A New Model of the Gravitational Lens 0957+561 and a Limit on the Hubble Constant

Details A New Model of the Gravitational Lens 0957+561 and a Limit on the Hubble Constant A New Model of the Gravitational Lens 0957+561 and a Limit on the Hubble Constant

Jun 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996apj...464...92g&link_type=abstract

Astrophysical Journal v.464, p.92

Astronomy and Astrophysics

Astronomy

101

Cosmology: Distance Scale, Cosmology: Gravitational Lensing, Galaxies: Quasars: Individual Alphanumeric: 0957+561

Scientific paper

We present a simple mass model for the lensing galaxy in the gravitationally lensed quasar 0957 + 561. We represent the galaxy as a softened power-law sphere (SPLS), a generalization of the singular isothermal sphere with three parameters-ρ_0_, the central density; θ_c_, the angular core radius; and η, the radial index, which is defined such that mass increases as reta^ 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 high-resolution 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 best-fit 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 mass-to-light 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 one-dimensional 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.

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