Radiative Equilibrium and Temperature Correction in Monte Carlo Radiation Transfer

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Abstract
We describe a general radiative equilibrium and temperature correction procedure for use in Monte Carlo radiation transfer codes with sources of temperature-independent opacity, such as astrophysical dust. The technique utilizes the fact that Monte Carlo simulations track individual photon packets, so we may easily determine where their energy is absorbed. When a packet is absorbed, it heats a particular cell within the envelope, raising its temperature. To enforce radiative equilibrium, the absorbed packet is immediately reemitted. To correct the cell temperature, the frequency of the reemitted packet is chosen so that it corrects the temperature of the spectrum previously emitted by the cell. The reemitted packet then continues being scattered, absorbed, and reemitted until it finally escapes from the envelope. As the simulation runs, the envelope heats up, and the emergent spectral energy distribution (SED) relaxes to its equilibrium value without iteration. This implies that the equilibrium temperature calculation requires no more computation time than the SED calculation of an equivalent pure scattering model with fixed temperature. In addition to avoiding iteration, our method conserves energy exactly because all injected photon packets eventually escape. Furthermore, individual packets transport energy across the entire system because they are never destroyed. This long-range communication, coupled with the lack of iteration, implies that our method does not suffer the convergence problems commonly associated with Λ-iteration. To verify our temperature correction procedure, we compare our results with standard benchmark tests, and finally we present the results of simulations for two-dimensional axisymmetric density structures.
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