Three-dimensional numerical cosmological radiative transfer in an inhomogeneous medium

A numerical scheme is proposed for the solution of the three-dimensional (3D) radiative transfer equation with variable optical depth. We show that time-dependent ray tracing is an attractive choice for simulations of astrophysical ionization fronts, particularly when one is interested in covering a wide range of optical depths within a three-dimensional clumpy medium. Our approach combines the explicit advection of radiation variables with the implicit solution of local rate equations given the radiation field at each point. Our scheme is well suited to the solution of problems for which line transfer is not important, and could, in principle, be extended to those situations also. This scheme allows us to calculate the propagation of supersonic ionization fronts into an inhomogeneous medium. The approach can be easily implemented on a single workstation and should also be fully parallelizable.     

The effects of radiative transfer on the reionization of an inhomogeneous universe

Assuming simple dynamics for the growth of density fluctuations, we implement six-dimensional (6D) radiative transfer calculations to elucidate the effects of photon propagation during the reionization of an inhomogeneous universe. The ionizing sources are postulated to be AGN-like in this paper. The present simulations reveal that radiative transfer effects are still prominent considerably after the percolation epoch, in which patchy ionized regions connect with each other. In other words, owing to the collective opacity, the Universe does not become perfectly transparent against ionizing radiation even though strongly self-shielded regions disappear. It turns out that the inhomogeneity of the medium enhances the opacity effects and delays the end of reionization. Owing to such radiative transfer effects, the reionization in an inhomogeneous universe proceeds fairly slowly, in contrast to the prompt reionization in a homogeneous universe, and as a result the surface of reionization is not so sharply edged, but highly uneven. As a signature of the uneven surface of reionization, the cosmic IR background (CIB) radiation, which is produced by Ly photons resulting from radiative recombination, could exhibit strong anisotropies, reflecting the amplitude of density fluctuations at the reionization era. The predicted CIB intensity lies on a level of possible detection by forthcoming IR space telescope facilities.     

Cosmological reionization around the first stars: Monte Carlo radiative transfer

We study the evolution of ionization fronts around the first protogalaxies by using high-resolution numerical cosmological (Λ+ cold dark matter, CDM, model) simulations and Monte Carlo radiative transfer methods. We present the numerical scheme in detail and show the results of test runs from which we conclude that the scheme is both fast and accurate. As an example of interesting cosmological application, we study the reionization produced by a stellar source of total mass M =2×10⁸ M_⊙ turning on at z ≈12, located at a node of the cosmic web. The study includes a spectral energy distribution of a zero-metallicity stellar population, and two initial mass functions (IMFs; Salpeter/Larson). The expansion of the ionization front (I-front) is followed as it breaks out from the galaxy and is channelled by the filaments into the voids, assuming (in a 2D representation) a characteristic butterfly shape. The ionization evolution is very well tracked by our scheme, as realized by the correct treatment of the channelling and shadowing effects resulting from overdensities. We confirm previous claims that both the shape of the IMF and the ionizing power metallicity dependence are important to correctly determine the reionization of the Universe.     

A new exact method for line radiative transfer

We present a new method, the coupled escape probability (CEP), for exact calculation of line emission from multi-level systems, solving only algebraic equations for the level populations. The CEP formulation of the classical two-level problem is a set of linear equations , and we uncover an exact analytic expression for the emission from two-level optically thick sources that holds as long as they are in the 'effectively thin' regime. In a comparative study of a number of standard problems, the CEP method outperformed the leading line transfer methods by substantial margins.
The algebraic equations employed by our new method are already incorporated in numerous codes based on the escape probability approximation. All that is required for an exact solution with these existing codes is to augment the expression for the escape probability with simple zone-coupling terms. As an application, we find that standard escape probability calculations generally produce the correct cooling emission by the C  ii 158-μm line but not by the ³P lines of O  i .     

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.     

Current models of the observable consequences of cosmic reionization and their detectability

A number of large current experiments aim to detect the signatures of the cosmic reionization at redshifts z > 6. Their success depends crucially on understanding the character of the reionization process and its observable consequences and designing the best strategies to use. We use large-scale simulations of cosmic reionization to evaluate the reionization signatures at redshifted 21-cm and small-scale cosmic microwave background (CMB) anisotropies in the best current model for the background universe, with fundamental cosmological parameters given by Wilkinson Microwave Anisotropy Probe three-year results. We find that the optimal frequency range for observing the 'global step' of the 21-cm emission is 120–150 MHz, while statistical studies should aim at 140–160 MHz, observable by GMRT. Some strongly non-Gaussian brightness features should be detectable at frequencies up to ∼190 MHz. In terms of sensitivity-signal trade-off relatively low resolutions, corresponding to beams of at least a few arcminutes, are preferable. The CMB anisotropy signal from the kinetic Sunyaev–Zel'dovich effect from reionized patches peaks at tens of μK at arcminute scales and has an rms of ∼1 μK, and should be observable by the Atacama Cosmology Telescope and the South Pole Telescope. We discuss the various observational issues and the uncertainties involved, mostly related to the poorly known reionization parameters and, to a lesser extend, to the uncertainties in the background cosmology.     

Inhomogeneous reionization of the intergalactic medium regulated by radiative and stellar feedbacks

We study the inhomogeneous reionization in a critical density CDM universe resulting from stellar sources, including Population III objects. The spatial distribution of the sources is obtained from high-resolution numerical N -body simulations. We calculate the source properties, taking into account a self-consistent treatment of both radiative (i.e. ionizing and H₂-photodissociating photons) and stellar (i.e. SN explosions) feedbacks regulated by massive stars. This allows us to describe the topology of the ionized and dissociated regions at various cosmic epochs, and to derive the evolution of H, He and H₂ filling factors, soft UV background, cosmic star formation rate and the final fate of ionizing objects. The main results are: (i) galaxies reionize the intergalactic medium by z ≈10 (with some uncertainty related to the gas clumping factor), whereas H₂ is completely dissociated already by z ≈25; (ii) reionization is mostly caused by the relatively massive objects which collapse via H line cooling, while objects the formation of which relies on H₂ cooling alone are insufficient for this purpose; (iii) the diffuse soft UV background is the major source of radiative feedback effects for z ≤15; at higher z direct flux from neighbouring objects dominates; (iv) the match of the calculated cosmic star formation history with that observed at lower redshifts suggests that the conversion efficiency of baryons into stars is ≈1 per cent; (v) we find that a very large population of dark objects which failed to form stars is present by z ≈8. We discuss and compare our results with similar previous studies.     

An implementation of radiative transfer in the cosmological simulation code gadget

We present a novel numerical implementation of radiative transfer in the cosmological smoothed particle hydrodynamics (SPH) simulation code gadget . It is based on a fast, robust and photon-conserving integration scheme where the radiation transport problem is approximated in terms of moments of the transfer equation and by using a variable Eddington tensor as a closure relation, following the Optically Thin Variable Eddington Tensor suggestion of Gnedin & Abel. We derive a suitable anisotropic diffusion operator for use in the SPH discretization of the local photon transport, and we combine this with an implicit solver that guarantees robustness and photon conservation. This entails a matrix inversion problem of a huge, sparsely populated matrix that is distributed in memory in our parallel code. We solve this task iteratively with a conjugate gradient scheme. Finally, to model photon sink processes we consider ionization and recombination processes of hydrogen, which is represented with a chemical network that is evolved with an implicit time integration scheme. We present several tests of our implementation, including single and multiple sources in static uniform density fields with and without temperature evolution, shadowing by a dense clump and multiple sources in a static cosmological density field. All tests agree quite well with analytical computations or with predictions from other radiative transfer codes, except for shadowing. However, unlike most other radiative transfer codes presently in use for studying re-ionization, our new method can be used on-the-fly during dynamical cosmological simulation, allowing simultaneous treatments of galaxy formation and the re-ionization process of the Universe.     

Radiation–hydrodynamical collapse of pre-galactic clouds in the ultraviolet background

To explain the effects of the ultraviolet (UV) background radiation on the collapse of pre-galactic clouds, we implement a radiation–hydrodynamical calculation, combining one-dimensional spherical hydrodynamics with an accurate treatment of the radiative transfer of ionizing photons. Both absorption and scattering of UV photons are explicitly taken into account. It turns out that a gas cloud contracting within the dark matter potential does not settle into hydrostatic equilibrium, but undergoes run-away collapse even under the presence of the external UV field. The cloud centre is shown to become self-shielded against ionizing photons by radiative transfer effects before shrinking to the rotation barrier. Based on our simulation results, we further discuss the possibility of H₂ cooling and subsequent star formation in a run-away collapsing core. The present results are closely relevant to the survival of subgalactic Population III objects as well as to metal injection into intergalactic space.     

Two-body relaxation in cosmological simulations

It is logically possible that early two-body relaxation in simulations of cosmological clustering influences the final structure of massive clusters. Convergence studies in which mass and spatial resolution are simultaneously increased cannot eliminate this possibility. We test the importance of two-body relaxation in cosmological simulations with simulations in which there are two species of particles. The cases of two mass ratios, √2:1 and 4:1, are investigated. Simulations are run with both a spatially fixed softening length and adaptive softening using the publicly available codes gadget and mlapm , respectively.
The effects of two-body relaxation are detected in both the density profiles of haloes and the mass function of haloes. The effects are more pronounced with a fixed softening length, but even in this case they are not so large as to suggest that results obtained with one mass species are significantly affected by two-body relaxation.
The simulations that use adaptive softening are less affected by two-body relaxation and produce slightly higher central densities in the largest haloes. They run about three times faster than the simulations that use a fixed softening length.