TreeCol: a novel approach to estimating column densities in astrophysical simulations

We present TreeCol, a new and efficient tree-based scheme to calculate column densities in numerical simulations. Knowing the column density in any direction at any location in space is a prerequisite for modelling the propagation of radiation through the computational domain. TreeCol therefore forms the basis for a fast, approximate method for modelling the attenuation of radiation within large numerical simulations. It constructs a HEALPIX sphere at any desired location and accumulates the column density by walking the tree and by adding up the contributions from all tree nodes whose line of sight contributes to the pixel under consideration. In particular, when combined with widely-used tree-based gravity solvers, the new scheme requires little additional computational cost. In a simulation with N resolution elements, the computational cost of TreeCol scales as NlogN, instead of the N^5/3 scaling of most other radiative transfer schemes. TreeCol is naturally adaptable to arbitrary density distributions and is easy to implement and to parallelize, particularly if a tree structure is already in place for calculating the gravitational forces. We describe our new method and its implementation into the smoothed particle hydrodynamics (SPH) code GADGET2 (although note that the scheme is not limited to particle-based fluid dynamics). We discuss its accuracy and performance characteristics for the examples of a spherical protostellar core and for the turbulent interstellar medium. We find that the column density estimates provided by TreeCol are on average accurate to better than 10 per cent. In another application, we compute the dust temperatures for solar neighbourhood conditions and compare with the result of a full-fledged Monte Carlo radiation-transfer calculation. We find that both methods give similar answers. We conclude that TreeCol provides a fast, easy to use and sufficiently accurate method of calculating column densities that comes with little additional computational cost when combined with an existing tree-based gravity solver.