We can take four approaches to solving the central concentration problem. First, the density profiles of galaxies are not a complete mystery, and we could apply the constraints derived from observations of other (early-type) galaxies to the time delay systems. Second, we could make new observations of the existing time delay lenses in order to obtain additional data that would constrain the density profiles. Third, we could measure the time delays in the systems where the lens galaxies already have well-constrained densities. Fourth, we can use the statistical properties of time delay lenses to break the degeneracies seen in individual lenses.
If we assume that the time delay lenses have the same density structure as other early-type galaxies, then models close to isothermal are favored. For lenses with extended or multi-component sources, the lens models constrain the density distributions and the best fit models are usually very close to isothermal (e.g., Cohn et al. 2001; Winn, Rusin, & Kochanek 2003). Stellar dynamical observations of lenses also favor isothermal models (e.g., Treu & Koopmans 2002a). Stellar dynamical (e.g., Romanowsky & Kochanek 1999; Gerhard et al. 2001) and X-ray (e.g., Loewenstein & Mushotzky 2003) observations of nearby early-type galaxies generally find flat rotation curves on the relevant scales. Finally, weak lensing analyses require significant dark matter on large scales in early-type galaxies (McKay et al. 2002). In general, the data on early-type galaxies seem to prefer isothermal models on the scales relevant to interpreting time delays, while constant M / L models are firmly ruled out. If we must ultimately rely on the assumption that the density profiles of time delay lenses are similar to those of other early-type galaxies, the additional uncertainty added by this assumption will be small and calculable. Moreover, the assumption is no different from the assumptions of homogeneity used in other studies of the distance scale.
We can avoid any such assumptions by determining
the density profiles
of the time delay lenses directly. One approach is to measure the
kinematic properties of the lens galaxy. Since the mass
inside the Einstein ring is fixed by the image geometry, the velocity
dispersion is controlled by the central concentration of the density.
Treu & Koopmans
(2002b)
apply this method to PG1115+080 and
argue that the observed velocity dispersion
requires a mass distribution between the isothermal and constant
M / L limits with H0 =
59+12-7 km s-1 Mpc-1.
Note, however, that with this velocity dispersion the
lens galaxy does not lie on the fundamental plane, which is very
peculiar. A second approach is to use deep infrared imaging to
determine the structure of the lensed host galaxy of the quasar
(Kochanek, Keeton, &
McLeod 2001).
The location and width of the Einstein ring
depends on both the radial and angular structure of the potential,
although the sensitivity to the radial structure of the lens
is weak when the annulus bracketing the lensed images is thin
(
R /
<R> small;
Saha & Williams
2001).
This method will work best for asymmetric two-image lenses
(R /
<R> 
1).
The necessary data can be obtained with HST for most time delay
lenses.
We can also focus our monitoring campaigns on lenses already known to have well-constrained density profiles. For the reasons we have already discussed, systems with multi-component sources, well-studied images of the host galaxy or stellar dynamical measurements will have better constrained density profiles than those without any additional constraints. We can also avoid most of the uncertainties in the density profile by measuring the time delays of very low-redshift lenses. When the lens is very close to the observer, the images lie very close to the center of the lens where the stellar mass dominates. A constant M / L model then becomes a very good approximation and we need worry little about the amount or the distribution of the dark matter. The one such candidate at present, Q2237+0305 at zl = 0.04, will have very short delays, but these could be measured by an X-ray monitoring program using the Chandra observatory.
Finally, the statistical properties of larger samples of time delay lenses
will also help to solve the problem. We already saw in
Section 6
that the "simple" time delay lenses must have very similar densities,
independent of H0. This already means that the
implications for H0
no longer depend on individual lenses. In some ways the similarity of
the densities is not an advantage - it is actually easier to determine
H0 if the density distributions are inhomogeneous
(Kochanek 2003b).
On the other hand, there are well-defined approaches to using the
statistical properties of lens models to estimate parameters that cannot
be determined from the models of the individual systems (see
Kochanek 2001).
The statistics of the problematic flux ratios
observed in the lenses (see Section 5) may
also provide a means of estimating
<
>.
Schechter &
Wambsganss (2002)
point out that in four-image quasar lenses there is a tendency for the
brightest saddle point image to be demagnified compared to reasonable
lens models. Microlensing by the stars can naturally explain the
observations if the surface density of stars is a small fraction of
the total surface density near the images
(*
<< <>),
which would rule out constant M / L models where
*
<>.