标题： 一种引力透镜0957+561的新模型和哈勃常数的限制 显示英文标题

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

摘要： 我们提出一个简单的质量模型，用于引力透镜类星体0957+561中的透镜星系。该模型是奇异等温球体的推广，包括一个核心半径$r_c$和一个幂律指数$\eta$，其定义为质量在大半径处按$r^\eta$增加。我们将围绕透镜星系的星系团近似为一个由其汇聚$\kappa$和剪切$\gamma$描述的二次势。我们将该模型拟合到最近的高分辨率VLBI图，该图显示了0957+561的两个像。我们得到了径向指数$1.07 < \eta <1.18$的紧密约束，这意味着透镜星系几乎是等温的，并且质量与光度比在至$15 h^{-1}$kpc范围内增加。 我们还得到了核心半径的上限，$r_c < 330 h^{-1}$pc。 我们使用该模型计算哈勃常数$H_0$作为两个像之间时间延迟$\Delta\tau_{BA}$的函数：$H_0 = \left({ 82.5^{+5.9} _{-3.0} }\right) (1 - \kappa) \left({ \Delta\tau_{BA}/1.1 \,{\rm yr} }\right)^{-1}$km/s/Mpc。 一旦测量了$\Delta \tau_{BA}$，这将提供$H_0$的上限，因为$\kappa$不能为负。 此外，如果测量了透镜星系的一维速度弥散$\sigma$，则可以消除由于$\kappa$引起的模型退化。 我们得到$H_0 = \left({ 82.5^{+8.7} _{-5.6} }\right) (\sigma / 322\,{\rm km/s})^2 \left({ \Delta \tau_{BA} /1.1 \,{\rm yr} }\right)^{-1}$km/s/Mpc。 我们研究了透镜星系的椭率和透镜星系团的不均匀性的影响，发现这些对我们的结果影响很小。 显示英文摘要

摘要： 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.