Photophoresis in a Dilute, Optically Thick Medium and Dust Motion in Protoplanetary Disks

TL;DR

This paper derives analytical expressions for photophoretic forces on particles in optically thick, dilute gases, and explores their implications for dust dynamics in protoplanetary disks, highlighting effects on porous grains.

Contribution

It provides new analytical formulas for photophoretic forces considering thermal conduction and radiation, applied to dust in protoplanetary disks with porous grains.

Findings

Porous silicate grains experience significant photophoretic forces.

Photophoresis can cause dust levitation and relative velocities in disks.

Analytical approximations simplify modeling of dust dynamics.

Abstract

We derive expressions for the photophoretic force on opaque spherical particles in a dilute gas in the optically thick regime where the radiation field is in local thermal equilibrium. Under those conditions, the radiation field has a simple form, leading to well defined analytical approximations for the photophoretic force that also consider both the internal thermal conduction within the particle, and the effects of heat conduction and radiation to the surrounding gas. We derive these results for homogeneous spherical particles; and for the double layered spheres appropriate for modeling solid grains with porous aggregate mantles. Then, as a specific astrophysical application of these general physical results, we explore the parameter space relevant to the photophoresis driven drift of dust in protoplanetary disks. We show that highly porous silicate grains have sufficiently low thermal conductivities that photophoretic effects, such as significant relative velocities between particles with differing porosity or levitation above the midplane, are expected to occur.