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 first galaxies: assembly, cooling and the onset of turbulence

We investigate the properties of the first galaxies at   z ≳ 10  with highly resolved numerical simulations, starting from cosmological initial conditions and taking into account all relevant primordial chemistry and cooling. A first galaxy is characterized by the onset of atomic hydrogen cooling, once the virial temperature exceeds  ≃10⁴ K  , and its ability to retain photoheated gas. We follow the complex accretion and star formation history of a  ≃5 × 10⁷ M_⊙  system by means of a detailed merger tree and derive an upper limit on the number of Population III (Pop III) stars formed prior to its assembly. We investigate the thermal and chemical evolution of infalling gas and find that partial ionization at temperatures  ≳10⁴ K  catalyses the formation of  H₂  and hydrogen deuteride, allowing the gas to cool to the temperature of the cosmic microwave background. Depending on the strength of radiative and chemical feedback, primordial star formation might be dominated by intermediate-mass Pop III stars formed during the assembly of the first galaxies. Accretion on to the nascent galaxy begins with hot accretion, where gas is accreted directly from the intergalactic medium and shock heated to the virial temperature, but is quickly accompanied by a phase of cold accretion, where the gas cools in filaments before flowing into the parent halo with high velocities. The latter drives supersonic turbulence at the centre of the galaxy and could lead to very efficient chemical mixing. The onset of turbulence in the first galaxies thus likely marks the transition to Pop II star formation.     

The first generation of stars in the Λ cold dark matter cosmology

We have performed a large set of high-resolution cosmological simulations using smoothed particle hydrodynamics to study the formation of the first luminous objects in the Lambda cold dark matter cosmology. We follow the collapse of primordial gas clouds in eight early structures and document the scatter in the properties of the first star-forming clouds. Our first objects span formation redshifts from   z ∼ 10  to ∼50 and cover an order of magnitude in halo mass. We find that the physical properties of the central star-forming clouds are very similar in all of the simulated objects despite significant differences in formation redshift and environment. This suggests that the formation path of the first stars is largely independent of the collapse redshift; the physical properties of the clouds have little correlation with spin, mass or assembly history of the host halo. The collapse of protostellar objects at higher redshifts progresses much more rapidly due to the higher densities, which accelerates the formation of molecular hydrogen, enhances initial cooling and shortens the dynamical time-scales. The mass of the star-forming clouds cover a broad range, from a few hundred to a few thousand solar masses, and exhibit various morphologies: some have disc-like structures which are nearly rotational supported; others form flattened spheroids; still others form bars. All of them develop a single protostellar 'seed' which does not fragment into multiple objects up to the moment that the central gas becomes optically thick to H₂ cooling lines. At this time, the instantaneous mass accretion rate on to the centre varies significantly from object to object, with disc-like structures having the smallest mass accretion rates. The formation epoch and properties of the star-forming clouds are sensitive to the values of cosmological parameters.     

On the first generation of stars

We argue that the first stars may have spanned the conventional mass range rather than be identified with the very massive objects  (∼100–10³ M_⊙)  favoured by numerical simulations. Specifically, we find that magnetic field generation processes acting in the first protostellar systems suffice to produce fields that exceed the threshold for magneto-rotational instability (MRI) to operate, and thereby allow the MRI dynamo to generate equipartition-amplitude magnetic fields on protostellar mass scales below  ∼50 M_⊙  . Such fields allow primordial star formation to occur at essentially any metallicity by regulating angular momentum transfer, fragmentation, accretion and feedback in much the same way as occurs in conventional molecular clouds.     

Angular momentum and clustering properties of early dark matter haloes

In this paper, we study the angular momentum properties of simulated dark matter haloes at high redshifts that likely host the first stars in the Universe. Calculating the spin distributions of these  10⁶– 10⁷ M_⊙  haloes in redshift slices from   z = 15  to 6, we find that they are well fit by a lognormal distribution as is found for lower redshift and more massive haloes in earlier work. We find that both the mean value of the spin and dispersion are largely unchanged with redshift for all haloes. Our key result is that subsamples of low- and high-spin, 10⁶ and  10⁷ M_⊙  , haloes show difference in clustering strength. In both mass bins, higher spin haloes are more strongly clustered in concordance with a tidal torquing picture for the growth of angular momentum in dark matter haloes in the cold dark matter paradigm.     

Understanding the redshift evolution of the luminosity functions of Lyman α emitters

We present a semi-analytical model of star formation which explains simultaneously the observed ultraviolet (UV) luminosity function (LF) of high-redshift Lyman break galaxies (LBGs) and LFs of Lyman α emitters. We consider both models that use the Press–Schechter (PS) and Sheth–Tormen (ST) halo mass functions to calculate the abundances of dark matter haloes. The Lyman α LFs at   z ≲ 4  are well reproduced with only ≲10 per cent of the LBGs emitting Lyman α lines with rest equivalent width greater than the limiting equivalent width of the narrow band surveys. However, the observed LF at   z > 5  can be reproduced only when we assume that nearly all LBGs are Lyman α emitters. Thus, it appears that  4 < z < 5  marks the epoch when a clear change occurs in the physical properties of the high-redshift galaxies. As Lyman α escape depends on dust and gas kinematics of the interstellar medium (ISM), this could mean that on an average the ISM at   z > 5  could be less dusty, more clumpy and having more complex velocity field. All of these will enable easier escape of the Lyman α photons. At   z > 5  , the observed Lyman α LF are well reproduced with the evolution in the halo mass function along with very minor evolution in the physical properties of high-redshift galaxies. In particular, up to   z = 6.5  , we do not see the effect of evolving intergalactic medium opacity on the Lyman α escape from these galaxies.     

Reconstruction of the early Universe as a convex optimization problem

We show that the deterministic past history of the Universe can be uniquely reconstructed from knowledge of the present mass density field, the latter being inferred from the three-dimensional distribution of luminous matter, assumed to be tracing the distribution of dark matter up to a known bias. Reconstruction ceases to be unique below those scales – a few Mpc – where multistreaming becomes significant. Above 6 h ⁻¹ Mpc we propose and implement an effective Monge–Ampère–Kantorovich method of unique reconstruction. At such scales the Zel'dovich approximation is well satisfied and reconstruction becomes an instance of optimal mass transportation, a problem which goes back to Monge. After discretization into N point masses one obtains an assignment problem that can be handled by effective algorithms with not more than O ( N ³) time complexity and reasonable CPU time requirements. Testing against N -body cosmological simulations gives over 60 per cent of exactly reconstructed points.
We apply several interrelated tools from optimization theory that were not used in cosmological reconstruction before, such as the Monge–Ampère equation, its relation to the mass transportation problem, the Kantorovich duality and the auction algorithm for optimal assignment. A self-contained discussion of relevant notions and techniques is provided.     

The fragmentation of pre-enriched primordial objects

Recent theoretical investigations have suggested that the formation of the very first stars, forming out of metal-free gas, was fundamentally different from the present-day case. The question then arises which effect was responsible for this transition in the star formation properties. In this paper, we study the effect of metallicity on the evolution of the gas in a collapsing dark matter mini-halo. We model such a system as an isolated 3 σ peak of mass     that collapses at     , using smoothed particle hydrodynamics. The gas has a supposed level of pre-enrichment of either     or 10⁻³ Z_⊙. We assume that H₂ has been radiatively destroyed by the presence of a soft UV background. Metals therefore provide the only viable cooling at temperatures below 10⁴ K. We find that the evolution proceeds very differently for the two cases. The gas in the lower metallicity simulation fails to undergo continued collapse and fragmentation, whereas the gas in the higher metallicity case dissipatively settles into the centre of the dark matter halo. The central gas, characterized by densities     , and a temperature,     , that closely follows that of the cosmic microwave background, is gravitationally unstable and undergoes vigorous fragmentation. We discuss the physical reason for the existence of a critical metallicity,     , and its possible dependence on redshift. Compared with the pure H/He case, the fragmentation of the     gas leads to a larger relative number of low-mass clumps.     

Gamma-ray bursts from stellar remnants: probing the Universe at high redshift

A gamma-ray burst (GRB) releases an amount of energy similar to that of a supernova explosion, which combined with its rapid variability suggests an origin related to neutron stars or black holes. Since these compact stellar remnants form from the most massive stars not long after their birth, GRBs should trace the star formation rate in the Universe; we show that the GRB flux distribution is consistent with this. Because of the strong evolution of the star formation rate with redshift, it follows that the dimmest known bursts have z  ∼ 6, much above the value usually quoted and beyond the most distant quasars. This explains the absence of bright galaxies in well-studied GRB error boxes. The increased distances imply a peak luminosity of 8.3 × 10⁵¹ erg s⁻¹ and a rate density of 0.025 per million years per galaxy. These values are 20 times higher and 150 times lower, respectively, than are implied by fits with non-evolving GRB rates. This means either that GRBs are caused by a much rarer phenomenon than mergers of binary neutron stars, or that their gamma-ray emission is often invisible to us due to beaming. Precise burst locations from optical transients will discriminate between the various models for GRBs from stellar deaths, because the distance between progenitor birth place and burst varies greatly among them. The dimmest GRBs are then the most distant known objects, and may probe the Universe at an age when the first stars were forming.