provided by quintessence, an effective negative pressure fluid permeating the Universe. Recent results indicate that the energy density ρ and the pressure p of this fluid are constrained by − ρ ≤ p ≲−0.6 ρ . As p =− ρ is equivalent to the pure cosmological constant model, it is appropriate to analyse this particular, but important, case further.
We study the linear theory of perturbations in a Friedmann–Robertson–Walker universe with a cosmological constant. We obtain the equations for the evolution of the perturbations in the fully relativistic case, for which we analyse the single-fluid and two-fluid cases. We obtain solutions to these equations in appropriate limits. We also study the Newtonian approximation. We find that for a positive cosmological constant universe (i) the perturbations will grow more slowly in the relativistic regime for a two-fluid composed of dark matter and radiation, and (ii) in the Newtonian regime the perturbations stop growing.     

Compton dragged gamma-ray bursts: the spectrum

Recently several studies have jointly analysed data from different cosmological probes with the motivation of estimating cosmological parameters. Here we generalize this procedure to allow freedom in the relative weights of various probes. This is done by including in the joint χ ² function a set of 'hyper-parameters', which are dealt with using Bayesian considerations. The resulting algorithm, which assumes uniform priors on the log of the hyper-parameters, is very simple: instead of minimizing     (where     is per data set j ) we propose to minimize     (where N _j is the number of data points per data set j ). We illustrate the method by estimating the Hubble constant H ₀ from different sets of recent cosmic microwave background (CMB) experiments (including Saskatoon, Python V, MSAM1, TOCO and Boomerang ). The approach can be generalized for combinations of cosmic probes, and for other priors on the hyper-parameters.     

The distribution of ejected subhaloes and its implication for halo assembly bias

Using a high-resolution cosmological N -body simulation, we identify the ejected population of subhaloes, which are haloes at redshift   z = 0  but were once contained in more massive 'host' haloes at high redshifts. The fraction of the ejected subhaloes in the total halo population of the same mass ranges from 9 to 4 per cent for halo masses from  ∼10¹¹  to  ∼10¹²  h ⁻¹ M_⊙  . Most of the ejected subhaloes are distributed within four times the virial radius of their hosts. These ejected subhaloes have distinct velocity distribution around their hosts in comparison to normal haloes. The number of subhaloes ejected from a host of given mass increases with the assembly redshift of the host. Ejected subhaloes in general reside in high-density regions, and have a much higher bias parameter than normal haloes of the same mass. They also have earlier assembly times, so that they contribute to the assembly bias of dark matter haloes seen in cosmological simulations. However, the assembly bias is not dominated by the ejected population, indicating that large-scale environmental effects on normal haloes are the main source for the assembly bias.     

Prospects for Observations of Gravitationally Lensed Sources by Submillimeter Space Observatories

The prospects for observations of gravitationally lensed extragalactic sources in the far-infrared and submillimeter ranges of the electromagnetic spectrum by the planned space observatories with active cooling of the telescope mirror to cryogenic temperatures are considered. The possibility of solving topical cosmological and astrophysical problems related to the observations of gravitationally lensed sources is discussed. The number counts of lensed sources have been performed for various wavelengths in the range from 70 to 2000 µm. The redshift and magnification distributions of lensed sources and the mass distribution of lenses have been obtained. We have constructed model photometric sky maps for which the contribution from lensed sources has been calculated for the first time.

     

Two-body relaxation in cosmological simulations

It is logically possible that early two-body relaxation in simulations of cosmological clustering influences the final structure of massive clusters. Convergence studies in which mass and spatial resolution are simultaneously increased cannot eliminate this possibility. We test the importance of two-body relaxation in cosmological simulations with simulations in which there are two species of particles. The cases of two mass ratios, √2:1 and 4:1, are investigated. Simulations are run with both a spatially fixed softening length and adaptive softening using the publicly available codes gadget and mlapm , respectively.
The effects of two-body relaxation are detected in both the density profiles of haloes and the mass function of haloes. The effects are more pronounced with a fixed softening length, but even in this case they are not so large as to suggest that results obtained with one mass species are significantly affected by two-body relaxation.
The simulations that use adaptive softening are less affected by two-body relaxation and produce slightly higher central densities in the largest haloes. They run about three times faster than the simulations that use a fixed softening length.     

Gravitational lensing by elliptical galaxies

The fraction of high-redshift sources which are multiply imaged by intervening galaxies is strongly dependent on the cosmological constant, and so can be a useful probe of the cosmological model. However its power is limited by various systematic (and random) uncertainties in the calculation of lensing probabilities, one of the most important of which is the dynamical normalization of elliptical galaxies. Assuming ellipticals' mass distributions can be modelled as isothermal spheres, the mass normalization depends on the velocity anisotropy, the luminosity density, the core radius and the area over which the velocity dispersion is measured. The differences in the lensing probability and optical depth produced by using the correct normalization can be comparable to the differences between even the most extreme cosmological models. The existing data are not sufficient to determine the correct normalization with enough certainty to allow lensing statistics to be used to their full potential. However, as the correct lensing probability is almost certainly higher than is usually assumed, upper bounds on the cosmological constant are not weakened by these possibilities.     

Submillimetre-wave gravitational lenses and cosmology

One of the most direct routes for investigating the geometry of the Universe is provided by the numbers of strongly magnified gravitationally lensed galaxies as compared with those that are either weakly magnified or de-magnified. In the submillimetre waveband the relative abundance of strongly lensed galaxies is expected to be larger as compared with the optical or radio wavebands, both in the field and in clusters of galaxies. The predicted numbers depend on the properties of the population of faint galaxies in the submillimetre waveband, which was formerly very uncertain; however, recent observations of lensing clusters have reduced this uncertainty significantly and confirm that a large sample of galaxy–galaxy lenses could be detected and investigated using forthcoming facilities, including the FIRST and Planck Surveyor space missions and a large ground-based millimetre/submillimetre-wave interferometer array (MIA). We discuss how this sample could be used to impose limits on the values of cosmological parameters and the total density and form of evolution of the mass distribution of bound structures, even in the absence of detailed lens modelling for individual members of the sample. The effects of different world models on the form of the magnification bias expected in sensitive submillimetre-wave observations of clusters are also discussed, because an MIA could resolve and investigate images in clusters in detail.     

The low-redshift evolution of the Lyman-β forest

The low-redshift evolution of the intergalactic medium is investigated using hydrodynamic cosmological simulations. The assumed cosmological model is a critical density cold dark matter universe. The imposed uniform background of ionizing radiation has the amplitude, shape and redshift evolution as computed from the observed quasar luminosity function by Haardt &38; Madau. We have analysed simulated Lyman-α spectra using Voigt-profile fitting, mimicking the procedure with which quasar spectra are analysed. Our simulations reproduce the observed evolution of the number of Lyman-α absorption lines over the whole observed interval of z  = 0.5 to 4. In particular, our simulations show that the decrease in the rate of evolution of Lyman-α absorption lines at z  ≤ 2, as observed by the Hubble Space Telescope , can be explained by the steep decline in the photoionizing background resulting from the rapid decline in quasar numbers at low redshift.     

A critical-density closed universe in BransDicke theory

In a BransDicke (BD) cosmological model, the energy density associated with some scalar field decreases as a ^{2[( o +1/2)/( _o +1)]} with the scalefactor a ( t ) of the universe, giving matter with an equation of state In this model, the universe could be closed but still have a non-relativistic matter density corresponding to its critical value, _o =1. Different cosmological expressions, such as luminosity distance, angular diameter, number count and ratio of the redshift thicknessangular size, are determined in terms of the redshift for this model.