GRAVITATIONAL LENSING, TIME-DELAY, AND ANGULAR DIAMETER DISTANCE

Combining a model of the mass distribution in the gravitational lens Q0957 + 561 with measurements of the velocity dispersion of the primary lensing galaxy and the time delay between the two images, the Hubble constant has been recently estimated to be H0 = 37 +/- 14 km s-1 Mpc-1. The result depends weakly on the assumed value of q0 and may have systematic errors due to nonuniqueness of the model. It is shown here that the quantity that is most directly measured using a gravitational lens system is not H0 but rather the angular diameter distance d(OL) from the observer to the lens. The determination of d(OL) requires neither a knowledge of the distance to the source nor any cosmological assumption other than local isotropy and homogeneity transverse to the line of sight, again with possible systematic effects. In the case of Q0957 + 561, where the lens is at a redshift of z(L) = 0.36, the result is d(OL) = 1700 +/- 600 Mpc. If the mass distribution of the cluster surrounding the primary lens in Q0957 + 561 can be determined through independent observations, then it may be possible to estimate both H0 and q0.