Photoionization heating from ultraviolet (UV) radiation incidents on the atmospheres of hot Jupiters may drive planetary mass loss. Observations of stellar Lyman-α (Lyα) absorption have suggested that the hot Jupiter HD 209458b is losing atomic hydrogen. We construct a model of escape that includes realistic heating and cooling, ionization balance, tidal gravity, and pressure confinement by the host star wind. We show that mass loss takes the form of a hydrodynamic (Parker) wind, emitted from the planet's dayside during lulls in the stellar wind. When dayside winds are suppressed by the confining action of the stellar wind, nightside winds might pick up if there is sufficient horizontal transport of heat. A hot Jupiter loses mass at maximum rates of ~2 × 1012 g s–1 during its host star's pre-main-sequence phase and ~2 × 1010 g s–1 during the star's main-sequence lifetime, for total maximum losses of ~0.06% and ~0.6% of the planet's mass, respectively. For UV fluxes F UV 104 erg cm–2 s–1, the mass-loss rate is approximately energy limited and scales as . For larger UV fluxes, such as those typical of T Tauri stars, radiative losses and plasma recombination force to increase more slowly as F 0.6 UV. Dayside winds are quenched during the T Tauri phase because of confinement by overwhelming stellar wind pressure. During this early stage, nightside winds can still blow if the planet resides outside the stellar Alfven radius; otherwise, even nightside winds are stifled by stellar magnetic pressure, and mass loss is restricted to polar regions. We conclude that while UV radiation can indeed drive winds from hot Jupiters, such winds cannot significantly alter planetary masses during any evolutionary stage. They can, however, produce observable signatures. Candidates for explaining why the Lyman-α photons of HD 209458 are absorbed at Doppler-shifted velocities of ±100 km s–1 include charge-exchange in the shock between the planetary and stellar winds.

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