Non-parametric reconstruction of cluster mass distribution from strong lensing: modelling Abell 370

We describe a new non-parametric technique for reconstructing the mass distribution in galaxy clusters with strong lensing, i.e. from multiple images of background galaxies. The observed positions and redshifts of the images are considered as rigid constraints, and through the lens (ray-trace) equation they provide us with linear constraint equations. These constraints confine the mass distribution to some allowed region, which is then found by linear programming. Within this allowed region we study in detail the mass distribution with minimum mass-to-light variation, and also some other distributions, such as the smoothest mass distribution.
The method is applied to the extensively studied cluster Abell 370, which hosts a giant luminous arc and several other multiply imaged background galaxies. Our mass maps are constrained by the observed positions and redshifts (spectroscopic or model-inferred by previous authors) of the giant arc and multiple-image systems. The reconstructed maps obtained for Abell 370 reveal a detailed mass distribution, with substructure quite different from the light distribution. The method predicts the bimodal nature of the cluster, and that the projected mass distribution is indeed elongated along the axis defined by the two dominant cD galaxies. However, the peaks in the mass distribution appear to be offset from the centres of the cDs.
We also present an estimate for the total mass of the central region of the cluster. This is in good agreement with previous mass determinations. The total mass of the central region is M =(2.0–2.7)×10¹⁴ M⊙ h ⁻¹₅₀, depending on the solution chosen.     

Weighing a galaxy bar in the lens Q2237 +=0305

In the gravitational lens system Q2237+0305 the cruciform quasar image geometry is twisted by 10c by the lens effect of a bar in the lensing galaxy. This effect can be used to measure the mass of the bar. We construct a new lensing model for this system with a power-law elliptical bulge and a Ferrers bar. The observed ellipticity of the optical isophotes of the galaxy leads to a nearly isothermal elliptical profile for the bulge, with a total quasar magnification of 16⁺⁵₋₄. We measure a bar mass of (7.5 ∼ 1.5) −10⁸ h ⁻¹₇₅ M⊙ in the region inside the quasar images.     

The Planck Surveyor mission and gravitational lenses

An extremely sensitive all-sky survey will be carried out in the millimetre/submillimetre waveband by the forthcoming ESA mission Planck Surveyor . The main scientific goal of the mission is to make very accurate measurements of the spatial power spectrum of primordial anisotropies in the cosmic microwave background radiation; however, hundreds of thousands of distant dusty galaxies and quasars will also be detected. These sources are much more likely to be gravitationally lensed by intervening galaxies compared with sources discovered in surveys in other wavebands. Here the number of lenses expected in the survey is estimated, and techniques for discriminating between lensed and unlensed sources are discussed. A practical strategy for this discrimination is presented, based on exploiting the remarkable sensitivity and resolving power of large ground-based millimetre/submillimetre-wave interferometer arrays. More than a thousand gravitational lenses could be detected: a sample that would be an extremely valuable resource in observational cosmology.     

Spectroscopy of the optical Einstein ring 0047 – 2808

We present optical and near-infrared spectroscopic observations of the optical Einstein ring 0047 – 2808. We detect both [O III ] lines λλ4959, 5007 near ∼ 2.3 μm, confirming the redshift of the lensed source as z  = 3.595. The Lyα line is redshifted relative to the [O III ] line by 140 ± 20 km s⁻¹. Similar velocity shifts have been seen in nearby starburst galaxies. The [O III ] line is very narrow, 130 km s⁻¹ FWHM. If the ring is the image of the centre of a galaxy, the one-dimensional stellar velocity dispersion σ = 55 km s⁻¹ is considerably smaller than the value predicted by Baugh et al. for the somewhat brighter Lyman-break galaxies. The Lyα line is significantly broader than the [O III ] line, probably due to resonant scattering. The stellar central velocity dispersion of the early-type deflector galaxy at z  = 0.485 is 250 ± 30 km s⁻¹. This value is in good agreement both with the value predicted from the radius of the Einstein ring (and a singular isothermal sphere model for the deflector), and with the value estimated from the D _n −σ relation.     

Extended source effects in astrometric gravitational microlensing

Extended source size effects have been detected in photometric monitoring of gravitational microlensing events. We study similar effects in the centroid motion of an extended source lensed by a point mass. We show that the centroid motion of a source with uniform surface brightness can be obtained analytically. For a source with a circularly symmetric limb-darkening profile, the centroid motion can be expressed as a one-dimensional integral, which can be evaluated numerically. We find that when the impact parameter is comparable to the source radius, the centroid motion is significantly modified by the finite source size. In particular, when the impact parameter is smaller than the source radius, the trajectories become clover-leaf like. Such astrometric motions can be detected using space interferometers such as the Space Interferometry Mission . Such measurements offer exciting possibilities for determining stellar parameters, such as stellar radius, to excellent accuracy.     

Observational tests of x-matter models

We study gravitational lensing statistics, matter power spectra and the angular power spectra of the cosmic microwave background (CMB) radiation in x-matter models. We adopt an equation of state of x-matter which can express a wide range of matter from pressureless dust to the cosmological constant. A new ingredient in this model is the sound speed of the x-component, in addition to the equation of state w ₀ =  p _x0/ρ_x0. Except for the cosmological constant case, the perturbations of x-matter itself are considered. Our primary interest is in the effect of non-zero sound speed on the structure formation and the CMB spectra. It is found that there exist parameter ranges where x-matter models are consistent with all current observations. The x-matter generally leaves imprints in the CMB anisotropy and the matter power spectrum, which should be detectable in future observations.     

Lens models with density cusps

Lens models appropriate for representing cusped galaxies and clusters are developed. The analogue of the odd-number theorem for cusped density distributions is given. Density cusps are classified into strong, isothermal or weak, according to their lensing properties. Strong cusps cause multiple imaging for any source position, whereas isothermal and weak cusps give rise to only one image for distant sources. Isothermal cusps always possess a pseudo-caustic. When the source crosses the pseudo-caustic, the number of images changes by unity.   Two families of cusped galaxy and cluster models are examined in detail. The double power-law family has an inner cusp, followed by a transition region and an outer envelope. One member of this family — the isothermal double power-law model — possesses an exceedingly scarce property, namely the lens equation is exactly solvable for any source position. This means that the magnifications, the time delay and the lensing cross-sections are all readily available. The model has a three-dimensional density that is cusped like r ⁻² at small radii and falls off like r ⁻⁴ asymptotically. Thus, it provides a very useful representation of the lensing properties of a galaxy or cluster of finite total mass with a flat rotation curve. The second set of models studied is the single power-law family. These are single density cusps of infinite extent. The properties of the critical curves and caustics and the behaviour of the lenses in the presence of external shear are all discussed in some detail.     

Microlensing-induced spectral variability in Q 2237+0305

We present both photometry and spectra of the individual images of the quadruple gravitational lens system Q 2237+0305. Comparison of spectra obtained at two epochs, separated by ∼3 yr, shows evidence for significant changes in the emission line-to-continuum ratio of the strong ultraviolet C  IV  λ1549, C  III ] λ1909 and Mg  II  λ2798 lines. The short, ∼1 day, light-travel time differences between the sight lines to the four individual quasar images rule out any explanation based on intrinsic variability of the source. The spectroscopic differences thus represent direct detection of microlensing-induced spectroscopic differences in a quasar. The observations allow constraints to be placed on the relative spatial scales in the nucleus of the quasar, with the ultraviolet continuum arising in a region of ≲0.05 pc in extent, while the broad emission-line material is distributed on scales much greater than this.     

Theory and statistics of weak lensing from large-scale mass inhomogeneities

Weak lensing by large-scale mass inhomogeneities in the Universe induces correlations in the observed ellipticities of distant sources. We first review the harmonic analysis and statistics required of these correlations and discuss calculations for the predicted signal. We consider the ellipticity correlation function, the mean-square ellipticity, the ellipticity power spectrum and a global maximum-likelihood analysis to isolate a weak-lensing signal from the data. Estimates for the sensitivity of a survey of a given area, surface density, and mean intrinsic source ellipticity are presented. We then apply our results to the FIRST radio-source survey. We predict an rms ellipticity of roughly 0.011 in 1 × 1 deg² pixels and 0.018 in 20 × 20 arcmin² pixels if the power spectrum is normalized to σ₈ Ω^0.53 = 0.6, as indicated by the cluster abundance. The signal is significantly larger in some models if the power spectrum is normalized instead to the COBE anisotropy. The uncertainty in the predictions from imprecise knowledge of the FIRST redshift distribution is about 25 per cent in the rms ellipticity. We show that FIRST should be able to make a statistically significant detection of a weak-lensing signal for cluster-abundance-normalized power spectra.