A New Mass Degeneracy in Gravitational Lenses: Is there a crisis between a large H₀ 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.