The importance of Einstein rings

We develop a theory of Einstein rings and demonstrate it using the infrared Einstein ring images of the quasar host galaxies observed in PG 1115+080, B1608+656, and B1938+666. The shape of an Einstein ring accurately and inde pendently determines the shape of the lens potential and the shape of the l ensed host galaxy. We find that the host galaxies of PG 1115+080, B1608+656 , and B1938+666 have axis ratios of 0.58 +/- 0.02, 0.69 +/- 0.02, and 0.62 +/- 0.14, respectively, including the uncertainties in the lens models. The Einstein rings break the degeneracies in the mass distributions or Hubble constants inferred from observations of gravitational lenses. In particular , the Einstein ring in PG 1115+080 rules out the centrally concentrated mas s distributions that lead to a high Hubble constant (H-o >60 km s(-1) Mpc(- 1)) given the measured time delays. Deep, detailed observations of Einstein rings will be revolutionary for constraining mass models and determining t he Hubble constant from time-delay measurements.