Analytic time delays and H-0 estimates for gravitational lenses

We study gravitational lens time delays for a general family of lensing pot entials, which includes the popular singular isothermal elliptical potentia l and singular isothermal elliptical density distribution but allows genera l angular structure. Using a novel approach, we show that the time delay ca n be cast in a very simple form, depending only on the observed image posit ions. Including an external shear changes the time delay in proportion to t he shear strength, and varying the radial profile of the potential changes the time delay approximately linearly. These analytic results can be used t o obtain simple estimates of the time delay and the Hubble constant in obse rved gravitational lenses. The naive estimates for four of five time delay lenses show surprising agreement with each other and with local measurement s of H-0; the complicated Q0957+561 system is the only outlier. The agreeme nt suggests that it is reasonable to use simple isothermal lens models to i nfer H-0, although it is still important to check this conclusion by examin ing detailed models and by measuring more lensing time delays.