The determination of H0 using gravitational lens time
delays has come
of age. The last few years have seen a dramatic increase in the number
of delay measurements, and there is no barrier other than sociology to
rapidly increasing the sample. The interpretation of time delays
requires a model for
the gravitational potential of the lens. Fortunately, the physics
determining time delays is well understood, and the only important
variable is the average surface density
<
> of the lens
near the
images for which the delay is measured. Unfortunately, there is a tendency
in the literature to conceal rather than to illuminate this understanding.
Provided a lens does not lie in a cluster where the cluster potential
cannot be described by a simple expansion, any lens model that includes
the parameters
needed to vary the average surface density of the lens near the images and
to change the ratio between the quadrupole moment of the lens and the
environment includes all the parameters needed to model time delays,
to estimate the Hubble constant, and to understand the systematic
uncertainties in the results. All differences between estimates of the
Hubble constant for the simple time delay lenses can be understood on
this basis.
Models for the four time delay lenses that can be modeled using a single lens galaxy predict that H0 = 48 ± 3 km s-1 Mpc-1 if the lens galaxies have isothermal density profiles with flat rotation curves, and H0 = 71 ± 3 km s-1 Mpc-1 if they have constant mass-to-light ratios. The Key Project estimate of H0 = 72 ± 8 km s-1 Mpc-1 agrees with the lensing results only if the lenses have little dark matter. We have strong theoretical prejudices and estimates from other observations of early-type galaxies that we should favor the isothermal models over the constant M / L models. We feel that we have reached the point where the results from gravitational lens time delays deserve serious attention and that there is a reasonable likelihood that the local estimates of H0 are too high. A modest investment of telescope time would allow the measurement of roughly 5-10 time delays per year, and these new delays would rapidly test the current results. Other observations of time delay lenses to measure the velocity dispersions of the lens galaxies or to determine the geometry of the lensed images of the quasar host galaxy can be used to constrain the mass distributions directly. The systematic problems associated with the density profile are soluble not only in theory but also in practice, and the investment of the community's resources would be significantly less that than already invested in the distance scale.
The time delay measurements also provide a new probe of the density structure of galaxies at the boundary between the baryonic and dark matter dominated parts of galaxies (projected distances of 1-2 effective radii). Even if we ignore the actual value of H0, we can still study the differences in the surface densities. For example, we can show that the present sample of simple lenses must have very similar surface densities. This region is very difficult to study with other probes.
Finally, the time delay measurements can be used to determine cosmological
parameters. Time delays basically measure the distance to the lens galaxy,
so we can make the same sorts of cosmological measurements
as Type Ia supernovae. If the variations in
<> between lens
galaxies
are small, as seem to be indicated by the present data, then the accuracy
of the differential measurements will be very good. The present sample
has little sensitivity to the cosmological model even with the mass
distribution fixed because the time delay uncertainties are still too
large and the redshift range is too restricted (zl =
0.31 to 0.72).
If we assume that other methods will determine the distance factors
more accurately and rapidly, then we can use the time delays to study
the evolution of galaxy mass distributions with redshift.
Acknowledgements. CSK thanks D. Rusin and J. Winn for their comments. CSK is supported by the Smithsonian Institution and NASA ATP grant NAG5-9265.