Cosmological radiative transfer codes comparison project - I. The static density field tests

Radiative transfer (RT) simulations are now at the forefront of numerical astrophysics. They are becoming crucial for an increasing number of astrophysical and cosmological problems; at the same time their computational cost has come within reach of currently available computational power. Further progress is retarded by the considerable number of different algorithms (including various flavours of ray tracing and moment schemes) developed, which makes the selection of the most suitable technique for a given problem a non-trivial task. Assessing the validity ranges, accuracy and performances of these schemes is the main aim of this paper, for which we have compared 11 independent RT codes on five test problems: (0) basic physics; (1) isothermal H II region expansion; (2) H II region expansion with evolving temperature; (3) I-front trapping and shadowing by a dense clump and (4) multiple sources in a cosmological density field. The outputs of these tests have been compared and differences analysed. The agreement between the various codes is satisfactory although not perfect. The main source of discrepancy appears to reside in the multifrequency treatment approach, resulting in different thicknesses of the ionized-neutral transition regions and the temperature structure. The present results and tests represent the most complete benchmark available for the development of new codes and improvement of existing ones. To further this aim all test inputs and outputs are made publicly available in digital form.