Marcelo A. Alvarez

Simulating Cosmic Reionization at Large Scales I: the Geometry of Reionization

We present the first large-scale radiative transfer simulat ions of cosmic reionization, in a simulation volume of (100 h 1 Mpc) 3 . This is more than a 2 orders of magnitude improvement over previous simulations. We achieve this by combining the results from extremely large, cosmological, N-body simulations with a new, fast and effici ent code for 3D radiative transfer, C 2 -Ray, which we have recently developed. These simulations allow us to do the first numerical studies of the large-scale structure of reionization w hich at the same time, and crucially, properly take account of the dwarf galaxy ionizing sources which are primarily responsible for reionization. In our realization, reionization starts around z � 21, and final overlap occurs by z � 11. The resulting electron-scattering optical depth is in goo d agreement with the firstyear WMAP polarization data. We show that reionization clearly proceeded in an inside-out fashion, with the high-density regions being ionized earli er, on average, than the voids. Ionization histories of smaller-size (5 to 10 comoving Mpc) subregions exabit a large scatter about the mean and do not describe the global reionization history well. This is true even when these subregions are at the mean density of the universe, which shows that small-box simulations of reionization have little predictive power for the evolut ion of the mean ionized fraction. The minimum reliable volume size for such predictions is � 30 Mpc. We derive the power-spectra of the neutral, ionized and total gas density fields and show t hat there is a significant boost of the density fluctuations in both the neutral and the ionized c omponents relative to the total at arcminute and larger scales. We find two populations of H II re gions according to their size, numerous, mid-sized (� 10 Mpc) regions and a few, rare, very large regions tens of Mpc in size. Thus, local overlap on fairly large scales of tens of Mp c is reached by z � 13, when our volume is only about 50% ionized, and well before the global overlap. We derive the statistical distributions of the ionized fraction and ionized gas densi ty at various scales and for the first time show that both distributions are clearly non-Gaussian. All these quantities are critical for predicting and interpreting the observational signals from reionization from a variety of observations like 21-cm emission, Ly-α emitter statistics, Gunn-Peterson optical depth and small-scale CMB secondary anisotropies due to patchy reionization.

The H II Region of the First Star

Simulations predict that the first stars in a ΛCDM universe formed at redshifts z > 20 in minihalos with masses of about 106 M☉. We have studied their radiative feedback by simulating the propagation of ionization fronts (I-fronts) created by these first Population III stars (M* = 15-500 M☉) at z = 20, within the density field of a cosmological simulation of primordial star formation, outward through the host minihalo and into the surrounding gas. A three-dimensional ray-tracing calculation tracks the I-front once the H II region evolves a champagne flow inside the minihalo, after the early D-type I-front detaches from the shock and runs ahead, becoming R type. We take account of the hydrodynamic back-reaction by an approximate model of the central wind. We find that the escape fraction of ionizing radiation from the host halo increases with stellar mass, with 0.7 fesc 0.9 for 80 M*/M☉ 500. To quantify the ionizing efficiency of these stars as they begin cosmic reionization, we find that for M* 80 M☉, the ratio of gas mass ionized to stellar mass is ~60,000, roughly half the number of ionizing photons released per stellar baryon. Nearby minihalos are shown to trap the I-front, so their centers remain neutral. This is contrary to the recent suggestion that these stars would trigger formation of a second generation by fully ionizing neighboring minihalos, stimulating H2 formation in their cores. Finally, we discuss how the evacuation of gas from the host halo reduces the growth and luminosity of miniquasars that may form from black hole remnants of the first stars.

Accretion onto the First Stellar Mass Black Holes

The first stars, forming at redshifts z > 15 in minihalos with M ~ 105-6 M ☉ may leave behind remnant black holes, which could conceivably have been the seeds for the supermassive black holes observed at z 7. We study remnant black hole growth through accretion, including for the first time the radiation emitted due to accretion, with adaptive mesh refinement cosmological radiation-hydrodynamical simulations. The effects of photoionization and heating dramatically affect the large-scale inflow, resulting in negligible mass growth. We compare cases with accretion luminosity included and neglected to show that accretion radiation drastically changes the environment within 100 pc of the black hole, increasing gas temperatures by an order of magnitude. Gas densities are reduced and further star formation in the same minihalo is prevented for the 200 million years we followed. Without radiative feedback included most seed black holes do not gain mass as efficiently as has been hoped for in previous theories, implying that black hole remnants of population III stars in minihalos are not likely to be miniquasars. Most importantly, however, our calculations demonstrate that if these black holes are indeed accreting close to the Bondi-Hoyle rate with 10% radiative efficiency they have a dramatic local effect in regulating star formation in the first galaxies. This suggests a novel mechanism for massive black hole formation—stellar-mass black holes may have suppressed fragmentation and star formation after falling into halos with virial temperatures ~104 K, facilitating massive black hole formation at their centers.

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.

C2-ray: A new method for photon-conserving transport of ionizing radiation

Abstract We present a new numerical method for calculating the transfer of ionizing radiation, called C2-ray (conservative, causal ray-tracing method). The transfer of ionizing radiation in diffuse gas presents a special challenge to most numerical methods which involve time- and spatial-differencing. Standard approaches to radiative transport require that grid cells must be small enough to be optically-thin while time steps are small enough that ionization fronts do not cross a cell in a single time step. This quickly becomes prohibitively expensive. We have developed an algorithm which overcomes these limitations and is, therefore, orders of magnitude more efficient. The method is explicitly photon-conserving, so the depletion of ionizing photons by bound-free opacity is guaranteed to equal the photoionizations these photons caused. As a result, grid cells can be large and very optically-thick without loss of accuracy. The method also uses an analytical relaxation solution for the ionization rate equations for each time step which can accommodate time steps which greatly exceed the characteristic ionization and ionization front crossing times. Together, these features make it possible to integrate the equation of transfer along a ray with many fewer cells and time steps than previous methods. For multi-dimensional calculations, the code utilizes short-characteristics ray tracing. The method scales as the product of the number of grid cells and the number of sources. C2-ray is well-suited for coupling radiative transfer to gas and N-body dynamics methods, on both fixed and adaptive grids, without imposing additional limitations on the time step and grid spacing. We present several tests of the code involving propagation of ionization fronts in one and three dimensions, in both homogeneous and inhomogeneous density fields. We compare to analytical solutions for the ionization front position and velocity, some of which we derive here for the first time. As an illustration, we apply C2-ray to simulate cosmic reionization in three-dimensional inhomogeneous cosmological density field. We also apply it to the problem of I-front trapping in a dense clump, using both a fixed and an adaptive grid.

THE IMPACT OF INHOMOGENEOUS REIONIZATION ON THE SATELLITE GALAXY POPULATION OF THE MILKY WAY

We use the publicly available subhalo catalogs from the via Lactea II simulation along with a Gpc-scale N-body simulation to understand the impact of inhomogeneous reionization on the satellite galaxy population of the Milky Way. The large-volume simulation is combined with a model for reionization that allows us to predict the distribution of reionization times for Milky Way mass halos. Motivated by this distribution, we identify candidate satellite galaxies in the simulation by requiring that any subhalo must grow above a specified mass threshold before it is reionized; after this time the ph otoionizing background will suppress both the formation of stars and the accretion of gas. We show that varying the reionization time over the range expected for Milky Way mass halos can change the number of satellite galaxies by roughly two orders of magnitude. This conclusion is in contradiction with a number of studies in the literature, and we conclude that this is a result of inconsistent application of the results of Gnedi n (2000); subtle changes in the assumptions about how reionization affects star formation in small galaxies c an lead to large changes in the effect of changing the reionization time on the number of satellites. We compare our satellite galaxies to observations using both abundance matching and stellar population synthesis methods to assign luminosities to our subhalos and account for observational completeness effects. Additionally, if we assume that the mass threshold is set by the virial temperature Tvir = 8 � 10 3 K we find that our model accurately matches the vmax distribution, radial distribution, and luminosity function of observed Milky Way satellites for a reionization time zreion = 8 +3 -2 , assuming that the via Lactea II subhalo distribution is representative of the Milky Way. This results in the presence of 540 +100 -340 satellite galaxies. Subject headings: cosmology:theory — large-scale structure of universe — dark matter

The Contribution of Star Formation and Merging to Stellar Mass Buildup in Galaxies

We present a formalism to reveal merging by subtracting the change in the galaxy stellar mass function (MF) due to mass-dependent star formation (SF) from the observed time derivative of the MF. We present the SF rate (SFR) in the FORS Deep Field as a function of stellar mass and time spanning 9 z > 0. At 10 < log M* < 11, galaxies are being preferentially destroyed at early times, while at later times the change in their numbers turns positive. This is an indication of the top-down buildup of the red sequence suggested by other recent observations.

CONNECTING REIONIZATION TO THE LOCAL UNIVERSE

We present results of combined N-body and three-dimensional reionization calculations to determine the relationship between reionization history and local environment in a volume of 1 Gpc h –1 across and a resolution of about 1 Mpc. We achieve this by applying three-dimensional simulations of reionization, based on the extended Press-Schechter formalism, to the same initial conditions as the N-body simulations. We resolve about 2 × 106 halos of mass greater than ~1012 M ☉ at z = 0, and determine the relationship between halo mass and reionization epoch for galaxies and clusters. For our fiducial reionization model, in which reionization begins at z ~ 15 and ends by z ~ 6, we find a strong bias for cluster-size halos to be in the regions that reionized first, at redshifts 10 < z < 15. Consequently, material in clusters was reionized within relatively small regions, on the order of a few Mpc, implying that all clusters in our calculation were reionized by their own progenitors. Milky Way mass halos were on average reionized later and by larger regions, with a distribution most similar to the global one, indicating that low-mass halos are nearly uncorrelated with reionization when only halo mass is taken as a prior. On average, most halos with mass less than 1013 M ☉ were reionized internally, while almost all halos with masses greater than 1014 M ☉ were reionized by their own progenitors. We briefly discuss the implications of this work in light of the missing satellites problem and how this new approach may be extended further.

Topology and sizes of H ii regions during cosmic reionization

We use the results of large-scale simulations of reionization to explore methods for characterizing the topology and sizes of HII regions during reionization. We use four independent methods for characterizing the sizes of ionized regions. Three of them give us a full size distribution: the friends-of-friends (FOF) method, the spherical average method (SPA) and the power spectrum (PS) of the ionized fraction. These latter three methods are complementary: While the FOF method captures the size distribution of the small scale H II regions, which contribute only a small amount to the total ionization fraction, the spherical average method provides a smoothed measure for the average size of the H II regions constituting the main contribution to the ionized fraction, and the power spectrum does the same while retaining more details on the size distribution. Our fourth method for characterizing the sizes of the H II regions is the average size which results if we divide the total volume of the H II regions by their total surface area, (i.e. 3V/A), computed in terms of the ratio of the corresponding Minkowski functionals of the ionized fraction field. To characterize the topology of the ionized regions, we calculate the evolution of the Euler Characteristic. We find that the evolution of the topology during the first half of reionization is consistent with inside-out reionization of a Gaussian density field. We use these techniques to investigate the dependence of size and topology on some basic source properties, such as the halo mass-to-light ratio, susceptibility of haloes to negative feedback from reionization, and the minimum halo mass for sources to form. We find that suppression of ionizing sources within ionized regions slows the growth of H II regions, and also changes their size distribution. Additionally, the topology of simulations including suppression is more complex. (abridged)

The 21 cm Background from the Cosmic Dark Ages: Minihalos and the Intergalactic Medium before Reionization

The H atoms inside minihalos (i.e., halos with virial temperatures Tvir ≤ 104 K, in the mass range roughly from 104 to 108 M☉) during the cosmic dark ages in a ΛCDM universe produce a redshifted background of collisionally pumped 21 cm line radiation that can be seen in emission relative to the cosmic microwave background (CMB). Previously, we used semianalytical calculations of the 21 cm signal from individual halos of different mass and redshift and the evolving mass function of minihalos to predict the mean brightness temperature of this 21 cm background and its angular fluctuations. Here we use high-resolution cosmological N-body and hydrodynamic simulations of structure formation at high redshift (z 8) to compute the mean brightness temperature of this background from both minihalos and the intergalactic medium (IGM) prior to the onset of Lyα radiative pumping. We find that the 21 cm signal from gas in collapsed, virialized minihalos dominates over that from the diffuse shocked gas in the IGM.