Gravitational Lenses With More Than Four Images: I. Classification of Caustics

We study the problem of gravitational lensing by an isothermal elliptical density galaxy in the presence of a tidal perturbation. When the perturbation is fairly strong and oriented near the galaxy's minor axis, the lens can produce image configurations with six or even eight highly magnified images lying approximately on a circle. We classify the caustic structures in the model and identify the range of models that can produce such lenses. Sextuple and octuple lenses are likely to be rare because they require special lens configurations, but a full calculation of the likelihood will have to include both the existence of lenses with multiple lens galaxies and the strong magnification bias that affects sextuple and octuple lenses. At optical wavelengths these lenses would probably appear as partial or complete Einstein rings, but at radio wavelengths the individual images could probably be resolved.Comment: 30 pages, including 12 postscript figures; accepted for publication in Ap

Analytic Time Delays and H_0 Estimates for Gravitational Lenses

We study gravitational lens time delays for a general family of lensing potentials, which includes the popular singular isothermal elliptical potential and singular isothermal elliptical density distribution but allows general angular structure. Using a novel approach, we show that the time delay can be cast in a very simple form, depending only on the observed image positions. Including an external shear changes the time delay proportional to the shear strength, and varying the radial profile of the potential changes the time delay approximately linearly. These analytic results can be used to obtain simple estimates of the time delay and the Hubble constant in observed gravitational lenses. The naive estimates for four of five time delay lenses show surprising agreement with each other and with local measurements of H_0; the complicated Q 0957+561 system is the only outlier. The agreement suggests that it is reasonable to use simple isothermal lens models to infer H_0, although it is still important to check this conclusion by examining detailed models and by measuring more lensing time delays.Comment: 16 pages with 2 embedded figures; submitted to Ap

Is B1422+231 a Golden Lens?

B1422+231 is a quadruply-imaged QSO with an exceptionally large lensing contribution from group galaxies other than the main lensing galaxy. We detect diffuse X-rays from the galaxy group in archival Chandra observations; the inferred temperature is consistent with the published velocity dispersion. We then explore the range of possible mass maps that would be consistent with the observed image positions, radio fluxes, and ellipticities. Under plausible but not very restrictive assumptions about the lensing galaxy, predicted time delays involving the faint fourth image are fairly well constrained around 7/h days.Comment: 17 pages, 9 figures, to appear in the June/03 issue of A

Effects of Ellipticity and Shear on Gravitational Lens Statistics

We study the effects of ellipticity in lens galaxies and external tidal shear from neighboring objects on the statistics of strong gravitational lenses. For isothermal lens galaxies normalized so that the Einstein radius is independent of ellipticity and shear, ellipticity {\it reduces} the lensing cross section slightly, and shear leaves it unchanged. Ellipticity and shear can significantly enhance the magnification bias, but only if the luminosity function of background sources is steep. Realistic distributions of ellipticity and shear {\it lower} the total optical depth by a few percent for most source luminosity functions, and increase the optical depth only for steep luminosity functions. The boost in the optical depth is noticeable (>5%) only for surveys limited to the brightest quasars (L/L_* > 10). Ellipticity and shear broaden the distribution of lens image separations but do not affect the mean. Ellipticity and shear naturally increase the abundance of quadruple lenses relative to double lenses, especially for steep source luminosity functions, but the effect is not enough (by itself) to explain the observed quadruple-to-double ratio. With such small changes to the optical depth and image separation distribution, ellipticity and shear have a small effect on cosmological constraints from lens statistics: neglecting the two leads to biases of just Delta Omega_M = 0.00 \pm 0.01 and Delta Omega_Lambda = -0.02 \pm 0.01 (where the errorbars represent statistical uncertainties in our calculations).Comment: Optical depth normalization discussed. Matches the published versio

Smoothing Algorithms and High-order Singularities in Gravitational Lensing

We propose a new smoothing method for obtaining surface densities from discrete particle positions from numerical simulations. This is an essential step for many applications in gravitational lensing. This method is based on the ``scatter'' interpretation of the discrete density field in the Smoothed Particle Hydrodynamics. We use Monte Carlo simulations of uniform density fields and one isothermal ellipsoid to empirically derive the noise properties, and best smoothing parameters (such as the number of nearest neighbors used). A cluster from high-resolution simulations is then used to assess the reality of high-order singularities such as swallowtails and butterflies in caustics, which are important for the interpretation of substructures in gravitational lenses. We also compare our method with the Delaunay tesselation field estimator using the galaxy studied by Bradac et al. (2004), and find good agreements. We show that higher order singularities are not only connected with bound subhaloes but also with the satellite streams. However, the presence of high-order singularities are sensitive to not only the fluctuation amplitude of the surface density, but also the detailed form of the underlying smooth lensing potential (such as ellipticity and external shear).Comment: ApJ, Accepted,(Released November 1st). The high resolution figures are availabel at http://202.127.29.4/mppg/english/data

Investigation of Gravitational Lens Mass Models

We have previously reported the discovery of strong gravitational lensing by faint elliptical galaxies using the WFPC2 on HST and here we investigate their potential usefulness in putting constraints on lens mass models. We compare various ellipsoidal surface mass distributions, including those with and without a core radius, as well as models in which the mass distributions are assumed to have the same axis ratio and orientation as the galaxy light. We also study models which use a spherical mass distribution having various profiles, both empirical and following those predicted by CDM simulations. These models also include a gravitational shear term. The model parameters and associated errors have been derived by 2-dimensional analysis of the observed HST WFPC2 images. The maximum likelihood procedure iteratively converges simultaneously on the model for the lensing elliptical galaxy and the lensed image components. The motivation for this study was to distinguish between these mass models with this technique. However, we find that, despite using the full image data rather than just locations and integrated magnitudes, the lenses are fit equally well with several of the mass models. Each of the mass models generates a similar configuration but with a different magnification and cross-sectional area within the caustic, and both of these latter quantities govern the discovery probability of lensing in the survey. These differences contribute to considerable cosmic scatter in any estimate of the cosmological constant using gravitational lenses.Comment: 10 pages with 6 embedded figures, tentatively scheduled to be published in the July 2001 issue of The Astronomical Journal. For additional information see http://mds.phys.cmu.edu/lense

Shear and Ellipticity in Gravitational Lenses

Galaxies modeled as singular isothermal ellipsoids with an axis ratio distribution similar to the observed axis ratio distribution of E and S0 galaxies are statistically consistent with both the observed numbers of two-image and four-image lenses and the inferred ellipticities of individual lenses. However, no four-image lens is well fit by the model (typical $\chi^2/N_{dof} \sim 20$), the axis ratio of the model can be significantly different from that of the observed lens galaxy, and the major axes of the model and the galaxy may be slightly misaligned. We found that models with a second, independent, external shear axis could fit the data well (typical $\chi^2/N_{dof} \sim 1$), while adding the same number of extra parameters to the radial mass distribution does not produce such a dramatic improvement in the fit. An independent shear axis can be produced by misalignments between the luminous galaxy and its dark matter halo, or by external shear perturbations due to galaxies and clusters correlated with the primary lens or along the line of sight. We estimate that the external shear perturbations have no significant effect on the expected numbers of two-image and four-image lenses, but that they can be important perturbations in individual lens models. However, the amplitudes of the external shears required to produce the good fits are larger than our estimates for typical external shear perturbations (10-15% shear instead of 1-3% shear) suggesting that the origin of the extra angular structure must be intrinsic to the primary lens galaxy in most cases.Comment: 38 pages, 9 figures, submitted to Ap

Breaking the Disk/Halo Degeneracy with Gravitational Lensing

The degeneracy between the disk and the dark matter contribution to galaxy rotation curves remains an important uncertainty in our understanding of disk galaxies. Here we discuss a new method for breaking this degeneracy using gravitational lensing by spiral galaxies, and apply this method to the spiral lens B1600+434 as an example. The combined image and lens photometry constraints allow models for B1600+434 with either a nearly singular dark matter halo, or a halo with a sizable core. A maximum disk model is ruled out with high confidence. Further information, such as the circular velocity of this galaxy, will help break the degeneracies. Future studies of spiral galaxy lenses will be able to determine the relative contribution of disk, bulge, and halo to the mass in the inner parts of galaxies.Comment: Replaced with minor revisions, a typo fixed, and reference added; 21 pages, 8 figures, ApJ accepte

Spectroscopic Analysis of H I Absorption Line Systems in 40 HIRES Quasars

We list and analyze H I absorption lines at redshifts 2 < z < 4 with column density (12 < log(N_HI) < 19) in 40 high-resolutional (FWHM = 8.0 km/s) quasar spectra obtained with the Keck+HIRES. We de-blend and fit all H I lines within 1,000 km/s of 86 strong H I lines whose column densities are log(N_HI/[cm^-2]) > 15. Unlike most prior studies, we use not only Lya but also all visible higher Lyman series lines to improve the fitting accuracy. This reveals components near to higher column density systems that can not be seen in Lya. We list the Voigt profile fits to the 1339 H I components that we found. We examined physical properties of H I lines after separating them into several sub-samples according to their velocity separation from the quasars, their redshift, column density and the S/N ratio of the spectrum. We found two interesting trends for lines with 12 < log(N_HI) < 15 which are within 200-1000 km/s of systems with log(N_HI) > 15. First, their column density distribution becomes steeper, meaning relatively fewer high column density lines, at z < 2.9. Second, their column density distribution also becomes steeper and their line width becomes broader by about 2-3 km/s when they are within 5,000 km/s of their quasar.Comment: 32 pages, 14 figures, accepted for publication in the Astronomical Journal. A complete version with all tables and figures is available at http://www.astro.psu.edu/users/misawa/pub/Paper/40hires.ps.g

Weak Lensing Analysis of the z~0.8 cluster CL 0152-1357 with the Advanced Camera for Surveys

We present a weak lensing analysis of the X-ray luminous cluster CL 0152-1357 at z~0.84 using HST/ACS observations. The unparalleled resolution and sensitivity of ACS enable us to measure weakly distorted, faint background galaxies to the extent that the number density reaches ~175 arcmin^-2. The PSF of ACS has a complicated shape that also varies across the field. We construct a PSF model for ACS from an extensive investigation of 47 Tuc stars in a modestly crowded region. We show that this model PSF excellently describes the PSF variation pattern in the cluster observation when a slight adjustment of ellipticity is applied. The high number density of source galaxies and the accurate removal of the PSF effect through moment-based deconvolution allow us to restore the dark matter distribution of the cluster in great detail. The direct comparison of the mass map with the X-ray morphology from Chandra observations shows that the two peaks of intracluster medium traced by X-ray emission are lagging behind the corresponding dark matter clumps, indicative of an on-going merger. The overall mass profile of the cluster can be well described by an NFW profile with a scale radius of r_s =309+-45 kpc and a concentration parameter of c=3.7+-0.5. The mass estimates from the lensing analysis are consistent with those from X-ray and Sunyaev-Zeldovich analyses. The predicted velocity dispersion is also in good agreement with the spectroscopic measurement from VLT observations. In the adopted WMAP cosmology, the total projected mass and the mass-to-light ratio within 1 Mpc are estimated to be 4.92+-0.44 10^14 solar mass and 95+-8 solar mass/solar luminosity, respectively.Comment: Accepted for publication in Astrophysical Journal. 58 pages, 26 figures. Figures have been degraded to meet size limit; a higher resolution version available at http://acs.pha.jhu.edu/~mkjee/ms_cl0152.pd