A SHARP view of H0LiCOW: H₀ from three time-delay gravitational lens systems with adaptive optics imaging

We present the measurement of the Hubble constant, H₀, 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 H₀. 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 H₀ = 82.8⁺₋⁹₈⁴₃ km s⁻¹ Mpc⁻¹ for PG 1115+080, H₀ = 70.1⁺₋⁵₄³₅ km s⁻¹ Mpc⁻¹ for HE 0435−1223, and H₀ = 77.0⁺₋⁴₄⁰₆ km s⁻¹ Mpc⁻¹ for RXJ 1131−1231. The joint AO-only result for the three lenses is H₀ = 75.6⁺₋³₃²₃ km s⁻¹ Mpc⁻¹. The joint result of the AO + HST analysis for the three lenses is H₀ = 76.8⁺₋²₂⁶₆ km s⁻¹ Mpc⁻¹. All of these results assume a flat Λ cold dark matter cosmology with a uniform prior on Ω_m in [0.05, 0.5] and H₀ 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 H₀. The full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper.