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. The model is a generalization of the singular isothermal sphere and includes a core radius, $r_c$, and a power-law index, $\eta$, defined such that mass increases as $r^{\eta }$ at large radius. We approximate the galaxy cluster surrounding the lensing galaxy with a quadratic potential described by its convergence $\kappa$ and shear $\gamma$. We fit the model to a recent high resolution VLBI map of the two images of 0957+561. We obtain a tight constraint on the radial index, $1.07<\eta <1.18$, which means that the lens galaxy is nearly isothermal with increasing mass-to-light ratio out to $15h^{-1}$ kpc. We also obtain an upper limit on the core radius, $r_c<330h^{-1}$ pc. We use the model to calculate the Hubble constant $H_0$ as a function of the time delay $\Delta {\tau }_{BA}$ between the two images: $H_0=\left(82.5_{-3.0}^{+5.9}\right)(1-\kappa ){\left(\Delta {\tau }_{BA}/1.1\mathrm{yr}\right)}^{-1}$ km/s/Mpc. Once $\Delta {\tau }_{BA}$ is measured, this will provide an upper bound on $H_0$ since $\kappa$ cannot be negative. In addition, the model degeneracy due to $\kappa$ can be eliminated if the one-dimensional velocity dispersion $\sigma$ of the lensing galaxy is measured. We then have $H_0=\left(82.5_{-5.6}^{+8.7}\right)(\sigma /322km/s{)}^2{\left(\Delta {\tau }_{BA}/1.1\mathrm{yr}\right)}^{-1}$ km/s/Mpc. We investigate the effects of ellipticity in the lensing galaxy and clumpiness in the lensing cluster and find that these cause little change in our results.

Submitted to ApJ. 49 pages; aaspp latex + 5 postscript figures, uuencoded gzipped tar archive. Hardcopies available by request. Also available from http://cfa-www.harvard.edu/~nagrogin/papers/0957/

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