**B.5.5. The Future of Time Delay Measurements**

We understand the theory of time delays very well - the only important variable in the lens structure is the average surface density <> of the lens near the images for which the delay is measured. The angular structure of the potential has an effect on the delays, but it is either small or well-constrained by the observed image positions. 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 variables needed to model time delays, to estimate the Hubble constant, and to understand the systematic uncertainties in the results. Unfortunately, there is a tendency in the literature to confuse rather than to illuminate this understanding, even though all differences between estimates of the Hubble constant for the simple time delay lenses can be understood on this basis.

The problem with time delays lies with the confusing state of the data. The
four simplest time delay lenses, PG1115+080, SBS1520+530, B1600+434 and
HE2149-2745, can only match the currently preferred
estimate of
*H*_{0} 72
± 8 km s^{-1} Mpc^{-1} (Freedman et al.
[2001],
Spergel et al.
[2003])
if they have nearly constant *M* / *L* mass distributions. If
they have the favored quasi-isothermal mass distributions, then
*H*_{0} 48
± 3 km s^{-1} Mpc^{-1}. This leads to
a conundrum: why do simple lenses with time delay measurements have
falling rotation curves, while simple lenses with direct estimates of
the mass profile do not? This is further confused by B1608+656 and
B0218+357, which due to their observational complexity
would be the last systems I would attempt to understand, but in current
analyses can be both isothermal and have high *H*_{0}. In
resolving this problem it is not enough to search for a "Golden Lens."
*There is no such thing!* While chanting "My lens is better than
your lens!" may be satisfying, it
contributes little to understanding the basic problem.

The difficulty at the moment is that systems I would view as problematic
(B0218+357 due to problems in astrometry or B1608+656
due to the interacting
lens galaxies) allow both mass distributions with flat rotation curves and
*H*_{0} = 72 km s^{-1} Mpc^{-1}, while
systems that should be simpler to interpret
(the simple lenses in Table B.5.2) do
not. Yet the preponderance
of evidence on the mass distributions of lens galaxies suggests that they
are fairly homogeneous in structure and have roughly flat rotation curves
(Section B.4). The simplest way to clarify
this problem is to measure
accurate time delays for many more systems. At a fixed value of the Hubble
constant we will either find significant scatter in the surface densities
near the images of simple lenses or we will not.