  In protoplanetary disks, the differential gravity-driven settling of dust
grains with respect to gas and with respect to grains of varying sizes
determines the observability of grains, and sets the conditions for grain
growth and eventually planet formation. In this work we explore the effect of
photophoresis on the settling of large dust grains in the inner regions of
actively accreting protoplanetary disks. Photophoretic forces on dust grains
result from the collision of gas molecules with differentially heated grains.
We undertake one dimensional dust settling calculations to determine the
equilibrium vertical distribution of dust grains in each column of the disk. In
the process we introduce a new treatment of the photophoresis force which is
consistent at all optical depths with the representation of the radiative
intensity field in a two-stream radiative transfer approximation. The
levitation of large dust grains creates a photophoretic dust trap several scale
heights above the mid-plane in the inner regions of the disk where the
dissipation of accretion energy is significant. We find that differential
settling of dust grains is radically altered in these regions of the disk, with
large dust grains trapped in a layer below the stellar irradiation surface in
where the dust to gas mass ratio can be enhanced by a factor of a hundred for
the relevant particles. The photophoretic trapping effect has a strong
dependence on particle size and porosity.
