An algorithm for Monte Carlo time-dependent radiation transfer

A new Monte Carlo algorithm for calculating time-dependent radiative transfer under the assumption of local thermodynamic equilibrium is presented. Unlike flux-limited diffusion, the method is polychromatic, includes scattering, and is able to treat the optically-thick and free-streaming regimes simultaneously. The algorithm is tested on a variety of 1D and 2D problems, and good agreement with benchmark solutions is found. The method is used to calculate the time-varying spectral energy distribution from a circumstellar disc illuminated by a protostar whose accretion luminosity is varying. It is shown that the time-lag between the optical variability and the infrared variability results from a combination of the photon traveltime and the thermal response in the disc, and that the lag is an approximately linear function of wavelength.