2006ApJ...645..920S

We present a ray-tracing technique for radiative transfer modeling of complex three-dimensional (3D) structures that include dense regions of high optical depth, such as that in dense molecular clouds, circumstellar disks, envelopes of evolved stars, and dust tori around active galactic nuclei. The corresponding continuum radiative transfer problem is described, and the numerical requirements for inverse 3D density and temperature modeling are defined. We introduce a relative intensity and transform the radiative transfer equation along the rays to solve machine precision problems and to relax strong gradients in the source term. For the optically thick regions where common ray tracers are forced to perform small trace steps, we give two criteria for making use of a simple approximative solver crossing the optically thick region quickly. Using an example of a density structure with optical depth changes of 6 orders of magnitude and sharp temperature variations, we demonstrate the accuracy of the proposed scheme using a common fifth-order Runge-Kutta ray tracer with adaptive step-size control. In our test case, the gain in computational speed is about a factor of 870. The method is applied in order to calculate the temperature distribution within a massive molecular cloud core for different boundary conditions for the radiation field.