Volker Bromm

The Formation of the First Stars. I. The Primordial Star-forming Cloud

To constrain the nature of the very first stars, we investigate the collapse and fragmentation of primordial, metal-free gas clouds. We explore the physics of primordial star formation by means of three-dimensional simulations of the dark matter and gas components, using smoothed particle hydrodynamics, under a wide range of initial conditions, including the initial spin, the total mass of the halo, the redshift of virialization, the power spectrum of the DM fluctuations, the presence of HD cooling, and the number of particles employed in the simulation. We find characteristic values for the temperature, T ~ a few 100 K, and the density, n ~ 103-104 cm-3, characterizing the gas at the end of the initial free-fall phase. These values are rather insensitive to the initial conditions. The corresponding Jeans mass is MJ ~ 103 M?. The existence of these characteristic values has a robust explanation in the microphysics of H2 cooling, connected to the minimum temperature that can be reached with the H2 coolant, and to the critical density at which the transition takes place between levels being populated according to non-LTE (NLTE), and according to LTE. In all cases, the gas dissipatively settles into an irregular, central configuration that has a filamentary and knotty appearance. The fluid regions with the highest densities are the first to undergo runaway collapse due to gravitational instability, and to form clumps with initial masses ~103 M?, close to the characteristic Jeans scale. These results suggest that the first stars might have been quite massive, possibly even very massive with M* 100 M?. After a gas element has undergone runaway collapse, and has reached densities in excess of 108 cm-3, a sink particle is created. This procedure allows us to follow the evolution of the overall system beyond the point where the first nonlinear region would otherwise force the calculation to a halt. These later evolutionary stages, during which the clumps grow in mass due to accretion and merging with other clumps, are quite sensitive to the initial conditions. The key process in building up very massive clumps, with masses up to a few times 104 M?, is merging between clumps. Since the merging rate sensitively depends on the density of the gas, halos with the highest degree of central concentration are able to assemble the most massive clumps. Among these are halos with a low spin (? 0.01), and with DM fluctuations imprinted according to a white-noise spectrum.

The First stars

▪ Abstract We review recent theoretical results on the formation of the first stars in the universe, and emphasize related open questions. In particular, we discuss the initial conditions for Population III star formation, as given by variants of the cold dark matter cosmology. Numerical simulations have investigated the collapse and the fragmentation of metal-free gas, showing that the first stars were predominantly very massive. The exact determination of the stellar masses, and the precise form of the primordial initial mass function, is still hampered by our limited understanding of the accretion physics and the protostellar feedback effects. We address the importance of heavy elements in bringing about the transition from an early star formation mode dominated by massive stars to the familiar mode dominated by low-mass stars at later times. We show how complementary observations, both at high redshifts and in our local cosmic neighborhood, can be utilized to probe the first epoch of star formation.

The formation of a star cluster: predicting the properties of stars and brown dwarfs

We present results from the largest numerical simulation of star formation to resolve the fragmentation process down to the opacity limit. The simulation follows the collapse and fragmentation of a large-scale turbulent molecular cloud to form a stellar cluster and, simultaneously, the formation of circumstellar discs and binary stars. This large range of scales enables us to predict a wide variety of stellar properties for comparison with observations. The calculation clearly demonstrates that star formation is a highly-dynamic and chaotic process. Star formation occurs in localized bursts within the cloud via the fragmentation both of dense molecular cloud cores and of massive circumstellar discs. Star-disc encounters form binaries and truncate discs. Stellar encounters disrupt bound multiple systems. We find that the observed statistical properties of stars are a natural consequence of star formation in such a dynamical environment. The cloud produces roughly equal numbers of stars and brown dwarfs, with masses down to the opacity limit for fragmentation (5 Jupiter masses). The initial mass function is consistent with a Salpeter slope (Γ = -1.35) above 0.5 M O ., a roughly flat distribution (r = 0) in the range 0.006-0.5 M O ., and a sharp cut-off below 0.005 M O .. This is consistent with recent observational surveys. The brown dwarfs form by the dynamical ejection of low-mass fragments from dynamically unstable multiple systems before the fragments have been able to accrete to stellar masses. Close binary systems (with separations ≤10 au) are not formed by fragmentation in situ. Rather, they are produced by hardening of initially wider multiple systems through a combination of dynamical encounters, gas accretion, and/or the interaction with circumbinary and circumtriple discs. Finally, we find that the majority of circumstellar discs have radii less than 20 au due to truncation in dynamical encounters. This is consistent with observations of the Orion Trapezium cluster and implies that most stars and brown dwarfs do not form large planetary systems.

FORMATION OF THE FIRST SUPERMASSIVE BLACK HOLES

We consider the physical conditions under which supermassive black holes could have formed inside the first galaxies. Our smoothed particle hydrodynamics simulations indicate that metal-free galaxies with a virial temperature of ~104 K and suppressed H2 formation (due to an intergalactic UV background) tend to form a binary black hole system that contains a substantial fraction (10%) of the total baryonic mass of the host galaxy. Fragmentation into stars is suppressed without substantial H2 cooling. Our simulations follow the condensation of ~5 × 106 M☉ around the two centers of the binary down to a scale of 0.1 pc. Low-spin galaxies form a single black hole instead. These early black holes lead to quasar activity before the epoch of reionization. Primordial black hole binaries lead to gravitational radiation emission at redshifts z 10 that would be detectable by Laser Interferometer Space Antenna.

FORMING THE FIRST STARS IN THE UNIVERSE: THE FRAGMENTATION OF PRIMORDIAL GAS

In order to constrain the initial mass function of the first generation of stars (Population III), we investigate the fragmentation properties of metal-free gas in the context of a hierarchical model of structure formation. We investigate the evolution of an isolated 3 sigma peak of mass 2x106 M middle dot in circle that collapses at zcoll approximately 30 using smoothed particle hydrodynamics. We find that the gas dissipatively settles into a rotationally supported disk that has a very filamentary morphology. The gas in these filaments is Jeans unstable with MJ approximately 103 M middle dot in circle. Fragmentation leads to the formation of high-density (n>108 cm-3) clumps that subsequently grow in mass by accreting the surrounding gas and by merging with other clumps up to masses of approximately 104 M middle dot in circle. This suggests that the very first stars were rather massive. We explore the complex dynamics of the merging and tidal disruption of these clumps by following their evolution over a few dynamical times.

Generic Spectrum and Ionization Efficiency of a Heavy Initial Mass Function for the First Stars

We calculate the generic spectral signature of an early population of massive stars at high redshifts. For metal-free stars with mass above 300 M☉, we find that the combined spectral luminosity per unit stellar mass is almost independent of the mass distribution of these stars. To zeroth order, the generic spectrum resembles a blackbody with an effective temperature of ~105 K, making these stars highly efficient at ionizing hydrogen and helium. The production rate of ionizing radiation per stellar mass by stars more massive than ~300 M☉ is larger by ~1 order of magnitude for hydrogen and He I and by ~2 orders of magnitude for He II than the emission from a standard initial mass function. This would result in unusually strong hydrogen and helium recombination lines from the surrounding interstellar medium. It could also alleviate the current difficulty of ionizing the intergalactic medium at z 6 with the cosmic star formation rate inferred at somewhat lower redshifts.

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 formation of the first low-mass stars from gas with low carbon and oxygen abundances

The first stars in the Universe are predicted to have been much more massive than the Sun. Gravitational condensation, accompanied by cooling of the primordial gas via molecular hydrogen, yields a minimum fragmentation scale of a few hundred solar masses. Numerical simulations indicate that once a gas clump acquires this mass it undergoes a slow, quasi-hydrostatic contraction without further fragmentation; lower-mass stars cannot form. Here we show that as soon as the primordial gas—left over from the Big Bang—is enriched by elements ejected from supernovae to a carbon or oxygen abundance as small as ∼0.01–0.1 per cent of that found in the Sun, cooling by singly ionized carbon or neutral oxygen can lead to the formation of low-mass stars by allowing cloud fragmentation to smaller clumps. This mechanism naturally accommodates the recent discovery of solar-mass stars with unusually low iron abundances (10-5.3 solar) but with relatively high (10-1.3 solar) carbon abundance. The critical abundances that we derive can be used to identify those metal-poor stars in our Galaxy with elemental patterns imprinted by the first supernovae. We also find that the minimum stellar mass at early epochs is partially regulated by the temperature of the cosmic microwave background.

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.