Radiative transfer in axisymmetric dust clouds

Abstract

Summary In this paper we present a method of solution of the equation of radiative transfer for an axisymmetric distribution of dust around a central source. There is abundant observational evidence that points towards the existence of flattened density structures around a wide range of systems of astrophysical interest such as protostars, stars with circumstellar dust shells, reflection nebulae, active galactic nuclei and starburst galaxies. Results obtained with spherically symmetric models are clearly inappropriate in these cases and earlier attempts to solve the axisymmetric problem adopt simplifying assumptions that do not allow realistic modelling. The programme we have developed integrates the equation of radiative transfer exactly in the sense that it does not neglect any terms in the equation and treats multiple anisotropic scattering. The emergent spectral energy and intensity distributions are obtained for different viewing angles for models with different density distributions and optical depths. The method applies to an arbitrary density distribution, but in this paper we are presenting models of clouds in which the thickness of the disc increases linearly with distance from the central source and the disc is symmetric about the equatorial plane. The density is assumed to decline with radius as r−2 and with a power-law dependence on azimuthal angle Θ. We also present a model that gives an excellent fit to the spectrum of VY CMa, a late M supergiant which has long been thought to be surrounded by a circumstellar disc. The model predicts an unusual viewing angle, just inside the surface of the flared disc.