  Surveys have looked for H alpha emission from accreting gas giants but found
very few objects. Analyses of the detections and non-detections have assumed
that the entire gas flow feeding the planet is in radial free-fall. However,
hydrodynamical simulations suggest that this is far from reality. We calculate
the H alpha emission from multidimensional accretion onto a gas giant,
following the gas flow from Hill-sphere scales down to the circumplanetary disc
(CPD) and the planetary surface. We perform azimuthally-symmetric
radiation-hydrodynamics simulations around the planet and use modern tabulated
gas and dust opacities. Crucially, contrasting with most previous simulations,
we do not smooth the gravitational potential and do follow the flow down to the
planetary surface, where grid cells are 0.01 Jupiter radii small radially. We
find that only roughly one percent of the net gas inflow into the Hill sphere
reaches directly the planet. As expected for ballistic infall trajectories,
most of the gas falls at too large a distance on the CPD to generate H alpha.
Including radiation transport removes the high-velocity sub-surface flow
previously seen in hydrodynamics-only simulations, so that only the free planet
surface and the inner regions of the CPD emit substantially H alpha. Unless
magnetospheric accretion, which we neglect here, additionally produces H alpha,
the corresponding H alpha production efficiency is much smaller than usually
assumed, which needs to be taken into account when analysing (non-)detection
statistics.
