Nickolay Y. Gnedin

Effect of Reionization on Structure Formation in the Universe

I use simulations of cosmological reionization to quantify the effect of photoionization on the gas fraction in low-mass objects, in particular the characteristic mass scale below which the gas fraction is reduced compared to the universal value. I show that this characteristic scale can be up to an order of magnitude lower than the linear-theory Jeans mass, and that even if one defines the Jeans mass at a higher overdensity, it does not track the evolution of this characteristic suppression mass. Instead, the filtering mass, which corresponds directly to the scale over which baryonic perturbations are smoothed in linear perturbation theory, provides a remarkably good fit to the characteristic mass scale. Thus, it appears that the effect of reionization on structure formation in both the linear and nonlinear regimes is described by a single characteristic scale, the filtering scale of baryonic perturbations. In contrast to the Jeans mass, the filtering mass depends on the full thermal history of the gas instead of the instantaneous value of the sound speed, so it accounts for the finite time required for pressure to influence the gas distribution in the expanding universe. In addition to the characteristic suppression mass, I study the full shape of the probability distribution to find an object with a given gas mass among all the objects with the same total mass, and I show that the numerical results can be described by a simple fitting formula that again depends only on the filtering mass. This simple description of the probability distribution may be useful for semianalytical modeling of structure formation in the early universe.

Equation of state of the photoionized intergalactic medium

We develop an efficient method to study the effects of reionization history on the temperature-density relation of the intergalactic medium in the low density limit (overdensity less than 5). It is applied to the study of photo-reionization models in which the amplitude, spectrum and onset epoch of the ionizing flux, as well as the cosmology, are systematically varied. We find that the mean temperature-density relation at z=2-4 is well approximated by a power-law equation of state for uniform reionization models. We derive analytical expressions for its evolution and exhibit its asymptotic behavior: it is found that for sufficiently early reionization, imprints of reionization history prior to z=10 on the temperature-density relation are washed out. In this limit the temperature at cosmic mean density is proportional to (\Omega_b h/\sqrt\Omega_0)^{1/1.7}. While the amplitude of the radiation flux at the ionizing frequency of HI is found to have a negligible effect on the temperature-density relation as long as the universe reionizes before z=5, the spectrum can change the overall temperature by about 20%, through variations in the abundances of helium species. However the slope of the mean equation of state is found to lie within a narrow range for all reionization models we study, where reionization takes place before z=5. We discuss the implications of these findings for the observational properties of the Lyman-alpha forest. In particular, uncertainties in the temperature of the intergalactic medium, due to the uncertain reionization history of our universe, introduces a 30% scaling in the amplitude of the column density distribution while the the slope of the distribution is only affected by about 5%. Finally, we discuss how a fluctuating ionizing field affects the above results. We argue that under

The Santa Barbara Cluster Comparison Project: A Comparison of Cosmological Hydrodynamics Solutions

We have simulated the formation of an X-ray cluster in a cold dark matter universe using 12 different codes. The codes span the range of numerical techniques and implementations currently in use, including smoothed particle hydrodynamics (SPH) and grid methods with fixed, deformable, or multilevel meshes. The goal of this comparison is to assess the reliability of cosmological gasdynamical simulations of clusters in the simplest astrophysically relevant case, that in which the gas is assumed to be nonradiative. We compare images of the cluster at different epochs, global properties such as mass, temperature and X-ray luminosity, and radial profiles of various dynamical and thermodynamical quantities. On the whole, the agreement among the various simulations is gratifying, although a number of discrepancies exist. Agreement is best for properties of the dark matter and worst for the total X-ray luminosity. Even in this case, simulations that adequately resolve the core radius of the gas distribution predict total X-ray luminosities that agree to within a factor of 2. Other quantities are reproduced to much higher accuracy. For example, the temperature and gas mass fraction within the virial radius agree to within about 10%, and the ratio of specific dark matter kinetic to gas thermal energies agree to within about 5%. Various factors, including differences in the internal timing of the simulations, contribute to the spread in calculated cluster properties. Based on the overall consistency of results, we discuss a number of general properties of the cluster we have modeled.

Cosmological Reionization by Stellar Sources

I use cosmological simulations that incorporate a physically motivated approximation to three- dimensional radiative transfer that recovers correct asymptotic ionization front propagation speeds for some cosmologically relevant density distributions to investigate the process of the reionization of the universe by ionizing radiation from protogalaxies. Reionization proceeds in three stages and occupies a large redshift range from z D 15 until z D 5. During the —rst, ii preoverlap ˇˇ stage, H II regions gradually expand into the low-density intergalactic medium, leaving behind neutral high-density protrusions. During the second, ii overlap ˇˇ stage, that occurs in about 10% of the Hubble time, H II regions merge and the ionizing background rises by a large factor. During the third, ii postoverlap ˇˇ stage, remaining high-density regions are being gradually ionized as the required ionizing photons are being produced. Residual —uctuations in the ionizing background reach signi—cant (more than 10%) levels for the Lya forest absorption systems with column densities above 1014¨1015 cm~2 at z \ 3¨4. Subject headings: cosmology: theorygalaxies: formationintergalactic medium ¨ large-scale structure of universe

Probing the Universe with the Lyα forest — I. Hydrodynamics of the low-density intergalactic medium

We introduce an efficient and accurate alternative to full hydrodynamic simulations, Hydro-PM (HPM), for the study of the low column density Lyman-alpha forest (NHI <∼ 10 14 cm−2). It consists of a Particle-Mesh (PM) solver, modified to compute, in addition to the gravitational potential, an effective potential due to the gas pressure. Such an effective potential can be computed from the density field because of a tight correlation between density and pressure in the low density limit (δ <∼ 10), which can be calculated for any photo-reionization history by a method outlined in Hui & Gnedin (1997). Such a correlation exists, in part, because of minimal shock-heating in the low density limit. We compare carefully the density and velocity fields as well as absorption spectra, computed using HPM versus hydrodynamic simulations, and find good agreement. We show that HPM is capable of reproducing measurable quantities, such as the column density distribution, computed from full hydrodynamic simulations, to a precision comparable to that of observations. We discuss how, by virtue of its speed and accuracy, HPM can enable us to use the Lyman-alpha forest as a cosmological probe. We also discuss in detail the smoothing of the gas (or baryon) fluctuation relative to that of the dark matter on small scales due to finite gas pressure: (1) It is shown the conventional wisdom that the linear gas fluctuation is smoothed on the Jeans scale is incorrect for general reionization (or reheating) history; the correct linear filtering scale is in general smaller than the Jeans scale after reheating, but larger prior to it. (2) It is demonstrated further that in the mildly nonlinear regime, a PM solver, combined with suitable pre-filtering of the initial conditions, can be used to model the low density IGM. But such an approximation is shown to be less accurate than HPM, unless a non-uniform pre-filtering scheme is implemented.

The Fate of the First Galaxies. II. Effects of Radiative Feedback

We use three-dimensional cosmological simulations with radiative transfer to study the formation and evolution of the first galaxies in a ΛCDM cosmology. The simulations include continuum radiative transfer using the optically thin variable Eddington tensor (OTVET) approximation and line radiative transfer in the H2 Lyman-Werner bands of the UV background radiation. Chemical and thermal processes are treated in detail, particularly the ones relevant for H2 formation and destruction. We find that the first luminous objects (small-halo objects) are characterized by bursting star formation (SF) that is self-regulated by a feedback process acting on cosmological instead of galactic scales. The global SF history is regulated by the mean number of ionizing photons that escape from each source, UVfesc. It is almost independent of the assumed SF efficiency parameter, *, and the intensity of the dissociating background. The main feedback process that regulates the SF is the reformation of H2 in front of H II regions and inside relic H II regions. The H II regions remain confined inside filaments, maximizing the production of H2 in overdense regions through cyclic destruction/reformation of H2. If UVfesc > 10-7/*, the SF is self-regulated, photoevaporation of small-halo objects dominates the metal pollution of the low-density intergalactic medium, and the mass of produced metals depends only on fesc. If UVfesc 10-7/*, positive feedback dominates, and small-halo objects constitute the bulk of the mass in stars and metals until at least redshift z ~ 10. Small-halo objects cannot reionize the universe because the feedback mechanism confines the H II regions inside the large-scale structure filaments. In contrast to massive objects (large halos), which can reionize voids, small-halo objects partially ionize only the dense filaments while leaving the voids mostly neutral.

Multi-dimensional cosmological radiative transfer with a Variable Eddington Tensor formalism

Abstract We present a new approach to numerically model continuum radiative transfer based on the Optically Thin Variable Eddington Tensor (OTVET) approximation. Our method insures the exact conservation of the photon number and flux (in the explicit formulation) and automatically switches from the optically thick to the optically thin regime. It scales as N log N with the number of hydrodynamic resolution elements and is independent of the number of sources of ionizing radiation (i.e. works equally fast for an arbitrary source function). We also describe an implementation of the algorithm in a Soften Lagrangian Hydrodynamic code (SLH) and a multi-frequency approach appropriate for hydrogen and helium continuum opacities. We present extensive tests of our method for single and multiple sources in homogeneous and inhomogeneous density distributions, as well as a realistic simulation of cosmological reionization.

Feedback from Galaxy Formation: Production and Photodissociation of Primordial H2

We use one-dimensional radiative transfer simulations to study the evolution of H2 gas-phase (H- catalyzed) formation and photodissociation regions in the primordial universe. We find a new positive feedback mechanism capable of producing shells of H2 in the intergalactic medium (IGM), which are optically thick in some Lyman-Werner bands. While these shells exist, this feedback effect is important in reducing the H2 dissociating background flux and the size of photodissociation spheres around each luminous object. The maximum background opacity of the IGM in the H2 Lyman-Werner bands is ? ? 1-2 for a relic molecular fraction x = 2 ? 10-6, about 6 times greater than that found by Haiman, Abel, & Rees. Therefore, the relic molecular hydrogen can decrease the photodissociation rate by about an order of magnitude. The problem is relevant to the formation of small primordial galaxies with masses MDM 108 M? that rely on molecular hydrogen cooling to collapse. Alternatively, the universe may have remained dark for several hundred million years after the birth of the first stars, until galaxies with virial temperature Tvir 104 K formed.We use one-dimensional radiative transfer simulations to study the evolution of H_2 gas-phase (H^- catalyzed) formation and photo-dissociation regions in the primordial universe. We find a new positive feedback mechanism capable of producing shells of H_2 in the intergalactic medium, which are optically thick in some Lyman-Werner bands. While these shells exist, this feedback effect is important in reducing the H_2 dissociating background flux and the size of photo-dissociation spheres around each luminous object. The maximum background opacity of the IGM in the H_2 Lyman-Werner bands is \tau_{H_2} ~ 1-2 for a relic molecular fraction x_{H_2}=2 x 10^{-6}, about 6 times greater than found by Haiman, Abel & Rees. Therefore, the relic molecular hydrogen can decrease the photo-dissociation rate by about an order of magnitude. The problem is relevant to the formation of small primordial galaxies with masses M_{DM} 10^4 K formed.

Reheating of the Universe and Population III

We note that current observational evidence strongly favors a conventional recombination of ionized matter subsequent to redshift z = 1200, followed by reionization prior to redshift z = 5 and compute how this would have occurred in a standard scenario for the growth of structure. Extending prior semianalytic work, we show by direct, high-resolution numerical simulations (of a COBE normalized CDM + Λ model) that reheating will occur in the interval 20 > z > 7, followed by reionization and accompanied by a significant increase in the Jeans mass. However, the evolution of the Jeans mass does not significantly affect star formation in dense, self-shielded clumps of gas, which are detached from the thermal evolution of the rest of the universe. On average, the growth of the Jeans mass tracks the growth of the nonlinear mass scale, a result we suspect is due to nonlinear feedback effects. Cooling on molecular hydrogen leads to a burst of star formation prior to reheating, which produces Population III stars with Ω* reaching 10-5.5 and /Z☉ reaching 10-3.7 by z ~ 14. Star formation subsequently slows down as molecular hydrogen is depleted by photodestruction and the rise of the temperature. At later times, z < 10, when the characteristic virial temperature of gas clumps reach 104 degrees, star formation increases again as hydrogen line cooling become efficient. Objects containing Population III stars accrete mass with time and, as soon as they reach 104 K virial temperature, engage in renewed star formation and turn into normal Population II objects having an old Population III metal-poor component.

Generation of the Primordial Magnetic Fields during Cosmological Reionization

We investigate the generation of magnetic fields by the Biermann battery in cosmological ionization fronts, using new simulations of the reionization of the universe by stars in protogalaxies. Two mechanisms are primarily responsible for magnetogenesis: (1) the breakout of ionization fronts from protogalaxies and (2) the propagation of ionization fronts through the high-density neutral filaments that are part of the cosmic web. The first mechanism is dominant prior to overlapping of ionized regions (z ≈ 7), whereas the second continues to operate even after that epoch. However, after overlap the field strength increase is largely due to the gas compression occurring as cosmic structures form. As a consequence, the magnetic field at z ≈ 5 closely traces the gas density, and it is highly ordered on megaparsec scales. The mean mass-weighted field strength is B0 ≈ 10-19 G in the simulation box. There is a relatively well-defined, nearly linear correlation between B0 and the baryonic mass of virialized objects, with B0 ≈ 10-18 G in the most massive objects (M ≈ 109 M☉) in our simulations. This is a lower limit, as lack of numerical resolution prevents us from following small-scale dynamical processes that could amplify the field in protogalaxies. Although the field strengths we compute are probably adequate as seed fields for a galactic dynamo, the field is too small to have had significant effects on galaxy formation, on thermal conduction, or on cosmic-ray transport in the intergalactic medium. It could, however, be observed in the intergalactic medium through innovative methods based on analysis of γ-ray burst photon arrival times.