A SHARP view of H0LiCOW: H[SUB]0[/SUB] from three time-delay gravitational lens systems with adaptive optics imaging

We present the measurement of the Hubble constant, H[SUB]0[/SUB], with three strong gravitational lens systems. We describe a blind analysis of both PG 1115+080 and HE 0435-1223 as well as an extension of our previous analysis of RXJ 1131-1231. For each lens, we combine new adaptive optics (AO) imaging from the Keck Telescope, obtained as part of the SHARP (Strong-lensing High Angular Resolution Programme) AO effort, with Hubble Space Telescope (HST) imaging, velocity dispersion measurements, and a description of the line-of-sight mass distribution to build an accurate and precise lens mass model. This mass model is then combined with the COSMOGRAIL-measured time delays in these systems to determine H[SUB]0[/SUB]. We do both an AO-only and an AO + HST analysis of the systems and find that AO and HST results are consistent. After unblinding, the AO-only analysis gives H[SUB]0[/SUB]=82.8^{+9.4}_{-8.3} km s^{-1} Mpc^{-1} for PG 1115+080, H[SUB]0[/SUB]=70.1^{+5.3}_{-4.5} km s^{-1} Mpc^{-1} for HE 0435-1223, and H[SUB]0[/SUB]=77.0^{+4.0}_{-4.6} km s^{-1} Mpc^{-1} for RXJ 1131-1231. The joint AO-only result for the three lenses is H[SUB]0[/SUB]=75.6^{+3.2}_{-3.3} km s^{-1} Mpc^{-1}. The joint result of the AO + HST analysis for the three lenses is H[SUB]0[/SUB]=76.8^{+2.6}_{-2.6} km s^{-1} Mpc^{-1}. All of these results assume a flat Λ cold dark matter cosmology with a uniform prior on Ω[SUB]m[/SUB] in [0.05, 0.5] and H[SUB]0[/SUB] in [0, 150] km s^{-1} Mpc^{-1}. This work is a collaboration of the SHARP and H0LiCOW teams, and shows that AO data can be used as the high-resolution imaging component in lens-based measurements of H[SUB]0[/SUB]. The full time- delay cosmography results from a total of six strongly lensed systems are presented in a companion paper. <P />