Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A New Model of the Gravitational Lens 0957+561 and a Limit on the Hubble
  Constant   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 $15 h^{-1}$ kpc. We also obtain an upper limit on the core radius, $r_c
< 330 h^{-1}$ 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: $H_0 =
\left({ 82.5^{+5.9} _{-3.0} }\right) (1 - \kappa) \left({ \Delta\tau_{BA}/1.1
\,{\rm yr} }\right)^{-1}$ 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 $H_0 = \left({ 82.5^{+8.7} _{-5.6} }\right) (\sigma / 322\,{\rm
km/s})^2 \left({ \Delta \tau_{BA} /1.1 \,{\rm yr} }\right)^{-1}$ 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.

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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas