  A substantial fraction of all ionizing photons originate from radiative
recombinations. However, in radiative transfer calculations this recombination
radiation is often assumed to be absorbed 'on-the-spot' because for most
methods the computational cost associated with the inclusion of gas elements as
sources is prohibitive. We present a new, CPU and memory efficient
implementation for the transport of ionizing recombination radiation in the
TRAPHIC radiative transfer scheme. TRAPHIC solves the radiative transfer
equation by tracing photon packets at the speed of light and in a
photon-conserving manner in spatially adaptive smoothed particle hydrodynamics
simulations. Our new implementation uses existing features of the TRAPHIC
scheme to add recombination radiation at no additional cost in the limit in
which the fraction of the simulation box filled with radiation approaches 1. We
test the implementation by simulating an HII region in photoionization
equilibrium and comparing to reference solutions presented in the literature,
finding excellent agreement. We apply our implementation to discuss the
evolution of the HII region to equilibrium. We show that the widely used case A
and B approximations yield accurate ionization profiles only near the source
and near the ionization front, respectively. We also discuss the impact of
recombination radiation on the geometry of shadows behind optically thick
absorbers. We demonstrate that the shadow region may be completely ionized by
the diffuse recombination radiation field and discuss the important role of
heating by recombination radiation in the shadow region.
