It is well known that measurements of H _ { 0 } from gravitational lens time delays scale as H _ { 0 } \propto 1 - \kappa _ { E } where \kappa _ { 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 \kappa _ { E } .
The properties of the radial mass distribution constrained by lens data are R _ { E } and the dimensionless quantity \xi = R _ { E } \alpha ^ { \prime \prime } ( R _ { E } ) / ( 1 - \kappa _ { E } ) where \alpha ^ { \prime \prime } ( 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 \rho \propto r ^ { - n } , have a one-to-one correspondence between \xi and \kappa _ { E } ( for a power law model , \xi = 2 ( n - 2 ) and \kappa _ { E } = ( 3 - n ) / 2 = ( 2 - \xi ) / 4 ) .
This means that highly constrained lens models with few parameters quickly lead to very precise but inaccurate estimates of \kappa _ { E } and hence H _ { 0 } .
Based on experiments with a broad range of plausible dark matter halo models , it is unlikely that any current estimates of H _ { 0 } from gravitational lens time delays are more accurate than \sim 10 \% , regardless of the reported precision .