Progenitor Halos Research Articles

DARK MATTER CORES IN THE FORNAX AND SCULPTOR DWARF GALAXIES: JOINING HALO ASSEMBLY AND DETAILED STAR FORMATION HISTORIES

We combine the detailed Star Formation Histories of the Fornax and Sculptor dwarf Spheroidals with the Mass Assembly History of their dark matter (DM) halo progenitors to estimate if the energy deposited by Supernova type II (SNeII) is sufficient to create a substantial DM core. Assuming the efficiency of energy injection of the SNeII into DM particles is $\epsilon_{\rm gc}=0.05$, we find that a single early episode, $z \gtrsim z_{\rm infall}$, that combines the energy of all SNeII due to explode over 0.5 Gyr, is sufficient to create a core of several hundred parsecs in both Sculptor and Fornax. Therefore, our results suggest that it is energetically plausible to form cores in Cold Dark Matter (CDM) halos via early episodic gas outflows triggered by SNeII. Furthermore, based on CDM merger rates and phase-space density considerations, we argue that the probability of a subsequent complete regeneration of the cusp is small for a substantial fraction of dwarf-size haloes.

DARK-MATTER HALO ASSEMBLY BIAS: ENVIRONMENTAL DEPENDENCE IN THE NON-MARKOVIAN EXCURSION-SET THEORY

In the standard excursion set model for the growth of structure, the statistical properties of halos are governed by the halo mass and are independent of the larger scale environment in which the halos reside. Numerical simulations, however, have found the spatial distributions of halos to depend not only on their mass but also on the details of their assembly history and environment. Here we present a theoretical framework for incorporating this "assembly bias" into the excursion set model. Our derivations are based on modifications of the path integral approach of Maggiore & Riotto (2010) that models halo formation as a non-Markovian random walk process. The perturbed density field is assumed to evolve stochastically with the smoothing scale and exhibits correlated walks in the presence of a density barrier. We write down conditional probabilities for multiple barrier crossings, and derive from them analytic expressions for descendant and progenitor halo mass functions and halo merger rates as a function of both halo mass and the linear overdensity of the larger-scale environment of the halo. Our results predict a higher halo merger rate and higher progenitor halo mass function in regions of higher overdensity, consistent with the behavior seen in N-body simulations.

THE VELOCITY FUNCTION OF DARK MATTER HALOS AT R = 20 kpc: REMARKABLY LITTLE EVOLUTION SINCE z ≈ 4

We investigate the evolution in the dark matter halo circular velocity function, measured at a fixed physical radius of 20 kpc (v_20), which is likely to be a good proxy for galaxy circular velocity, in the Millennium-II simulation. We find that the v_20 function evolves remarkably little since z ~ 4. We analyze the histories of the main progenitors of halos, and we find that the dark matter distribution within the central 20 kpc of massive halos has been in place since early times. This provides evidence for the inside-out growth of haloes. The constancy of the central circular velocity of halos may offer a natural explanation for the observational finding that the galaxy circular velocity is an excellent predictor of various galaxy properties. Our results also indicate that we can expect a significant number of galaxies with high circular velocities already at z=4 (more than one per 10^6 (Mpc/h)^3 with circular velocities in excess of 450 km/s, and more than one per 10^4.5 (Mpc/h)^3 with circular velocities in excess of 350 km/s). Finally, adding baryonic mass and using a simple model for halo adiabatic contraction, we find remarkable agreement with the velocity dispersion functions inferred observationally by Bezanson et al. (2011) up to z ~ 1 and down to about 220 km/s.

Satellite survival in highly resolved Milky Way class haloes

Surprisingly little is known about the origin and evolution of the Milky Way's satellite galaxy companions. UV photoionisation, supernova feedback and interactions with the larger host halo are all thought to play a role in shaping the population of satellites that we observe today, but there is still no consensus as to which of these effects, if any, dominates. In this paper, we revisit the issue by re-simulating a Milky Way class dark matter (DM) halo with unprecedented resolution. Our set of cosmological hydrodynamic Adaptive Mesh Refinement (AMR) simulations, called the Nut suite, allows us to investigate the effect of supernova feedback and UV photoionisation at high redshift with sub-parsec resolution. We subsequently follow the effect of interactions with the Milky Way-like halo using a lower spatial resolution (50pc) version of the simulation down to z=0. This latter produces a population of simulated satellites that we compare to the observed satellites of the Milky Way and M31. We find that supernova feedback reduces star formation in the least massive satellites but enhances it in the more massive ones. Photoionisation appears to play a very minor role in suppressing star and galaxy formation in all progenitors of satellite halos. By far the largest effect on the satellite population is found to be the mass of the host and whether gas cooling is included in the simulation or not. Indeed, inclusion of gas cooling dramatically reduces the number of satellites captured at high redshift which survive down to z=0.

Do globular clusters possess dark matter haloes? A case study in NGC 2419

We use recently published measurements of the kinematics, surface brightness and stellar mass-to-light ratio of the globular cluster NGC 2419 to examine the possibility that this Galactic halo satellite is embedded in a low-mass dark matter halo. NGC 2419 is a promising target for such a study, since its extreme Galactocentric distance and large mass would have greatly facilitated the retention of dark matter. A Markov-Chain Monte Carlo approach is used to investigate composite dynamical models containing a stellar and a dark matter component. We find that it is unlikely that a significant amount of dark matter (less than approx. 6% of the luminous mass inside the tidal limit of the cluster) can be present if the stars follow an anisotropic Michie model and the dark matter a double power law model. However, we find that more general models, derived using a new technique we have developed to compute non-parametric solutions to the spherical Jeans equation, suggest the presence of a significant dark matter fraction (approximately twice the stellar mass). Thus the presence of a dark matter halo around NGC 2419 cannot be fully ruled out at present, yet any dark matter within the 10 arcmin visible extent of the cluster must be highly concentrated and cannot exceed 1.1x10^6 Solar masses (99% confidence), in stark contrast to expectations for a plausible progenitor halo of this structure.

DETAILED ABUNDANCES OF TWO VERY METAL-POOR STARS IN DWARF GALAXIES

The most metal-poor stars in dwarf spheroidal galaxies (dSphs) can show the nucleosynthetic patterns of one or a few supernovae. These supernovae could have zero metallicity, making metal-poor dSph stars the closest surviving links to Population III stars. Metal-poor dSph stars also help to reveal the formation mechanism of the Milky Way halo. We present the detailed abundances from Keck/HIRES spectroscopy for two very metal-poor stars in two Milky Way dSphs. One star, in the Sculptor dSph, has [Fe I/H] = -2.40. The other star, in the Ursa Minor dSph, has [Fe I/H] = -3.16. Both stars fall in the previously discovered low-metallicity, high-[alpha/Fe] plateau. Most abundance ratios of very metal-poor stars in these two dSphs are largely consistent with very metal-poor halo stars. However, the abundances of Na and some r-process elements lie at the lower end of the envelope defined by inner halo stars of similar metallicity. We propose that the metallicity dependence of supernova yields is the cause. The earliest supernovae in low-mass dSphs have less gas to pollute than the earliest supernovae in massive halo progenitors. As a result, dSph stars at -3 < [Fe/H] < -2 sample supernovae with [Fe/H] << -3, whereas halo stars in the same metallicity range sample supernovae with [Fe/H] ~ -3. Consequently, enhancements in [Na/Fe] and [r/Fe] were deferred to higher metallicity in dSphs than in the progenitors of the inner halo.

Shallow dark matter cusps in galaxy clusters

We study the evolution of the stellar and dark matter components in a galaxy cluster of $10^{15} \, \rm{M_{\odot}}$ from $z=3$ to the present epoch using the high-resolution collisionless simulations of Ruszkowski & Springel (2009). At $z=3$ the dominant progenitor halos were populated with spherical model galaxies with and without accounting for adiabatic contraction. We apply a weighting scheme which allows us to change the relative amount of dark and stellar material assigned to each simulation particle in order to produce luminous properties which agree better with abundance matching arguments and observed bulge sizes at $z=3$. This permits the study of the effect of initial compactness on the evolution of the mass-size relation. We find that for more compact initial stellar distributions the size of the final Brightest Cluster Galaxy grows with mass according to $r\propto M^{2}$, whereas for more extended initial distributions, $r\propto M$. Our results show that collisionless mergers in a cosmological context can reduce the strength of inner dark matter cusps with changes in logarithmic slope of 0.3 to 0.5 at fixed radius. Shallow cusps such as those found recently in several strong lensing clusters thus do not necessarily conflict with CDM, but may rather reflect on the initial structure of the progenitor galaxies, which was shaped at high redshift by their formation process.

Signatures of minor mergers in the Milky Way disc - I. The SEGUE stellar sample

It is now known that minor mergers are capable of creating structure in the phase-space distribution of their host galaxy's disc. In order to search for such imprints in the Milky Way, we analyse the SEGUE F/G-dwarf and the Schuster et al. (2006) stellar samples. We find similar features in these two completely independent stellar samples, consistent with the predictions of a Milky Way minor-merger event. We next apply the same analyses to high-resolution, idealised N-body simulations of the interaction between the Sagittarius dwarf galaxy and the Milky Way. The energy distributions of stellar particle samples in small spatial regions in the host disc reveal strong variations of structure with position. We find good matches to the observations for models with a mass of Sagittarius' dark matter halo progenitor $\lessapprox 10^{11}$ M$_{\odot}$. Thus, we show that this kind of analysis could be used to provide unprecedentedly tight constraints on Sagittarius' orbital parameters, as well as place a lower limit on its mass.

Moka: a new tool for strong lensing studies

Strong gravitational lensing is a powerful tool for probing the matter distribution in the cores of massive dark matter haloes. Recent and ongoing analyses of galaxy cluster surveys (MACS, CFHTLS, SDSS, SGAS, CLASH, LoCuSS) have adressed the question of the nature of the dark matter distribution in clusters. N-body simulations of cold dark-matter haloes consistently find that haloes should be characterized by a concentration-mass relation that decreases monotonically with halo mass, and populated by a large amount of substructures, representing the cores of accreted progenitor halos. It is important for our understanding of dark matter to test these predictions. We present MOKA, a new algorithm for simulating the gravitational lensing signal from cluster-sized haloes. It implements the most recent results from numerical simulations to create realistic cluster-scale lenses with properties independent of numerical resolution. We perform systematic studies of the strong lensing cross section as a function of halo structures. We find that the strong lensing cross sections depend most strongly on the concentration and on the inner slope of the density profile of a halo, followed in order of importance by halo triaxiality and the presence of a bright central galaxy.

The substructure hierarchy in dark matter haloes

We present a new algorithm for identifying the substructure within simulated dark matter haloes. The method is an extension of that proposed by Tormen et al. (2004) and Giocoli et al. (2008a), which identifies a subhalo as a group of self-bound particles that prior to being accreted by the main progenitor of the host halo belonged to one and the same progenitor halo (hereafter satellite). However, this definition does not account for the fact that these satellite haloes themselves may also have substructure, which thus gives rise to sub-subhaloes, etc. Our new algorithm identifies substructures at all levels of this hierarchy, and we use it to determine the mass function of all substructure (counting sub-haloes, sub-subhaloes, etc.). On average, haloes which formed more recently tend to have a larger mass fraction in substructure and to be less concentrated than average haloes of the same mass. We provide quantitative fits to these correlations. Even though our algorithm is very different from that of Gao et al. (2004), we too find that the subhalo mass function per unit mass at redshift z = 0 is universal. This universality extends to any redshift only if one accounts for the fact that host haloes of a given mass are less concentrated at higher redshifts, and concentration and substructure abundance are anti-correlated. This universality allows a simple parametrization of the subhalo mass function integrated over all host halo masses, at any given time. We provide analytic fits to this function which should be useful in halo model analyses which equate galaxies with halo substructure when interpreting clustering in large sky surveys. Finally, we discuss systematic differences in the subhalo mass function that arise from different definitions of (host) halo mass.

Universal merger histories of dark-matter haloes

We study merger histories of dark-matter haloes in a suite of N-body simulations that span different cosmological models. The simulated cases include the up-to-date WMAP5 cosmology and other test cases based on the Einstein-deSitter cosmology with different power spectra. We provide a robust fitting function for the conditional mass function (CMF) of progenitor haloes of a given halo. This fit is valid for the different cosmological models and for different halo masses and redshifts, and it is a significant improvement over earlier estimates. Based on this fit, we develop a simple and accurate technique for transforming the merger history of a given simulated halo into haloes of different mass, redshift and cosmology. Other statistics such as main-progenitor history and merger rates are accurately transformed as well. This method can serve as a useful tool for studying galaxy formation. It is less sensitive to the low accuracy of the fit at small time-steps, and it can thus replace the more elaborate task of construction Monte-Carlo realizations. As an alternative approach, we confirm the earlier finding by Neistein & Dekel that the main-progenitor follows a log-normal distribution. This property of merger trees allows us to better capture their behaviour as a function of time and descendant mass, but a broader suite of simulations is required for evaluating the dependence of the log-normal parameters on the cosmological model.

Population III star clusters in the reionized Universe

In reionized regions of the Universe, gas can only collapse to form stars in dark matter (DM) haloes which grow to be sufficiently massive. If star formation is prevented in the minihalo progenitors of such DM haloes at redshifts z≳ 20, then these haloes will not be self-enriched with metals and so may host Population (Pop) III star formation. We estimate an upper limit for the abundance of Pop III star clusters which thus form in the reionized Universe, as a function of redshift. Depending on the minimum DM halo mass for star formation, between of the order of 1 and of the order of 1000, Pop III star clusters per square degree may be observable at 2 ≲z≲ 7. Thus, there may be a sufficient number density of Pop III star clusters for detection in surveys such as the Deep-Wide Survey (DWS) to be conducted by the James Webb Space Telescope. We predict that Pop III clusters formed after reionization are most likely to be found at z≳ 3 and within ∼40 arcsec (∼1 Mpc comoving) of DM haloes with masses of ∼1011 M⊙, the descendants of the haloes at z∼ 20 which host the first galaxies that begin reionization. However, if star formation is inefficient in the haloes hosting Pop III clusters due to the photoionizing background radiation, these clusters may not be bright enough for detection by the Near-Infrared Camera which will conduct the DWS. None the less, if the stellar initial mass function (IMF) is top-heavy the clusters may have sufficiently high luminosities in both Lyα and He iiλ1640 to be detected and for constraints to be placed on the Pop III IMF. While a small fraction of DM haloes with masses as high as ∼109 M⊙ at redshifts z≲ 4 are not enriched due to star formation in their progenitors, external metal enrichment due to galactic winds is likely to preclude Pop III star formation in a large fraction of otherwise unenriched haloes, perhaps even preventing star formation in pristine haloes altogether after reionization is complete at z∼ 6.

CHEMICAL EVOLUTION IN HIERARCHICAL MODELS OF COSMIC STRUCTURE. II. THE FORMATION OF THE MILKY WAY STELLAR HALO AND THE DISTRIBUTION OF THE OLDEST STARS

This paper presents theoretical star formation and chemical enrichment histories for the stellar halo of the Milky Way based on new chemodynamical modeling. The goal of this study is to assess the extent to which metal-poor stars in the halo reflect the star formation conditions that occurred in halo progenitor galaxies at high redshift, before and during the epoch of reionization. Simple prescriptions that translate dark-matter halo mass into baryonic gas budgets and star formation histories yield models that resemble the observed Milky Way halo in its total stellar mass, metallicity distribution, and the luminosity function and chemical enrichment of dwarf satellite galaxies. These model halos in turn allow an exploration of how the populations of interest for probing the epoch of reionization are distributed in physical and phase space, and of how they are related to lower-redshift populations of the same metallicity. The fraction of stars dating from before a particular time or redshift depends strongly on radius within the galaxy, reflecting the "inside-out" growth of cold-dark-matter halos, and on metallicity, reflecting the general trend toward higher metallicity at later times. These results suggest that efforts to discover stars from z > 6 - 10 should select for stars with [Fe/H] <~ -3 and favor stars on more tightly bound orbits in the stellar halo, where the majority are from z > 10 and 15 - 40% are from z > 15. The oldest, most metal-poor stars - those most likely to reveal the chemical abundances of the first stars - are most common in the very center of the Galaxy's halo: they are in the bulge, but not of the bulge. These models have several implications for the larger project of constraining the properties of the first stars and galaxies using data from the local Universe.

Dark matter halo growth - II. Diffuse accretion and its environmental dependence

Dark matter haloes in Lambda CDM simulations grow by mergers with other haloes as well as accretion of "diffuse" non-halo material. We quantify the mass growth rates via these two processes, dM_mer/dt and dM_dif/dt, and their dependence on halo environment using the ~500,000 haloes in the Millennium simulation. Adopting a local mass density parameter as a measure of halo environment, we find the two rates show strong but opposite environmental dependence, with mergers playing an increasingly important role for halo growths in overdense regions and diffuse accretion dominating growth in voids. This behaviour is independent of the mass cuts used to define haloes vs non-haloes. For galaxy-scale haloes, these two opposite correlations largely cancel out, but a weak environmental dependence remains that results in a slightly lower mean total growth rate, and hence an earlier mean formation redshift, for haloes in denser regions. The mean formation redshift of the ~5000 cluster-mass haloes, on the other hand, appears to have no correlation with halo environment. The origin of the positive correlation of dM_mer/dt with local density can be traced to the surrounding mass reservoir outside the haloes, where more progenitor haloes are available in denser regions. The negative correlation of dM_dif/dt with density, however, is not explained by the available diffuse mass in the reservoir, which is in fact larger in denser regions. The non-halo component may therefore be partially comprised of truly diffuse dark matter particles that are dynamically hotter and are accreted at a suppressed rate in denser regions. We also discuss the implications of these results for how to modify the Extended Press-Schechter model of halo growth, which in its original form does not predict environmental dependence.

THE HALO MERGER RATE IN THE MILLENNIUM SIMULATION AND IMPLICATIONS FOR OBSERVED GALAXY MERGER FRACTIONS

We developed a new method to extract halo merger rates from the Millennium Simulation. First, by removing superfluous mergers that are artifacts of the FOF halo finder, we find a lower merger rate compared to previous work. The reductions are more significant at lower redshifts, lower halo masses, and minor mergers. Our approach agrees better with predictions from the EPS model. Second, we find that the FOF halo finder overestimates the halo mass by up to 50% for halos that are about to merge, which leads to an additional ~20% overestimate of the merger rate. Therefore, we define halo masses by including only gravitationally bound particles. We provide new best-fitting parameters for a global formula to account for these improvements. In addition, we extract the merger rate per progenitor halo, as well as per descendant halo. The former is the quantity that is related to observed galaxy merger fractions when they are measured via pair counting. At low mass/redshift the merger rate increases with mass and redshift. At high mass/redshift (for halos with masses a few times the "knee" of the mass function) these trends break down, and the merger rate per progenitor halo decreases with mass and increases only moderately with redshift. Defining the merger rate per progenitor halo also allows us to quantify the rate at which halos are being accreted onto larger halos. We provide an analytic formula to convert given merger rates per descendant halo into merger rates per progenitor halo. Finally, we perform a comparison between observed merger fractions and the fraction of halos that have undergone a major merger during the recent dynamical friction time, and find a fair agreement, within the large uncertainties of the observations. Our new halo merger trees are available at http://www.mpe.mpg.de/ir/MillenniumMergerTrees/.

Numerical simulations of hot halo gas in galaxy mergers

Galaxy merger simulations have explored the behaviour of gas within the galactic disk, yet the dynamics of hot gas within the galaxy halo has been neglected. We report on the results of high-resolution hydrodynamic simulations of colliding galaxies with hot halo gas. We explore a range of mass ratios, gas fractions and orbital configurations to constrain the shocks and gas dynamics within the progenitor haloes. We find that : (i) A strong shock is produced in the galaxy haloes before the first passage, increasing the temperature of the gas by almost an order of magnitude to $T\sim 10^{6.3}$ K. (ii) The X-ray luminosity of the shock is strongly dependent on the gas fraction; it is $\gtrsim 10^{39}$ erg/s for halo gas fractions larger than 10%. (iii) The hot diffuse gas in the simulation produces X-ray luminosities as large as $10^{42}$ erg/s. This contributes to the total X-ray background in the Universe. (iv) We find an analytic fit to the maximum X-ray luminosity of the shock as a function of merger parameters. This fit can be used in semi-analytic recipes of galaxy formation to estimate the total X-ray emission from shocks in merging galaxies. (v) $\sim$ 10-20% of the initial gas mass is unbound from the galaxies for equal-mass mergers, while $3-5%$ of the gas mass is released for the 3:1 and 10:1 mergers. This unbound gas ends up far from the galaxy and can be a feasible mechanism to enrich the IGM with metals.

EVOLUTION OF DARK MATTER PHASE-SPACE DENSITY DISTRIBUTIONS IN EQUAL-MASS HALO MERGERS

We use dissipationless N-body simulations to investigate the evolution of the true coarse-grained phase-space density distribution f(x,v) in equal-mass mergers between dark matter (DM) halos. The halo models are constructed with various asymptotic power-law indices ranging from steep cusps to core-like profiles and we employ the phase-space density estimator ``Enbid'' developed by Sharma & Steinmetz to compute f(x,v). The adopted force resolution allows robust phase-space density profile estimates in the inner ~1% of the virial radii of the simulated systems. We confirm that mergers result in a decrease of the coarse-grained phase-space density in accordance with expectations from Mixing Theorems for collisionless systems. We demonstrate that binary mergers between identical DM halos produce remnants that retain excellent memories of the inner slopes and overall shapes of the phase-space density distribution of their progenitors. The robustness of the phase-space density profiles holds for a range of orbital energies, and a variety of encounter configurations including sequences of several consecutive merger events, designed to mimic hierarchical merging, and collisions occurring at different cosmological epochs. If the progenitor halos are constructed with appreciably different asymptotic power-law indices, we find that the inner slope and overall shape of the phase-space density distribution of the remnant are substantially closer to that of the initial system with the steepest central density cusp. These results explicitly demonstrate that mixing is incomplete in equal-mass mergers between DM halos, as it does not erase memory of the progenitor properties. Our results also confirm the recent analytical predictions of Dehnen (2005) regarding the preservation of merging self-gravitating central density cusps.

A merger tree with microsolar mass resolution: application to γ-ray emission from subhalo population

The hierarchical growth of dark matter haloes, in which galaxies are hosted, has been studied and modelled using various approaches. In this paper, we use a modified version the Sheth & Lemson algorithm for a A cold dark matter power spectrum, and model the growth of a Milky Way sized halo with microsolar mass resolution, corresponding to the typical Jeans mass for a dark matter Weakly Interacting Massive Particle with mass of 100 GeV. We then compute the unevolved subhalo mass function and build up a Milky Way halo placing and evolving its satellites. This subhalo population is used to study the γ-ray emission from dark matter annihilation. In this case, the subhaloes which populate the host halo have been computed considering only progenitor haloes accreted by the main branch of the tree, so as to correctly treat the embedding of sub-subhaloes inside subhaloes. Each subhalo will indeed host at the present-time sub-subhaloes accreted when it was an isolated system. In order to compute the sub-subhalo population of a Milky Way dwarf galaxy, like Draco, and to study its γ-ray emission, we first estimate the Draco virial mass at merging redshift z m and then we run the merger tree from z m following the halo down to the dark matter Jeans mass. We then study the effect on the Fermi Large Area Telescope (GLAST) detectability for both subhaloes in the Milky Way and in Draco, and we show how subhaloes cannot be responsible for the boost factor needed for detection.

THE ROLE OF DRY MERGERS FOR THE FORMATION AND EVOLUTION OF BRIGHTEST CLUSTER GALAXIES

Using a resimulation technique, we perform high-resolution cosmological simulations of dry mergers in a massive galaxy cluster identified in the Millennium Run. Our initial conditions include well resolved compound galaxy models consisting of dark matter halos and stellar bulges that are used to replace the most massive cluster progenitor halos at redshift z=3. By construction, our galaxy models obey the stellar mass-size relation initially. We demonstrate that the brightest cluster galaxy (BCG) evolves away from the Kormendy relation as defined by the smaller mass galaxies (i.e., the relation bends). As a result of the comparatively large number of mergers the BCG experiences, its total mass-to-light ratio becomes significantly higher than in typical elliptical galaxies. We also show that the mixing processes between dark matter and stars lead to a small but numerically robust tilt in the fundamental plane and that the BCG lies on the tilted plane. Our model is consistent with the observed steepening of the logarithmic mass-to-light gradient as a function of the stellar mass. Surprisingly, we find only tentative weak distortion in the Faber-Jackson relation that depends on the aperture size, unlike expected based on studies of isolated merger simulations. This may be due to differences in the distribution of galaxy orbits, which is given in our approach directly by the cosmological context while it has to be assumed in isolated merger simulations, and the fact that the BCG is located deep in the cluster potential well.

FORMATION RATES OF POPULATION III STARS AND CHEMICAL ENRICHMENT OF HALOS DURING THE REIONIZATION ERA

The first stars in the universe formed out of pristine primordial gas clouds that were radiatively cooled to a few hundreds of degrees kelvin either via molecular or atomic (Lyman-α) hydrogen lines. This primordial mode of star formation was eventually quenched once radiative and/or chemical (metal enrichment) feedbacks marked the transition to Population II stars. In this paper, we present a model for the formation rate of Population III stars based on Press–Schechter modeling coupled with analytical recipes for gas cooling and radiative feedback. Our model also includes a novel treatment for metal pollution based on self-enrichment due to a previous episode of Population III star formation in progenitor halos. With this model, we derive the star formation history of Population III stars, their contribution to the reionization of the universe and the time of the transition from Population III star formation in minihalos (M ≈ 106 M☉, cooled via molecular hydrogen) to that in more massive halos (M ≳ 2 × 107 M☉, where atomic hydrogen cooling is also possible). We consider a grid of models highlighting the impact of varying the values for the free parameters used, such as star formation and feedback efficiency. The most critical factor is the assumption that only one Population III star is formed in a halo. In this scenario, metal-free stars contribute only to a minor fraction of the total number of photons required to reionize the universe. In addition, metal-free star formation is primarily located in minihalos, and chemically enriched halos become the dominant locus of star formation very early in the life of the universe—at redshift z ≈ 25—even assuming a modest fraction (0.5%) of enriched gas converted in stars. If instead multiple metal-free stars are allowed to form out of a single halo, then there is an overall boost of Population III star formation, with a consequent significant contribution to the reionizing radiation budget. In addition, the bulk of metal-free stars are produced in halos with M ≳ 2 × 107 M☉.