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.     

Gravitational lensing of extended high-redshift sources by dark matter haloes

High-redshift galaxies and quasi-stellar objects (QSOs) are most likely to be strongly lensed by intervening haloes between the source and the observer. In addition, a large fraction of lensed sources is expected to be seen in the submillimetre region, as a result of the enhanced magnification bias on the steep intrinsic number counts. We extend in three directions Blain's earlier study of this effect.
First, we use a modification of the Press–Schechter mass function and detailed lens models to compute the magnification probability distribution. We compare the magnification cross-sections of populations of singular isothermal spheres and Navarro, Frenk & White (NFW) haloes and find that they are very similar, in contrast to the image-splitting statistics which were recently investigated in other studies. The distinction between the two types of density profile is therefore irrelevant for our purposes.
Secondly, we discuss quantitatively the maximum magnification, μ _max, that can be achieved for extended sources (galaxies) with realistic luminosity profiles, taking into account the possible ellipticity of the lensing potential. We find that μ _max plausibly falls into the range     for sources of     effective radius at redshifts within     .
Thirdly, we apply our model for the lensing magnification to a class of sources following the luminosity evolution typical for a unified scheme of QSO formation. As a result of the peculiar steepness of their intrinsic number counts, we find that the lensed source counts at a fiducial wave length of 850 μm can exceed the unlensed counts by several orders of magnitude at flux densities ≳100 mJy, even with a conservative choice of the maximum magnification.     

Weak gravitational lensing by voids

We consider the prospects for detecting weak gravitational lensing by underdensities (voids) in the large-scale matter distribution. We derive the basic expressions for magnification and distortion by spherical voids. Clustering of the background sources and cosmic variance are the main factors that limit in principle the detection of lensing by voids. We conclude that only voids with radii larger than ∼100  h ⁻¹ Mpc have lensing signal-to-noise ratio larger than unity.     

Revisiting the magnification of type Ia supernovae with SDSS

We cross-correlate the sample of type Ia supernovae from Riess A. G. et al. with the SDSS DR2 photometric galaxy catalogue. In contrast to recent work, we find no detectable correlation between supernova magnitude and galaxy overdensity on scales ranging between 1 and 10 arcmin. Our results are in accord with theoretical expectations for gravitational lensing of supernovae by large-scale structure. Future supernova surveys such as SNAP will be capable of detecting unambiguously the predicted lensing signal.     

Effects of a deformation of a star on the gravitational lensing

We study analytically a gravitational lens due to a deformed star, which is modelled by using a monopole and a quadrupole moment. Positions of the images are discussed for a source on the principal axis. We present explicit expressions for the lens equation for this gravitational lens as a single real 10th-order algebraic equation. Furthermore, we compute an expression for the caustics as a discriminant for the polynomial. Another simple parametric representation of the caustics is also presented in a more tractable form. A simple expression for the critical curves is obtained to clarify a topological feature of the critical curves; the curves are simply connected if and only if the distortion is sufficiently large.     

Weak lensing from strong clustering

We investigate the effect of weak gravitational lensing in the limit of small angular scales where projected galaxy clustering is strongly non-linear. This is the regime likely to be probed by future weak lensing surveys. We use well-motivated hierarchical scaling arguments and the plane-parallel approximation to study multi-point statistical properties of the convergence field. These statistics can be used to compute the vertex amplitudes in tree models of hierarchical clustering; these can be compared with similar measurements from galaxy surveys, leading to a powerful probe of galaxy bias.     

Weak lensing predictions at intermediate scales

As pointed out in previous studies, the measurement of the skewness of the convergence field κ will be useful in breaking the degeneracy among the cosmological parameters constrained from weak lensing observations. The combination of shot noise and finite survey volume implies that such a measurement is likely to be performed in a range of intermediate scales (0.5 to 20 arcmin) where neither perturbation theory nor the hierarchical ansatz applies. Here we explore the behaviour of the skewness of κ at these intermediate scales, based on results for the non-linear evolution of the mass bispectrum. We combined different ray-tracing simulations to test our predictions, and we find that our calculations describe accurately the transition from the weakly non-linear to the strongly non-linear regime. We show that the single lens-plane approximation remains accurate even in the non-linear regime, and we explicitly calculate the corrections to this approximation. We also discuss the prospects of measuring the skewness in upcoming weak lensing surveys.     

Was Supernova 1997ff at z∼ 1.7 magnified by gravitational lensing?

The quest for the cosmological parameters has come to fruition with the identification of a number of supernovae at a redshift of     . Analyses of the brightness of these standard candles reveal that the Universe is dominated by a large cosmological constant. The recent identification of the     SN 1997ff in the northern Hubble Deep Field has provided further evidence for this cosmology. Here we examine the case for gravitational lensing of SN 1997ff owing to the presence of galaxies lying along our line of sight. We find that, while the alignment of SN 1997ff with foreground masses is not favourable for it to be multiply imaged and strongly magnified, two galaxies do lie close enough to result in significant magnification:     for the case where these elliptical galaxies have a velocity dispersion of 200 km s⁻¹. Given the small difference between supernova brightnesses in different cosmologies, detailed modelling of the gravitational lensing properties of the intervening matter is therefore required before the true cosmological significance of SN 1997ff can be deduced.     

Kinematic effect in gravitational lensing by clusters of galaxies

Gravitational lensing provides an efficient tool for the investigation of matter structures, independent of the dynamical or the hydrostatic equilibrium properties of the deflecting system. However, it depends on the kinematic status. In fact, either a translational motion or a coherent rotation of the mass distribution can affect the lensing properties. Here, light deflection by galaxy clusters in motion is considered. Even if gravitational lensing mass measurements of galaxy clusters are regarded as very reliable estimates, the kinematic effect should be considered. A typical peculiar motion with respect to the Hubble flow brings about a systematic error ≲0.3 per cent, independent of the mass of the cluster. On the other hand, the effect of the spin increases with the total mass. For cluster masses  ∼10¹⁵ M_⊙  , the effect of the gravitomagnetic term is ≲0.04 per cent on strong lensing estimates and ≲0.5 per cent in the weak-lensing analyses. The total kinematic effect on the mass estimate is then ≲1 per cent, which is negligible in current statistical studies. In the weak-lensing regime, the rotation imprints a typical angular modulation in the tangential shear distortion. This would allow, in principle, a detection of the gravitomagnetic field and a direct measurement of the angular velocity of the cluster but the required background source densities are well beyond current technological capabilities.     

Weak gravitational lensing in the standard cold dark matter model, using an algorithm for three-dimensional shear

We investigate the effects of weak gravitational lensing in the standard cold dark matter cosmology, using an algorithm that evaluates the shear in three dimensions. The algorithm has the advantage of variable softening for the particles, and our method allows the appropriate angular diameter distances to be applied to every evaluation location within each three-dimensional simulation box. We investigate the importance of shear in the distance–redshift relation, and find it to be very small. We also establish clearly defined values for the smoothness parameter in the relation, finding its value to be at least 0.83 at all redshifts in our simulations. From our results, obtained by linking the simulation boxes back to source redshifts of 4, we are able to observe the formation of structure in terms of the computed shear, and also note that the major contributions to the shear come from a very broad range of redshifts. We show the probability distributions for the magnification, source ellipticity and convergence, and also describe the relationships amongst these quantities for a range of source redshifts. We find a broad range of magnifications and ellipticities; for sources at a redshift of 4, 97.5 per cent of all lines of sight show magnifications up to 1.39 and ellipticities up to 0.23. There is clear evidence that the magnification is not linear in the convergence, as might be expected for weak lensing, but contains contributions from higher order terms in both the convergence and the shear. Our results for the one-point distribution functions are generally different from those obtained by other authors using two-dimensional (planar) approaches, and we suggest reasons for the differences. Our magnification distributions for sources at redshifts of 1 and 0.5 are also very different from the results used by other authors to assess the effect on the perceived value of the deceleration parameter, and we briefly address this question.     

Weak gravitational lensing in different cosmologies, using an algorithm for shear in three dimensions

We present the results of weak gravitational lensing statistics in four different cosmological N -body simulations. The data have been generated using an algorithm for the three-dimensional shear, which makes use of a variable softening facility for the N -body particle masses, and enables a physical interpretation for the large-scale structure to be made. Working in three dimensions also allows the correct use of the appropriate angular diameter distances.
Our results are presented on the basis of the filled-beam approximation in view of the variable particle softening scheme in our algorithm. The importance of the smoothness of matter in the Universe for the weak lensing results is discussed in some detail.
The low-density cosmology with a cosmological constant appears to give the broadest distributions for all the statistics computed for sources at high redshifts. In particular, the range in magnification values for this cosmology has implications for the determination of the cosmological parameters from high-redshift type Ia supernovae. The possibility of determining the density parameter from the non-Gaussianity in the probability distribution for the convergence is discussed.     

The JVAS/CLASS search for 6-arcsec to 15-arcsec image separation lensing

The Jodrell Bank–VLA Astrometric Survey (JVAS) and the Cosmic Lens All Sky Survey (CLASS) have been systematically searched for multiple gravitational imaging of sources with image separations between 6 arcsec and 15 arcsec, associated with galaxy group and cluster lensing masses. The radio and optical follow-up observations of all candidates are presented. From a total of ∼15 000 sources only one weak candidate remains and this is not contained in the statistically complete sample of flat-spectrum JVAS/CLASS sources of 11 670 sources. A simple Press–Schechter analysis is performed. For singular isothermal sphere lenses the lack of multiple image systems is inconsistent with the currently favoured cosmologies with     at the 4.2 σ level. Cored isothermal lenses reduce the expected number of lens systems and we suggest that the most probable interpretation of our results is that the surface mass density of groups and clusters of galaxies is not high enough to cause multiple imaging and the presence of the mass concentrations associated with individual galaxies is required to produce image separations such as those in B0957+561.     

A genetic algorithm for the non-parametric inversion of strong lensing systems

We present a non-parametric technique to infer the projected mass distribution of a gravitational lens system with multiple strong-lensed images. The technique involves a dynamic grid in the lens plane on which the mass distribution of the lens is approximated by a sum of basis functions, one per grid cell. We used the projected mass densities of Plummer spheres as basis functions. A genetic algorithm then determines the mass distribution of the lens by forcing images of a single source, projected back on to the source plane, to coincide as well as possible. Averaging several tens of solutions removes the random fluctuations that are introduced by the reproduction process of genomes in the genetic algorithm and highlights those features common to all solutions. Given the positions of the images and the redshifts of the sources and the lens, we show that the mass of a gravitational lens can be retrieved with an accuracy of a few percent and that, if the sources sufficiently cover the caustics, the mass distribution of the gravitational lens can also be reliably retrieved. A major advantage of the algorithm is that it makes full use of the information contained in the radial images, unlike methods that minimize the residuals of the lens equation, and is thus able to accurately reconstruct also the inner parts of the lens.