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 independently determines the shape of the lens potential and the shape of the lensed 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 mass distributions that lead to a high Hubble constant (H₀ > 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 the Hubble constant from time-delay measurements.