Sub-milliarcsec-scale structure of the gravitational lens B1600+434

In the gravitational lens system B1600+434 the brighter image, A, is known to show rapid variability which is not detected in the weaker image, B (Koopmans & de Bruyn 2000). Since correlated variability is one of the fundamental properties of gravitational lensing, it has been proposed that image A is microlensed by stars in the halo of the lensing galaxy (Koopmans & de Bruyn 2000). We present VLBA observations of B1600+434 at 15 GHz with a resolution of 0.5 milliarcsec to determine the source structure at high spatial resolution. The surface brightness of the images are significantly different, with image A being more compact. This is in apparent contradiction with the required property of gravitational lensing that surface brightness be preserved. Our results suggest that both the lensed images may show two-sided elongation at this resolution, a morphology which does not necessarily favour superluminal motion. Instead these data may suggest that image B is scatter-broadened at the lens so that its size is larger than that of A, and hence scintillates less than image A.Comment: 4 pages, 2 figures, accepted in AA Letter

Constraints on the Inner Mass Profiles of Lensing Galaxies from Missing Odd Images

Most gravitational lens systems consist of two or four observable images. The absence of detectable odd images allows us to place a lower limit on the power-law slope of the inner mass profile of lensing galaxies. Using a sample of six two-image radio-loud lens systems and assuming a singular power-law surface density (Sigma proportional to r^{-beta}) for the inner several kpc of the mass distribution, we find that there is less than a 10% probability that the data are consistent with profile slopes beta < 0.80. Furthermore, individual mass modeling yields beta > 0.85 for B0739+366 and beta > 0.91 for B1030+074. Modeling central black holes as additional point masses changes the constraints in these systems to beta > 0.84 and beta > 0.83, respectively. The inner mass profiles of lensing galaxies are therefore not much shallower than isothermal.Comment: Final published version, minor typos corrected, 13 page

Improved Cosmological Constraints from Gravitational Lens Statistics

We combine the Cosmic Lens All-Sky Survey (CLASS) with new Sloan Digital Sky Survey (SDSS) data on the local velocity dispersion distribution function of E/S0 galaxies, $\phi(\sigma)$, to derive lens statistics constraints on $\Omega_\Lambda$ and $\Omega_m$. Previous studies of this kind relied on a combination of the E/S0 galaxy luminosity function and the Faber-Jackson relation to characterize the lens galaxy population. However, ignoring dispersion in the Faber-Jackson relation leads to a biased estimate of $\phi(\sigma)$ and therefore biased and overconfident constraints on the cosmological parameters. The measured velocity dispersion function from a large sample of E/S0 galaxies provides a more reliable method for probing cosmology with strong lens statistics. Our new constraints are in good agreement with recent results from the redshift-magnitude relation of Type Ia supernovae. Adopting the traditional assumption that the E/S0 velocity function is constant in comoving units, we find a maximum likelihood estimate of $\Omega_\Lambda = 0.74$--0.78 for a spatially flat unvierse (where the range reflects uncertainty in the number of E/S0 lenses in the CLASS sample), and a 95% confidence upper bound of $\Omega_\Lambda<0.86$. If $\phi(\sigma)$ instead evolves in accord with extended Press-Schechter theory, then the maximum likelihood estimate for $\Omega_\Lambda$ becomes 0.72--0.78, with the 95% confidence upper bound $\Omega_\Lambda<0.89$. Even without assuming flatness, lensing provides independent confirmation of the evidence from Type Ia supernovae for a nonzero dark energy component in the universe.Comment: 35 pages, 15 figures, to be published in Ap

Strong lensing constraints on the velocity dispersion and density profile of elliptical galaxies

We use the statistics of strong gravitational lensing from the CLASS survey to impose constraints on the velocity dispersion and density profile of elliptical galaxies. This approach differs from much recent work, where the luminosity function, velocity dispersion and density profile were typically {\it assumed} in order to constrain cosmological parameters. It is indeed remarkable that observational cosmology has reached the point where we can consider using cosmology to constrain astrophysics, rather than vice versa. We use two different observables to obtain our constraints (total optical depth and angular distributions of lensing events). In spite of the relatively poor statistics and the uncertain identification of lenses in the survey, we obtain interesting constraints on the velocity dispersion and density profiles of elliptical galaxies. For example, assuming the SIS density profile and marginalizing over other relevant parameters, we find 168 km/s < sigma_* < 200 km/s (68% CL), and 158 km/s < sigma_* < 220 km/s (95% CL). Furthermore, if we instead assume a generalized NFW density profile and marginalize over other parameters, the slope of the profile is constrained to be 1.50 < beta < 2.00 (95% CL). We also constrain the concentration parameter as a function of the density profile slope in these models. These results are essentially independent of the exact knowledge of cosmology. We briefly discuss the possible impact on these constraints of allowing the galaxy luminosity function to evolve with redshift, and also possible useful future directions for exploration.Comment: Uses the final JVAS/CLASS sample, more careful choice of ellipticals, added discussion of possible biases. Final results essentially unchanged. Matches the MNRAS versio

Changes in the measured image separation of the gravitational lens system, PKS 1830-211

We present eight epochs of 43 GHz, dual-polarisation VLBA observations of the gravitational lens system PKS 1830-211, made over fourteen weeks. A bright, compact ``core'' and a faint extended ``jet'' are clearly seen in maps of both lensed images at all eight epochs. The relative separation of the radio centroid of the cores (as measured on the sky) changes by up to 87 micro arcsec between subsequent epochs. A comparison with the previous 43 GHz VLBA observations (Garrett et al. 1997) made 8 months earlier show even larger deviations in the separation of up to 201 micro arcsec. The measured changes are most likely produced by changes in the brightness distribution of the background source, enhanced by the magnification of the lens. A relative magnification matrix that is applicable on the milliarcsecond scale has been determined by relating two vectors (the ``core-jet'' separations and the offsets of the polarised and total intensity emission) in the two lensed images. The determinant of this matrix, -1.13 +/-0.61, is in good agreement with the measured flux density ratio of the two images. The matrix predicts that the 10 mas long jet, that is clearly seen in previous 15 and 8.4 GHz VLBA observations (Garrett et al. 1997, Guirado et al. 1999), should correspond to a 4 mas long jet trailing to the south-east of the SW image. The clear non-detection of this trailing jet is a strong evidence for sub-structure in the lens and may require more realistic lens models to be invoked, e.g. Nair & Garrett (2000).Comment: 8 pages, 5 figure

A determination of H_0 with the CLASS gravitational lens B1608+656: II. Mass models and the Hubble constant from lensing

EDITED FROM PAPER: We present mass models of the four-image gravitational lens system B1608+656. A mass model for the lens galaxies has been determined that reproduces the image positions, two out of three flux-density ratios and the model time delays. Using the time delays determined by Fassnacht et al. (1999a), we find that the best isothermal mass model gives H_0=59^{+7}_{-6} km/s/Mpc for Omega_m=1 and Omega_l=0.0, or H_0=(65-63)^{+7}_{-6} km/s/Mpc for Omega_m=0.3 and Omega_l = 0.0-0.7 (95.4% statistical confidence). A systematic error of +/-15 km/s/Mpc is estimated. This cosmological determination of H_0 agrees well with determinations from three other gravitational lens systems (i.e. B0218+357, Q0957+561 and PKS1830-211), SNe Ia, the S-Z effect and local determinations. The current agreement on H_0 from four out of five gravitational lens systems (i) emphasizes the reliability of its determination from isolated gravitational lens systems and (ii) suggests that a close-to-isothermal mass profile can describe disk galaxies, ellipticals and central cluster ellipticals. The average of H_0 from B0218+357, Q0957+561, B1608+656 and PKS1830-211, gives H_0(GL)=69 +/-7 km/s/Mpc for a flat universe with Omega_m=1 or H_0(GL)=74 +/-8 km/s/Mpc for Omega_m=0.3 and Omega_l=0.0-0.7. When including PG1115+080, these values decrease to 64 +/-11 km/s/Mpc and 68 +/-13 km/s/Mpc (2-sigma errors), respectively.Comment: Accepted for publication in ApJ. 34 pages, 4 figure