Thomas H. Greif

Simulations on a moving mesh: the clustered formation of population III protostars

The cosmic dark ages ended a few hundred million years after the big bang, when the first stars began to fill the universe with new light. It has generally been argued that these stars formed in isolation and were extremely massive—perhaps 100 times as massive as the Sun. In a recent study, Clark and collaborators showed that this picture requires revision. They demonstrated that the accretion disks that build up around Population III stars are strongly susceptible to fragmentation and that the first stars should therefore form in clusters rather than in isolation. We here use a series of high-resolution hydrodynamical simulations performed with the moving mesh code AREPO to follow up on this proposal and to study the influence of environmental parameters on the level of fragmentation. We model the collapse of five independent minihalos from cosmological initial conditions, through the runaway condensation of their central gas clouds, to the formation of the first protostar, and beyond for a further 1000 years. During this latter accretion phase, we represent the optically thick regions of protostars by sink particles. Gas accumulates rapidly in the circumstellar disk around the first protostar, fragmenting vigorously to produce a small group of protostars. After an initial burst, gravitational instability recurs periodically, forming additional protostars with masses ranging from ~0.1 to 10 M ☉. Although the shape, multiplicity, and normalization of the protostellar mass function depend on the details of the sink-particle algorithm, fragmentation into protostars with diverse masses occurs in all cases, confirming earlier reports of Population III stars forming in clusters. Depending on the efficiency of later accretion and merging, Population III stars may enter the main sequence in clusters and with much more diverse masses than are commonly assumed.

The first stars: formation of binaries and small multiple systems

We investigate the formation of metal-free, Population III (Pop III), stars within a minihalo at z ≃ 20 with a smoothed particle hydrodynamics (SPH) simulation, starting from cosmological initial conditions. Employing a hierarchical, zoom-in procedure, we achieve sufficient numerical resolution to follow the collapsing gas in the centre of the minihalo up to number densities of 10 12 cm -3 . This allows us to study the protostellar accretion on to the initial hydrostatic core, which we represent as a growing sink particle, in improved physical detail. The accretion process, and in particular its termination, governs the final masses that were reached by the first stars. The primordial initial mass function, in turn, played an important role in determining to what extent the first stars drove early cosmic evolution. We continue our simulation for 5000 yr after the first sink particle has formed. During this time period, a disc-like configuration is assembled around the first protostar. The disc is gravitationally unstable, develops a pronounced spiral structure and fragments into several other protostellar seeds. At the end of the simulation, a small multiple system has formed, dominated by a binary with masses ∼40 and ∼10 M ⊙ . If Pop III stars were to form typically in binaries or small multiples, the standard model of primordial star formation, where single, isolated stars are predicted to form in minihaloes, would have to be modified. This would have crucial consequences for the observational signature of the first stars, such as their nucleosynthetic pattern, and the gravitational wave emission from possible Pop III black hole binaries.

The Formation and Fragmentation of Disks Around Primordial Protostars

Numerical simulations show that disks around the first stars in the universe were gravitationally unstable and fragmented. The very first stars to form in the universe heralded an end to the cosmic dark ages and introduced new physical processes that shaped early cosmic evolution. Until now, it was thought that these stars lived short, solitary lives, with only one extremely massive star, or possibly a very wide binary system, forming in each dark-matter minihalo. Here we describe numerical simulations that show that these stars were, to the contrary, often members of tight multiple systems. Our results show that the disks that formed around the first young stars were unstable to gravitational fragmentation, possibly producing small binary and higher-order systems that had separations as small as the distance between Earth and the Sun.

The First Stars: Mass Growth Under Protostellar Feedback

We perform three-dimensional cosmological simulations to examine the growth of metal-free, Population III (Pop III) stars under radiative feedback. We begin our simulation at z = 100 and trace the evolution of gas and dark matter until the formation of the first minihalo. We then follow the collapse of the gas within the minihalo up to densities of n = 10 12 cm −3 , at which point we replace the high-density particles with a sink particle to represent the growing protostar. We model the effect of Lyman-Werner (LW) radiation emitted by the protostar, and employ a ray-tracing scheme to follow the growth of the surrounding H ii region over the next 5000 yr. We find that a disk assembles around the first protostar, and that radiative feedback will not prevent further fragmentation of the disk to form multiple Pop III stars. Ionization of neutral hydrogen and photodissociation of H2 by LW radiation leads to heating of the dense gas to several thousand Kelvin, and this warm region expands outward at the gas sound speed. Once the extent of this warm region becomes equivalent to the size of the disk, the disk mass declines while the accretion rate onto the protostars is reduced by an order of magnitude. This occurs when the largest sink has grown to � 20 M⊙ while the second sink has grown to � 7 M⊙, and we estimate the main sink will approach an asymptotic value of 30 M⊙ by the time it reaches the main sequence. Our simulation thus indicates that the most likely outcome is a massive Pop III binary. However, we simulate only one minihalo, and the statistical variation between minihaloes may be substantial. If Pop III stars were typically unable to grow to more than a few tens of solar masses, this would have important consequences for the occurence of pair-instability supernovae in the early Universe as well as the Pop III chemical signature in the oldest stars observable today.

THE FIRST SUPERNOVA EXPLOSIONS : ENERGETICS, FEEDBACK, AND CHEMICAL ENRICHMENT

We perform three-dimensional smoothed particle hydrodynamics simulations in a realistic cosmological setting to investigate the expansion, feedback, and chemical enrichment properties of a 200 M⊙ pair-instability supernova in the high-redshift universe. We find that the SN remnant propagates for a Hubble time at z ≃ 20 to a final mass-weighted mean shock radius of 2.5 kpc (proper), roughly half the size of the H ii region, and in this process sweeps up a total gas mass of 2.5 × 10 5 M⊙. The morphology of the shock becomes highly anisotropic once it leaves the host halo and encounters filaments and neighboring minihalos, while the bulk of the shock propagates into the voids of the intergalactic medium. The SN entirely disrupts the host halo and terminates further star formation for at least 200 Myr, while in our specific case it exerts positive mechanical feedback on neighboring minihalos by shock-compressing their cores. In contrast, we do not observe secondary star formation in the dense shell via gravitational fragmentation, due to the previous photoheating by the progenitor star. We find that cooling by metal lines is unimportant for the entire evolution of the SN remnant, while the metal-enriched, interior bubble expands adiabatically into the cavities created by the shock, and ultimately into the voids with a maximum extent similar to the final mass-weighted mean shock radius. Finally, we conclude that dark matter halos of at least Mvir & 10 8 M⊙ must be assembled to recollect all components of the swept-up gas. Subject headings: cosmology: theory — galaxies: formation — galaxies: high-redshift — H ii regions — hydrodynamics — intergalactic medium — supernovae: general

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?10 4 K, and had typical masses?10M ⊙ . 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.

Local Radiative Feedback in the Formation of the First Protogalaxies

The first galaxies form under the influence of radiative feedback from the first generations of stars. This feedback acts to heat and ionize the gas within the H II regions surrounding the first stars, as well as to photodissociate hydrogen molecules within the larger Lyman-Werner (LW) bubbles that surround these sources. Using a ray-tracing method in three-dimensional cosmological simulations, we self-consistently track the formation of, and radiative feedback from, individual stars in the formation of a protogalaxy. We compute in detail the H II regions of each of these sources, as well as the regions affected by their molecule-dissociating radiation. We follow the thermal, chemical, and dynamical evolution of the primordial gas as it becomes incorporated into the protogalaxy. While the IGM is, in general, optically thick to LW photons only over physical distances of 30 kpc at redshifts z 20, the high molecule fraction that is built up in relic H II regions and their increasing volume-filling factor renders even the local IGM optically thick to LW photons over physical distances of a few kiloparsecs. We find that Population III relic black holes may begin accreting efficiently after ~60 Myr from the time of their formation, when the photo-heated relic H II region gas can cool and recollapse into the 106 M☉ minihalo which hosts the black hole. Population II.5 stars, postulated to have masses of the order of 10 M☉, can also likely form from this recollapsing relic H II region gas. Overall, we find that the local radiative feedback from Population III stars suppresses the star formation rate only slightly.

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 LymanWerner (LW) radiation. We show that the build-up of such a strong LW background is hindered by two effects. Firstly, 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 Tvir > 10 4 K and total mass > 10 8 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 effects of accretion luminosity upon fragmentation in the early universe

We introduce a prescription for the luminosity from accreting protostars into smoothed particle hydrodynamics simulation and apply the method to simulations of five primordial minihaloes generated from cosmological initial conditions. We find that accretion luminosity delays fragmentation within the haloes but does not prevent it. In haloes that slowly form a low number of protostars, the accretion luminosity can reduce the number of fragments that are formed before the protostars start ionizing their surroundings. However, haloes that rapidly form many protostars become dominated by dynamical processes, and the effect of accretion luminosity becomes negligible. Generally, the fragmentation found in the haloes is highly dependent on the initial conditions. Accretion luminosity does not substantially affect the accretion rates experienced by the protostars and is far less important than dynamical interactions, which can lead to ejections that effectively terminate the accretion. We find that the accretion rates on to the inner regions of the discs (20 au) around the protostars are highly variable, in contrast to the constant or smoothly decreasing accretion rates currently used in models of the pre-main-sequence evolution of Population III stars.

Accretion on to black holes formed by direct collapse

One possible scenario for the formation of massive black holes (BHs) in the early Universe is from the direct collapse of primordial gas in atomic-cooling dark matter haloes in which the gas is unable to cool efficiently via molecular transitions. We study the formation of such BHs, as well as the accretion of gas on to these objects and the high energy radiation emitted in the accretion process, by carrying out cosmological radiation hydrodynamic simulations. In the absence of radiative feedback, we find an upper limit to the accretion rate on to the central object which forms from the initial collapse of hot (≲ 10 4 K) gas of the order of 0.1 M ⊙ yr -1 . This is high enough for the formation of a supermassive star, the immediate precursor of a BH, with a mass of the order of 10 5 M ⊙ . Assuming that a fraction of this mass goes into a BH, we track the subsequent accretion of gas on to the BH self-consistently with the high energy radiation emitted from the accretion disc. Using a ray-tracing algorithm to follow the propagation of ionizing radiation, we model in detail the growth and evolution of the H II and He m regions which form around the accreting BH. We find that BHs with masses of the order of 10 4 M ⊙ initially accrete at close to the Eddington limit, but that the accretion rate drops to ~10 -5 M ⊙ yr -1 (of the order I per cent of the Eddington limit) after ~10 6 yr, due to the expansion of the gas near the BH in response to strong photoheating and radiation pressure. One distinctive signature of the accretion of gas on to BHs formed by direct collapse, as opposed to massive Pop III star formation, is an extremely high ratio of the luminosity emitted in He II λ1640 to that emitted in Hα (or Lyα), i.e. L 1640 /L Hα ≥ 2; this nebular emission could be detected by future facilities, such as the James Webb Space Telescope. Finally, we briefly discuss implications for the coevolution of BHs and their host galaxies.