TREVR2: Illuminating fast $N\log_2\,N$ radiative transfer

We present TREVR2 (Tree-based REVerse Ray Tracing 2), a fast, general algorithm for computing the radiation field, suitable for both particle and mesh codes. It is designed to self-consistently evolve chemistry for zoomed-in astrophysical simulations, such as cosmological galaxies with both internal sources and prescribed background radiation, rather than large periodic volumes. Light is propagated until absorbed, with no imposed speed limit other than those due to opacity changes (e.g. ionization fronts). TREVR2 searches outward from receiving gas in discrete directions set by the HEALPIX algorithm (unlike its slower predecessor TREVR), accumulating optical depth and adding the flux due to sources combined into progressively larger tree cells with distance. We demonstrate $N_\textrm{active}\log_2 N$ execution time with absorption and many sources. This allows multi-band RT costs comparable to tree-based gravity and hydrodynamics, and the usual speed-up when active particles evolve on individual timesteps. Sources embedded in non-homogeneous absorbing material introduce systematic errors. We introduce transmission averaging instead of absorption averaging which dramatically reduces these systematic effects. We outline other ways to address systematics including an explicit complex source model. We demonstrate the overall performance of the method via a set of astrophysical test problems.