A New Mass Degeneracy in Gravitational Lenses: Is there a crisis between   a large $H_0$ and the time delay by a large lens halo?
  Isothermal models and other simple smooth models of dark matter halos of gravitational lenses often predict a dimensionless time delay $H_0\Delta t$ much too small to be comfortable with the observed time delays $\Delta t$ and the widely accepted $H_0$ value ($\sim 70$ km/s/Mpc). This conflict or crisis of the CDM has been highlighted by several recent papers of Kochanek, who claims that the standard value of $H_0$ favors a strangely small halo as compact as the stellar light distribution with an overall nearly Keplerian rotation curve. In an earlier paper (Paper I, astro-ph/0209191) we argue that this is not necessarily the case, at least in a perfectly symmetrical Einstein cross system. Here we introduce a {\it new mass degeneracy} of lens systems to give a counter example to Kochanek's claims. We fit the time delay and image positions in the quadruple image system PG1115+080. Equally good fits are found between lens models with flat vs. Keplerian rotation curves. Time delays in both types of models can be fit with the standard value of $H_0$. We demonstrate that it may still be problematic to constrain the size of lens dark halos even if the data image positions are accurately given and the cosmology is precisely specified. 
HongSheng Zhao (1,2) and Bo Qin (1,2) ((1) NAOC Beijing and (2) IoA   Cambridge)