Occurrence of metal-free galaxies in the early Universe

The character of the first galaxies at redshifts z ≳ 10 strongly depends on their level of pre-enrichment, which is in turn determined by the rate of primordial star formation prior to their assembly. In order for the first galaxies to remain metal-free, star formation in minihaloes must be highly suppressed, most likely by H₂-dissociating Lyman–Werner (LW) radiation. We show that the build-up of such a strong LW background is hindered by two effects. First, the level of the LW background is self-regulated, being produced by the Population III (Pop III) star formation which it, in turn, suppresses. Secondly, the high opacity to LW photons which is built up in the relic H  ii regions left by the first stars acts to diminish the global LW background. Accounting for a self-regulated LW background, we estimate a lower limit for the rate of Pop III star formation in minihaloes at z ≳ 15. Further, we simulate the formation of a 'first galaxy' with virial temperature   T _vir≳ 10⁴ K  and total mass  ≳10⁸ M_⊙  at z ≳ 10, and find that complete suppression of previous Pop III star formation is unlikely, with stars of  ≳100 M_⊙  (Pop III.1) and  ≳10 M_⊙  (Pop III.2) likely forming. Finally, we discuss the implications of these results for the nature of the first galaxies, which may be observed by future missions such as the James Webb Space Telescope .     

The formation of the Hubble sequence of disc galaxies: the effects of early viscous evolution

We investigate a model of disc galaxies whereby viscous evolution of the gaseous disc drives material inwards to form a protobulge. We start from the standard picture of disc formation through the settling of gas into a dark halo potential well, with the disc initially coming into centrifugal equilibrium with detailed conservation of angular momentum. We derive generic analytic solutions for the disc–halo system after adiabatic compression of the dark halo, with free choice of the input virialized dark halo density profile and of the specific angular momentum distribution. We derive limits on the final density profile of the halo in the central regions. Subsequent viscous evolution of the disc is modelled by a variation of the specific angular momentum distribution of the disc, providing analytic solutions to the final disc structure. The assumption that the viscous evolution time-scale and the star formation time-scale are similar leads to predictions of the properties of the stellar components. Focusing on small 'exponential' bulges, i.e., ones that may be formed through a disc instability, we investigate the relationship between the assumed initial conditions, such as halo 'formation', or assembly, redshift z _f, spin parameter λ , baryonic fraction F , and final disc properties such as global star formation time-scale, gas fraction, and bulge-to-disc ratio. We find that the present properties of discs, such as the scalelength, are compatible with a higher initial formation redshift if the redistribution by viscous evolution is included than if it is ignored. We also quantify the dependence of final disc properties on the ratio F λ , thus including the possibility that the baryonic fraction varies from galaxy to galaxy, as perhaps may be inferred from the observations.     

Particle decay in the early Universe: predictions for 21 cm

The influence of ultra-high energy cosmic rays (UHECRs) and decaying dark matter particles on the emission and absorption characteristics of neutral hydrogen in 21 cm at redshifts   z = 10–50  is considered. In the presence of UHECRs, 21 cm can be seen in absorption with the brightness temperature   T _b=−(5–10) mK  in the range   z = 10–30  . Decaying particles can stimulate a 21-cm signal in emission with   T _b∼ 50–60 mK  at   z = 50  and   T _b≃ 10 mK  at   z ∼ 20  . Characteristics of the fluctuations of the brightness temperature, in particular its power spectrum, are also calculated. The maps of the power spectrum of the brightness temperature on the plane wavenumber redshift are shown to be sensitive to the parameters of UHECRs and decaying dark matter. Observational possibilities to detect manifestations of UHECRs and/or decaying particles in 21 cm with the future radio telescopes (LOFAR, 21CMA and SKA), and to distinguish contributions from them, are briefly discussed.     

An analytic model for the epoch of halo creation

In this paper we describe the Bayesian link between the cosmological mass function and the distribution of times at which isolated haloes of a given mass exist. By assuming that clumps of dark matter undergo monotonic growth on the time-scales of interest, this distribution of times is also the distribution of 'creation' times of the haloes. This monotonic growth is an inevitable aspect of gravitational instability. The spherical top-hat collapse model is used to estimate the rate at which clumps of dark matter collapse. This gives the prior for the creation time given no information about halo mass. Applying Bayes' theorem then allows any mass function to be converted into a distribution of times at which haloes of a given mass are created. This general result covers both Gaussian and non-Gaussian models. We also demonstrate how the mass function and the creation time distribution can be combined to give a joint density function, and discuss the relation between the time distribution of major merger events and the formula calculated. Finally, we determine the creation time of haloes within three N -body simulations, and compare the link between the mass function and creation rate with the analytic theory.     

Two populations of metal-free stars in the early Universe

We construct star formation histories at redshifts z ≳ 5 for two physically distinct populations of primordial, metal-free stars, motivated by theoretical and observational arguments that have hinted towards the existence of an intermediate stellar generation between Population III and Population I/II. Taking into account the cosmological parameters as recently revised by the Wilkinson Microwave Anisotropy Probe after three years of operation, we determine self-consistent reionization histories and discuss the resulting chemical enrichment from these early stellar generations. We find that the bulk of ionizing photons and heavy elements produced at high redshifts must have originated in Population II.5 stars, which formed out of primordial gas in haloes with virial temperatures ≳10⁴ K, and had typical masses ≳10 M_⊙. Classical Population III stars, formed in minihaloes and having masses ≳100 M_⊙, on the other hand, had only a minor impact on reionization and early metal enrichment. Specifically, we conclude that only ≃10 per cent by mass of metal-free star formation went into Population III.     

The cooling function of HD molecule revisited

We report new calculations of the cooling rate of primordial gas by the HD molecule, taking into account its ro-vibrational structure. The HD cooling function is calculated including radiative and collisional transitions for   J ≤ 8  rotational levels, and for the vibrational levels v = 0, 1, 2 and 3. The ro-vibrational level population is calculated from the balance equation assuming steady state. The cooling function is evaluated in the ranges of the kinetic temperatures, T _k, from 10² to  2 × 10⁴ K  and the number densities, n _H, from 1 to  10⁸ cm⁻³  . We find that the inclusion of collisional ro-vibrational transitions increases significantly the HD cooling efficiency, in particular for high densities and temperatures. For   n _H≳ 10⁵  and   T _k∼ 10⁴ K  the cooling function becomes more than an order of magnitude higher than previously reported. We give also the HD cooling rate in the presence of the cosmic microwave radiation field for radiation temperatures of 30, 85 and 276 K (redshifts of 10, 30 and 100). The tabulated cooling functions are available at http://www.cifus.uson.mx/Personal_Pages/anton/DATA/HD_cooling/HD_cool.html . We discuss the relevance to explore the effects of including our results into models and simulations of galaxy formation, especially in the regime when gas cools down from temperatures above ∼3000 K.     

Ram pressure stripping of disc galaxies orbiting in clusters – I. Mass and radius of the remaining gas disc

We present the first 3D hydrodynamical simulations of ram pressure stripping of a disc galaxy orbiting in a galaxy cluster. Along the orbit, the ram pressure that this galaxy experiences varies with time. In this paper, we focus on the evolution of the radius and mass of the remaining gas disc, and compare it with the classical analytical estimate proposed by Gunn & Gott. We find that this simple estimate works well in predicting the evolution of the radius of the remaining gas disc. Only if the ram pressure increases faster than the stripping time-scale, the disc radius remains larger than predicted. However, orbits with such short ram pressure peaks are unlikely to occur in other than compact clusters. Unlike the radius evolution, the mass-loss history for the galaxy is not accurately described by the analytical estimate. Generally, in the simulations the galaxy loses its gas more slowly than predicted.     

Constraints on σ8 from galaxy clustering in N-body simulations and semi-analytic models

We generate mock galaxy catalogues for a grid of different cosmologies, using rescaled N -body simulations in tandem with a semi-analytic model run using consistent parameters. Because we predict the galaxy bias, rather than fitting it as a nuisance parameter, we obtain an almost pure constraint on σ₈ by comparing the projected two-point correlation function we obtain to that from the Sloan Digital Sky Survey (SDSS). A systematic error arises because different semi-analytic modelling assumptions allow us to fit the r -band luminosity function equally well. Combining our estimate of the error from this source with the statistical error, we find  σ₈= 0.97 ± 0.06  . We obtain consistent results if we use galaxy samples with a different magnitude threshold, or if we select galaxies by b _J-band rather than r -band luminosity and compare to data from the 2dF Galaxy Redshift Survey (2dFGRS). Our estimate for σ₈ is higher than that obtained for other analyses of galaxy data alone, and we attempt to find the source of this difference. We note that in any case, galaxy clustering data provide a very stringent constraint on galaxy formation models.     

On the assembly history of dark matter haloes

We study the mass assembly history (MAH) of dark matter haloes. We compare MAHs obtained using (i) merger trees constructed with the extended Press–Schechter (EPS) formalism, (ii) numerical simulations and (iii) the Lagrangian perturbation code pinocchio . We show that the pinocchio MAHs are in excellent agreement with those obtained using numerical simulations, while the EPS formalism predicts MAHs that occur too late. pinocchio , which is much less CPU intensive than N -body simulation, can be run on a simple personal computer, and does not require any labour intensive post-simulation analysis, therefore provides a unique and powerful tool to investigate the growth history of dark matter haloes. Using a suite of 55 pinocchio simulations, with 256³ particles each, we study the MAHs of 12 924 cold dark matter (CDM) haloes in a ΛCDM concordance cosmology. This is by far the largest set of haloes used for any such analysis. For each MAH we derive four different formation redshifts, which characterize different epochs during the assembly history of a dark matter halo. We show that haloes less massive than the characteristic non-linear mass scale establish their potential wells much before they acquire most of their mass. The time when a halo reaches its maximum virial velocity roughly divides its mass assembly into two phases, a fast-accretion phase which is dominated by major mergers, and a slow-accretion phase dominated by minor mergers. Each halo experiences about 3 ± 2 major mergers since its main progenitor had a mass equal to 1 per cent of the final halo mass. This major merger statistic is found to be virtually independent of halo mass. However, the average redshift at which these major mergers occur is strongly mass dependent, with more massive haloes experiencing their major mergers later.     

Semi-analytic modelling of galaxy formation: the local Universe

Using semi-analytic models of galaxy formation, we investigate galaxy properties such as the Tully–Fisher relation, the B - and K -band LFs, cold gas contents, sizes, metallicities and colours, and compare our results with observations of local galaxies. We investigate several different recipes for star formation and supernova feedback, including choices that are similar to the treatment by Kauffmann, White & Guiderdoni and Cole et al., as well as some new recipes. We obtain good agreement with all of the key local observations mentioned above. In particular, in our best models, we simultaneously produce good agreement with both the observed B - and K -band LFs and the I -band Tully–Fisher relation. Improved cooling and supernova feedback modelling, inclusion of dust extinction and an improved Press–Schechter model all contribute to this success. We present results for several variants of the CDM family of cosmologies, and find that models with values of Ω₀≃0.3–0.5 give the best agreement with observations.     

The clustering of barred galaxies in the local Universe

We study the clustering properties of barred galaxies using data from the Sloan Digital Sky Survey. We compute projected redshift-space two-point cross-correlation functions   w _p( r _p)  for a sample of nearly 1000 galaxies for which we have performed detailed structural decompositions using the methods described in Gadotti. The sample includes 286 barred galaxies. The clustering of barred and unbarred galaxies of similar stellar mass is indistinguishable over all the scales probed (∼20 kpc–30 Mpc). This result also holds even if the sample is restricted to bars with bluer   g − i   colours (and hence younger ages). Our result also does not change if we split our sample of barred galaxies according to bar-to-total luminosity ratio, bar boxyness, effective surface brightness, length or the shape of the surface density profile within the bar. There is a hint that red, elliptical bars are more strongly clustered than red and less elliptical bars, on scales  ≳1 Mpc  , although the statistical significance is not high. We conclude that there is no significant evidence that bars are a product of mergers or interactions. We tentatively interpret the stronger clustering of the more elliptical bars as evidence that they are located in older galaxies, which reside in more massive haloes.     

Evaluating approximations for halo merging histories

We study the merging history of dark matter haloes in N -body simulations and semi-analytical 'merger trees' based on the extended Press–Schechter (EPS) formalism. The main focus of our study is the joint distribution of progenitor number and mass as a function of redshift and parent halo mass. We begin by investigating the mean quantities predicted directly by the Press–Schechter (PS) and EPS formalism, such as the halo mass and conditional mass functions, and compare these predictions with the results of the simulations. The higher moments of this distribution are not predicted by the EPS formalism alone and must be obtained from the merger trees. We find that the Press–Schechter model deviates from the simulations at the level of 30–50 per cent on certain mass scales, and that the sense of the discrepancy changes as a function of redshift. We show that this discrepancy is reflected in the higher moments of the distribution of progenitor mass and number. We investigate some related statistics such as the accretion rate and the mass ratio of the largest two progenitors. For galaxy sized haloes ( M ∼10¹² M_⊙), we find that the merging history of haloes, as represented by these statistics, is well reproduced in the merger trees compared with the simulations. The agreement deteriorates for larger mass haloes. We conclude that merger trees based on the extended Press–Schechter formalism provide a reasonably reliable framework for semi-analytical models of galaxy formation.     

On the distribution of haloes, galaxies and mass

The stochasticity in the distribution of dark haloes in the cosmic density field is reflected in the distribution function   P _V ( N _h| δ _m)  , which gives the probability of finding N _h haloes in a volume V with mass density contrast δ _m. We study the properties of this function using high-resolution N -body simulations, and find that   P _V ( N _h| δ _m)  is significantly non-Poisson. The ratio between the variance and the mean goes from ∼1 (Poisson) at  1+ δ _m≪1  to <1 (sub-Poisson) at  1+ δ _m∼1  to >1 (super-Poisson) at  1+ δ _m≫1  . The mean bias relation is found to be well described by halo bias models based on the Press–Schechter formalism. The sub-Poisson variance can be explained as a result of halo exclusion, while the super-Poisson variance at high δ _m may be explained as a result of halo clustering. A simple phenomenological model is proposed to describe the behaviour of the variance as a function of δ _m. Galaxy distribution in the cosmic density field predicted by semi-analytic models of galaxy formation shows similar stochastic behaviour. We discuss the implications of the stochasticity in halo bias to the modelling of higher order moments of dark haloes and of galaxies.