5.2 Gravitational Lenses

Refsdael (1964, 1966) noted that the arrival times for the light from two gravitationally lensed images of a background point source are dependent on the path lengths and the gravitational potential traversed in each case. Hence, a measurement of the time delay and the angular separation for different images of a variable quasar can be used to provide a measurement of H₀. This method offers tremendous potential because it can be applied at great distances and it is based on very solid physical principles. Moreover, the method is not very sensitive to _m and . Some of the practical difficulties in applying this method have already been discussed in the previous section.

A number of new results based on this technique have recently appeared. Estimates of time delay measurements are now available for 2 systems: 0957 + 561 (Kundic et al. 1997), and most recently, a new time delay has been measured for PG 1115 (Schechter et al. 1997; Keeton and Kochanek 1997).

In the case of 0957+561, progress has been made on several fronts. The time delay for this system has been a matter of some debate in the literature, with two different values of 410 and 536 days being advocated; extensive new optical data have now resolved this issue in favor of the smaller time delay (t = 417 ± 3 days (Kundic et al. 1997). Another large observational uncertainty has been due to the difficulty of measuring an accurate velocity dispersion for the lensing galaxy. Recent data from the Keck telescope have provided a new measurement of the velocity dispersion (Falco et al. 1997). In addition, there has been substantial progress in modeling this system (Grogin & Narayan 1996). Based on the new time delay and velocity dispersions measurements, and the model of Grogin and Narayan, Falco et al. have recently derived a value of H₀ = in the range 62-67 ± 8 km/sec/Mpc for this system. The velocity dispersion in the lensing galaxy appears to decrease very steeply as a function of position from the center of the galaxy; further higher-resolution measurements will be required to determine the reliability of these faint measurements.

Schechter et al. (1997) have undertaken an extensive optical monitoring program to measure two independent time delays in the quadruply-imaged quasar PG 1115+080. They fit a variety of models to this system, preferring a solution that yields a value of H₀ = 42 km/sec/Mpc ± 14% (for = 1). The model in this case consists of fitting isothermal spheres to both the lensing galaxy and a nearby group of galaxies. They also considered additional models that yield values of H₀ = 64 and 84 km/sec/Mpc. Keeton & Kochanek (1997) have considered a wider class of models. They stress the degeneracies that are inherent in these analyses; a number of models with differing radial profiles for the lensing galaxy and group, and with differing positions for the group, yield fits with chi-squared per degrees of freedom less than 1. They conclude that H₀ = 60 ± 17 km/sec/Mpc (1-).