AREPO-RT: radiation hydrodynamics on a moving mesh

We introduce AREPO-RT, a novel radiation hydrodynamic (RHD) solver for the unstructured moving-mesh code AREPO. Our method solves the moment-based radiative transfer equations using the M1 closure relation. We achieve second-order convergence by using a slope-limited linear spatial extrapolation and a first-order time prediction step to obtain the values of the primitive variables on both sides of the cell interface. A Harten-Lax-van Leer flux function, suitably modified for moving meshes, is then used to solve the Riemann problem at the interface. The implementation is fully conservative and compatible with the individual time-stepping scheme of AREPO. It incorporates atomic hydrogen (H) and helium (He) thermochemistry, which is used to couple the ultraviolet radiation field to the gas. Additionally, infrared (IR) radiation is coupled to the gas under the assumption of local thermodynamic equilibrium between the gas and the dust. We successfully apply our code to a large number of test problems, including applications such as the expansion of H II regions, radiation pressure-driven outflows, and the levitation of optically thick layer of gas by trapped IR radiation. The new implementation is suitable for studying various important astrophysical phenomena, such as the effect of radiative feedback in driving galactic scale outflows, radiation-driven dusty winds in high-redshift quasars, or simulating the reionization history of the Universe in a self-consistent manner.