For the quadruple gravitational lens PG 1115 + 080 , we combine recent measurements of the time delays with new lens models to determine the Hubble constant H _ { 0 } .
We explore the effects of systematic uncertainties in the lens models on the estimates of H _ { 0 } , and we discuss how the uncertainties can be reduced by future observations .
We find that the lens can not be fit by an isolated lens galaxy , but that it can be well fit by including a perturbation from the nearby group of galaxies .
To understand the full range of systematic uncertainties it is crucial to use an ellipsoidal galaxy and to let the group position vary .
In this case , the existing constraints can not break degeneracies in the models with respect to the profiles of the galaxy and group and to the position of the group .
Combining the known time delays with a range of lens models incorporating most of the plausible systematic effects yields H _ { 0 } = 51 _ { -13 } ^ { +14 } km s ^ { -1 } Mpc ^ { -1 } .
The constraints on the lens models , and hence on H _ { 0 } , can be improved by reducing the standard errors in the lens galaxy position from 50 mas to \sim 10 mas , reducing the uncertainties in the time delays to \sim 0.5 days , and constraining the lens mass distribution using HST photometry and the fundamental plane .
In particular , the time delay ratio r _ { ABC } \equiv \Delta \tau _ { AC } / \Delta \tau _ { BA } may provide the best constraint on the mass profile of the galaxy .