Radiative Equilibrium and Temperature Correction in Monte Carlo Radiation Transfer

We describe a general radiative equilibrium and temperature correctionprocedure for use in Monte Carlo radiation transfer codes with sources oftemperature-independent opacity, such as astrophysical dust. The techniqueutilizes the fact that Monte Carlo simulations track individual photon packets,so we may easily determine where their energy is absorbed. When a packet isabsorbed, it heats a particular cell within the envelope, raising itstemperature. To enforce radiative equilibrium, the absorbed packet isimmediately re-emitted. To correct the cell temperature, the frequency of there-emitted packet is chosen so that it corrects the temperature of the spectrumpreviously emitted by the cell. The re-emitted packet then continues beingscattered, absorbed, and re-emitted until it finally escapes from the envelope.As the simulation runs, the envelope heats up, and the emergent spectral energydistribution (SED) relaxes to its equilibrium value, without iteration. Thisimplies that the equilibrium temperature calculation requires no morecomputation time than the SED calculation of an equivalent pure scatteringmodel with fixed temperature. In addition to avoiding iteration, our methodconserves energy exactly, because all injected photon packets eventuallyescape. Furthermore, individual packets transport energy across the entiresystem because they are never destroyed. This long-range communication, coupledwith the lack of iteration, implies that our method does not suffer theconvergence problems commonly associated with lambda-iteration. To verify ourtemperature correction procedure, we compare our results to standard benchmarktests, and finally we present the results of simulations for two-dimensionalaxisymmetric density structures.