Modeling Galaxy Lenses

In order to use a gravitational lens to measure the Hubble constant accurately, it is necessary to derive a reliable model of the lens surface potential. If the analysis is restricted to the locations and magnifications of point images, the derived Hubble constant depends upon the class of mass models used to fit the data. However, when there is extended emission from an Einstein ring, it may be possible to derive a potential from the observed surface brightness in a model-independent manner. This procedure is illustrated with reference to B1608+656. The multi-band images are de-reddened, de-convolved and de-contaminated so that the luminous matter and the surface brightness contours in the Einstein ring are both faithfully mapped. This intensity distribution can then be used to reconstruct the potential. Progress in implementing this program is reported. The observed incidence of multiple-imaged galaxies on the Hubble Deep Fields is an order of magnitude smaller than naively predicted on the basis of radio lens surveys, like CLASS, but consistent with the rate computed using surface photometry of candidate lens galaxies assuming standard mass to light ratios. In order to resolve this paradox, it is suggested that most galaxy lenses are located in compact groups.Comment: Latex 10 pages 4 figures. To appear in ``Gravitational Lensing: Recent Progress and Future Goals'' Editors: Tereasa G. Brainerd and Christopher S. Kochane

Infrared Counterpart of the Gravitational Lens 1938+66.6

We report the detection of a very red source coincident with the gravitational lens 1938+66.6 (Patnaik et al. 1992) in K' (2.12 micron), H (1.6 micron), J (1.25 micron), and Thuan-Gunn r (0.65 micron) bands. 1938+66.6 has previously been detected as a partial radio ring indicating lensing. We find K'=17.1 +- 0.1 and r = 23.9 +- 0.2, making it a very red source with (r-K')=6.8 +- 0.25. We also observed in Thuan-Gunn g band (0.49 micron) and found g>24.5 at the 90% confidence level. We interpret our observations as a reddened gravitational lens on the basis of its optical-IR color and positional coincidence with the radio source.Comment: 8 pages, one PostScript figure; uses AAS LaTeX macros. Accepted for publication in The Astronomical Journa

Gravitational Lensing and the Extragalactic Distance Scale

The potential of gravitational lenses for providing direct, physical measurements of the Hubble constant, free from systematic errors associated with the traditional distance ladder, has long been recognized. However, it is only recently that there has been a convincing measurement of a time delay sufficiently accurate to carry out this program. By itself, an accurate time delay measurement does not produce an equivalently definite Hubble constant and the errors associated with models of the primary lens, propagation through the potential fluctuations produced by the large-scale structure and the global geometry of the universe must also be taken into account. The prospects for measuring several more time delays and the feasibility of making the corresponding estimates of the Hubble constant with total error smaller than ten percent are critically assessed.Comment: 16 pages, 3 eps figures, uses cupconf.sty. To appear in "The Extragalactic Distance Scale", eds. M. Livio, M. Donahue, and N. Panagia (Cambridge University Press

Keck Spectroscopy of the Gravitational Lens System PG 1115+080: Redshifts of the Lensing Galaxies

The quadruple system PG 1115+080 is the second gravitational lens with a reported measurement of the Hubble constant. In addition to the primary lens, three nearby galaxies are believed to contribute significantly to the lensing potential. In this paper we report accurate redshifts for all four galaxies and show that they belong to a single group at z_d = 0.311. This group has very similar properties to Hickson's compact groups of galaxies found at lower redshifts. We briefly discuss implications for the existing lens models and derive H_0 = 52 +/- 14 km/s/Mpc.Comment: revised to use the updated model of Keeton & Kochanek (astro-ph/9611216) and to correct the velocity dispersion of the group; 10 pages including 2 eps figures and 2 tables. Submitted to the Astronomical Journa

Magnification Ratio of the Fluctuating Light in Gravitational Lens 0957+561

Radio observations establish the B/A magnification ratio of gravitational lens 0957+561 at about 0.75. Yet, for more than 15 years, the optical magnfication ratio has been between 0.9 and 1.12. The accepted explanation is microlensing of the optical source. However, this explanation is mildly discordant with (i) the relative constancy of the optical ratio, and (ii) recent data indicating possible non-achromaticity in the ratio. To study these issues, we develop a statistical formalism for separately measuring, in a unified manner, the magnification ratio of the fluctuating and constant parts of the light curve. Applying the formalism to the published data of Kundi\'c et al. (1997), we find that the magnification ratios of fluctuating parts in both the g and r colors agrees with the magnification ratio of the constant part in g-band, and tends to disagree with the r-band value. One explanation could be about 0.1 mag of consistently unsubtracted r light from the lensing galaxy G1, which seems unlikely. Another could be that 0957+561 is approaching a caustic in the microlensing pattern.Comment: 12 pages including 1 PostScript figur

Precision Photometry for Q0957+561 Images A and B

Since the persuasive determination of the time-delay in Q0957+561, much interest has centered around shifting and subtracting the A and B light-curves to look for residuals due to microlensing. Solar mass objects in the lens galaxy produce variations on timescales of decades, with amplitudes of a few tenths of a magnitude, but MACHO's (with masses of order $10^{-3}$ to $10^{-7}M_\odot$) produce variations at only the 5% level. To detect such small variations, highly precise photometry is required. To that end, we have used 200 observations over three nights to examine the effects of seeing on the light-curves. We have determined that seeing itself can be responsible for correlated 5% variations in the light-curves of A and B. We have found, however, that these effects can be accurately removed, by subtracting the light from the lens galaxy, and by correcting for cross contamination of light between the closely juxtaposed A and B images. We find that these corrections improve the variations due to seeing from 5% to a level only marginally detectable over photon shot noise (0.5%).Comment: 21 Pages with 9 PostScript figures, AASTeX 4 (preprint style

The distribution of microlensed light curve derivatives: the relationship between stellar proper motions and transverse velocity

We present a method for computing the probability distribution of microlensed light curve derivatives both in the case of a static lens with a transverse velocity, and in the case of microlensing that is produced through stellar proper motions. The distributions are closely related in form, and can be considered equivalent after appropriate scaling of the input transverse velocity. The comparison of the distributions in this manner provides a consistent way to consider the relative contribution to microlensing (both large and small fluctuations) of the two classes of motion, a problem that is otherwise an extremely expensive computational exercise. We find that the relative contribution of stellar proper motions to the microlensing rate is independent of the mass function assumed for the microlenses, but is a function of optical depth and shear. We find that stellar proper motions produce a higher overall microlensing rate than a transverse velocity of the same magnitude. This effect becomes more pronounced at higher optical depth. With the introduction of shear, the relative rates of microlensing become dependent on the direction of the transverse velocity. This may have important consequences in the case of quadruply lensed quasars such as Q2237+0305, where the alignment of the shear vector with the source trajectory varies between images.Comment: 12 pages, including 9 figures. Submitted to M.N.R.A.S. Revised version includes a short section on the applicability of the metho

Bias and consistency in time delay estimation methods: case of the double quasar HE 1104-1805

We present a short re-evaluation of a recently published time delay estimate for the gravitational lens system HE 1104-1805 with emphasis on important methodological aspects: bias of the statistics, inconsistency of the methods and use of the purposeful selection of data points(or so-called "cleaning") at the preprocessing stage. We show how the inadequate use of simple analysis methods can lead to too strong conclusions. Our analysis shows that there are indications for the time delay in HE 1104-1805 to be between -0.9 and -0.7 years, but still with a large uncertainty.Comment: 5 pages, 5 figures, accepted as a Letter to the Editor in A&

The quasar Q0957+561: Lensed CO emission from a disk at z~1.4?

In recent years large efforts have been made to detect molecular gas towards high redshifted objects. Up to now the literature reports on only two cases of CO-detection in quasars at a redshift between 1 and 2 - Q0957+561, a gravitationally lensed system at z=1.41 (Planesas et al. 1999), and HR10 at z=1.44 (Andreani et al. 2000). According to Planesas et al. (1999), 12CO(2-1) emission was detected towards both the lensed images of Q0957+561 with the IRAM Plateau de Bure Interferometer (PdBI). In contrast to the optical spectra of the two images which support the idea that they are images of one and the same object, the CO-spectra were surprisingly different: the southern image (named CO-B) shows a single blueshifted line whereas a double-peaked line profile with a blue- and a redshifted part appears towards the northern image (CO-A). Based on the observations and on simulations with a gravitational lens program, we are tempted to argue that the line profile traces the presence of molecular gas of a disk in the host galaxy around the quasar. We have now new observations with the PdBI providing the necessary sensitivity to corroborate our disk model.Comment: 4 pages, 1 figure, to appear in "Proceedings of the 4th Cologne-Bonn-Zermatt-Symposium", ed. S. Pfalzner, C. Kramer, C. Straubmeier, and A. Heithausen (Springer Verlag