Over-constrained Gravitational Lens Models and the Hubble Constant
  It is well known that measurements of H0 from gravitational lens time delays
scale as H0~1-k_E where k_E is the mean convergence at the Einstein radius R_E
but that all available lens data other than the delays provide no direct
constraints on k_E. The properties of the radial mass distribution constrained
by lens data are R_E and the dimensionless quantity x=R_E a''(R_E)/(1-k_E)$
where a''(R_E) is the second derivative of the deflection profile at R_E. Lens
models with too few degrees of freedom, like power law models with densities
~r^(-n), have a one-to-one correspondence between x and k_E (for a power law
model, x=2(n-2) and k_E=(3-n)/2=(2-x)/4). This means that highly constrained
lens models with few parameters quickly lead to very precise but inaccurate
estimates of k_E and hence H0. Based on experiments with a broad range of
plausible dark matter halo models, it is unlikely that any current estimates of
H0 from gravitational lens time delays are more accurate than ~10%, regardless
of the reported precision.
