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.

We perform cosmological hydrodynamics simulations with non-equilibrium primordial chemistry to obtain 59 minihalos that host first stars. The obtained minihalos are used as initial conditions of local three dimensional radiation hydrodynamics simulations to investigate the formation of the first stars. We find two-thirds of the minihalos host multiple stars, while the rest of them have single stars. The mass of the stars found in our simulations are in the range of 1M ⊙ M 300M ⊙ , peaking at several×10M ⊙ . Most of the very massive stars of 140M ⊙ are born as single stars, although not all of the single stars are very massive. We also find a few stars of 1M ⊙ that are kicked by the gravitational three body interactions to the position distant from the center of mass. The frequency that a star forming minihalo contains a binary system is ∼ 50%. We also investigate the abundance pattern of the stellar remnants by summing up the contributions from the first stars in the simulations. Consequently, the pattern is compatible with that of the low metallicity Damped Lyman−α systems or the Extremely Metal Poor (EMP) stars , if the mass spectrum obtained in our experiment is shifted to the low mass side by 0.2 dex. If we consider the case that an EMP star is born in the remnant of the individual minihalo without mixing with others, the chemical signature of the pair instability supernova is more prominent, because most of them are born as single stars. Subject headings: early Universe-radiative transfer -first stars-metal poor stars

We study the formation and evolution of H ii regions around the first stars formed at redshifts z ¼ 10 30. We use a one-dimensional Lagrangian hydrodynamics code that self-consistently incorporates radiative transfer and nonequilibrium primordial gas chemistry. The star-forming region is defined as a spherical dense molecular gas cloud with a Population III star embedded at the center. We explore a large parameter space by considering, as plausible early star-forming sites, dark matter halos of mass M halo ¼ 10 5 10 8 M , gas density profiles with a power-law index w ¼ 1:5 2:25, and metal-free stars of mass M star ¼ 25 500 M . The formation of the H ii region is characterized by initial slow expansion of a weak D-type ionization front near the center, followed by rapid propagation of an R-type front throughout the outer gas envelope. We find that the transition between the two front types is indeed a critical condition for the complete ionization of halos of cosmological interest. In small-mass (P10 6 M ) halos, the transition takes place within a few 10 5 yr, yielding high escape fractions (>80%) of both ionizing and photodissociating photons. The gas is effectively evacuated by a supersonic shock, with the mean density within the halo decreasing to P1 cm À3 in a few million years. In larger mass (k10 7 M ) halos, the ionization front remains to be of D-type over the lifetime of the massive star, the H ii region is confined well inside the virial radius, and the escape fractions are essentially zero. We derive an analytic formula that reproduces well the results of our simulations for the critical halo mass below which the gas is completely ionized. We discuss immediate implications of the present results for the star formation history and early reionization of the universe.

The development of radiation hydrodynamical methods that are able to follow gas dynamics and radiative transfer (RT) self‐consistently is key to the solution of many problems in numerical astrophysics. Such fluid flows are highly complex, rarely allowing even for approximate analytical solutions against which numerical codes can be tested. An alternative validation procedure is to compare different methods against each other on common problems, in order to assess the robustness of the results and establish a range of validity for the methods. Previously, we presented such a comparison for a set of pure RT tests (i.e. for fixed, non‐evolving density fields). This is the second paper of the Cosmological Radiative Transfer Comparison Project, in which we compare nine independent RT codes directly coupled to gas dynamics on three relatively simple astrophysical hydrodynamics problems: (i) the expansion of an H ii region in a uniform medium, (ii) an ionization front in a 1/r2 density profile with a flat core and (iii) the photoevaporation of a uniform dense clump. Results show a broad agreement between the different methods and no big failures, indicating that the participating codes have reached a certain level of maturity and reliability. However, many details still do differ, and virtually every code has showed some shortcomings and has disagreed, in one respect or another, with the majority of the results. This underscores the fact that no method is universal and all require careful testing of the particular features which are most relevant to the specific problem at hand.

We perform a three dimensional radiation hydrodynamics simulation to investigate the formation of first stars from initial collapse of a primordial gas cloud to formation and growth of protostars. The simulation is integrated until ∼0.1 Myrs after the formation of the primary protostar by which the protostars have already settled onto main sequence stars. This is the first attempt of simulating first star formation to take into account the ultraviolet radiative feedback effect by the multiple protostars as well as the three dimensional effects such as fragmentation of the accretion disk. We find that the mass accretions onto the population III protostars are significantly suppressed by the radiative feedback from themselves. As a result, we find five stars formed in this particular simulation, and that the final mass of the stars are 60M ⊙ , including a star of 4.4M ⊙ . Formation of such a star hints at the existence of even lower-mass stars that would live today.