A New Model of the Gravitational Lens 0957+561 and a Limit on the Hubble Constant
Abstract
We present a simple mass model for the lensing galaxy in the gravitationally lensed quasar 0957 + 561. We represent the galaxy as a softened powerlaw sphere (SPLS), a generalization of the singular isothermal sphere with three parametersρ_0_, the central density; θ_c_, the angular core radius; and η, the radial index, which is defined such that mass increases as r^{eta}^ at large radius. As in previous studies, we approximate the galaxy cluster surrounding the lensing galaxy by means of a quadratic potential described by its convergence κ and shear γ. A feature of the model is that it does not require a large central compact mass. We fit the model to a recent highresolution VLBI map of the two images of 0957+561. The data provide a number of independent constraints, and the model fit has 6 degrees of freedom, which is a significant improvement over previous models. Although the reduced χ^2^ of the bestfit model is only 4.3, nevertheless we obtain a tight constraint on the radial index, 1.07 < η < 1.18, at the 95% confidence level. Thus, the galaxy has mass increasing slightly more rapidly than isothermal (η = 1) out to at least 15 h^1^ kpc. Since the light from the galaxy follows a de Vaucouleurs profile, we deduce that the masstolight ratio of the galaxy increases rapidly with increasing radius. We also obtain an upper limit on the core radius, namely θ_c_ < 0.11" or linear core radius < 330 h^1^ pc. We use the model to calculate the Hubble constant H_0_ as a function of the time delay ATBA {DELTA}t_BA_ between the two images. We obtain H_0_ = (60.5^+5.3^_2.2_)(1  κ)({DELTA}t_BA_/1.5 yr)^1^ km s^1^ Mpc^1^ , or = (82.5^+7.2^_3.0_)(1  κ)({DELTA}t_BA_/1.1 yr)^1^ km s^1^ Mpc^ 1^ Once {DELTA}t_BA_ is measured, this will provide an upper bound on H_0_ since κ cannot be negative. In addition, the model degeneracy due to κ can be eliminated if the onedimensional velocity dispersion σ of the lensing galaxy is measured. In this case, we find that H_0_ = (60.5^+6.4^_4.1_)(σ/322 km s^1^)^2^({DELTA}t_BA_/1.5 yr)^ 1^ km s^1^ Mpc^1^, or =(82.5^+8.7^_5.6_)(σ/322 km s^1^)^2^({DELTA}t_BA_/1.1 yr)^1^ km s^1^ Mpc^1^. We find that these results are virtually unchanged if we include the ellipticity of the lensing galaxy or clumpiness of the lensing cluster.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 1996
 DOI:
 10.1086/177302
 Bibcode:
 1996ApJ...464...92G
 Keywords:

 COSMOLOGY: DISTANCE SCALE;
 COSMOLOGY: GRAVITATIONAL LENSING;
 GALAXIES: QUASARS: INDIVIDUAL ALPHANUMERIC: 0957+561