Paul C. Clark

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.

MODELING COLLAPSE AND ACCRETION IN TURBULENT GAS CLOUDS: IMPLEMENTATION AND COMPARISON OF SINK PARTICLES IN AMR AND SPH

Star formation is such a complex process that accurate numerical tools are needed to quantitatively examine the mass distribution and accretion of fragments in collapsing, turbulent, magnetized gas clouds. To enable a numerical treatment of this regime, we implemented sink particles in the adaptive mesh refinement (AMR) hydrodynamics code FLASH. Sink particles are created in regions of local gravitational collapse, and their trajectories and accretion can be followed over many dynamical times. We perform a series of tests including the time integration of circular and elliptical orbits, the collapse of a Bonnor-Ebert sphere, and a rotating, fragmenting cloud core. We compare the collapse of a highly unstable singular isothermal sphere to the theory by Shu and show that the sink particle accretion rate is in excellent agreement with the theoretical prediction. To model eccentric orbits and close encounters of sink particles accurately, we show that a very small time step is often required, for which we implemented subcycling of the N-body system. We emphasize that a sole density threshold for sink particle creation is insufficient in supersonic flows, if the density threshold is below the opacity limit. In that case, the density can exceed the threshold in strong shocks that do not necessarily lead to local collapse. Additional checks for bound state, gravitational potential minimum, Jeans instability, and converging flows are absolutely necessary for meaningful creation of sink particles. We apply our new sink particle module for FLASH to the formation of a stellar cluster, and compare to a smoothed particle hydrodynamics (SPH) code with sink particles. Our comparison shows encouraging agreement of gas properties, indicated by column density distributions and radial profiles, and of sink particle formation times and positions. We find excellent agreement in the number of sink particles formed, and in their accretion and mass distributions.

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.

Gravitational fragmentation in turbulent primordial gas and the initial mass function of population III stars

We report results from numerical simulations of star formation in the early universe that focus on the dynamical behavior of metal-free gas under different initial and environmental conditions. In particular we investigate the role of turbulence, which is thought to ubiquitously accompany the collapse of high-redshift halos. We distinguish between two main cases: the birth of Population III.1 stars—those which form in the pristine halos unaffected by prior star formation—and the formation of Population III.2 stars—those forming in halos where the gas has an increased ionization fraction. We find that turbulent primordial gas is highly susceptible to fragmentation in both cases, even for turbulence in the subsonic regime, i.e., for rms velocity dispersions as low as 20% of the sound speed. Fragmentation is more vigorous and more widespread in pristine halos compared to pre-ionized ones. If such levels of turbulent motions were indeed present in star-forming minihalos, Population III.1 stars would be on average of somewhat lower mass, and form in larger groups, than Population III.2 stars. We find that fragment masses cover over two orders of magnitude, suggesting that the Population III initial mass function may have been much broader than previously thought. This prompts the need for a large, high-resolution study of the formation of dark matter minihalos that is capable of resolving the turbulent flows in the gas at the moment when the baryons become self-gravitating. This would help to determine the applicability of our results to primordial star formation.

The First Stellar Cluster

We report results from numerical simulations of star formation in the early universe that focus on gas at very high densities and very low metallicities. We argue that the gas in the central regions of protogalactic halos will fragment as long as it carries sufficient angular momentum. Rotation leads to the build-up of massive disklike structures which fragment to form protostars. At metallicities Z ≈ 10−5 Z☉, dust cooling becomes effective and leads to a sudden drop of temperature at densities above n = 1012 cm−3. This induces vigorous fragmentation, leading to a very densely packed cluster of low-mass stars. This is the first stellar cluster. The mass function of stars peaks below 1 M☉, similar to what is found in the solar neighborhood and comparable to the masses of the very low metallicity subgiant stars recently discovered in the halo of our Milky Way. We find that even purely primordial gas can fragment at densities 1014 cm −3 ≤ n≤ 1016 cm −3, although the resulting mass function contains only a few objects (at least a factor of 10 fewer than the Z = 10−5 Z☉ mass function) and is biased toward higher masses. A similar result is found for gas with Z = 10−6 Z☉. Gas with Z ≤ 10−6 Z☉ behaves roughly isothermally at these densities (with polytropic exponent γ ≈ 1.06), and the massive disklike structures that form due to angular momentum conservation will be marginally unstable. As fragmentation is less efficient, we expect stars with Z ≤ 10−6 Z☉ to be massive, with masses in excess of several tens of solar masses, consistent with the results from previous studies.

Is molecular gas necessary for star formation

On galactic scales, the surface density of star formation appears to be well correlated with the surface density of molecular gas. This has led many authors to suggest that there exists a causal relationship between the chemical state of the gas and its ability to form stars – in other words, the assumption that the gas must be molecular before star formation can occur. We test this hypothesis by modelling star formation within a dense cloud of gas with properties similar to a small molecular cloud using a series of different models of the chemistry, ranging from one in which the formation of molecules is not followed and the gas is assumed to remain atomic throughout, to one that tracks the formation of both H2 and CO. We find that the presence of molecules in the gas has little effect on the ability of the gas to form stars: star formation can occur just as easily in atomic gas as in molecular gas. At low densities (<104 cm−3), the gas is able to cool via C+ fine-structure emission almost as efficiently as via CO rotational line emission, while at higher densities, the main cooling process involves the transfer of energy from gas to dust, meaning that the presence of molecules is again unimportant. Cooling by H2 is particularly inefficient, accounting for as little as 1 per cent of the overall cooling in the cloud. Rather than the chemical makeup, we find that the most important factor controlling the rate of star formation is the ability of the gas to shield itself from the interstellar radiation field. As this is also a prerequisite for the survival of molecules within the gas, our results support a picture in which molecule formation and the formation of cold gas are both correlated with the column density of the cloud – and thus its ability to shield itself – rather than being directly correlated with each other.

Gravitational fragmentation and the formation of brown dwarfs in stellar clusters

We investigate the formation of brown dwarfs and very low mass stars through the gravitational fragmentation of infalling gas into stellar clusters. The gravitational potential of a forming stellar cluster provides the focus that attracts gas from the surrounding molecular cloud. Structures present in the gas grow, forming filaments flowing into the cluster centre. These filaments attain high gas densities due to the combination of the cluster potential and local self-gravity. The resultant Jeans masses are low, allowing the formation of very low mass fragments. The tidal shear and high-velocity dispersion present in the cluster preclude any subsequent accretion, thus resulting in the formation of brown dwarfs or very low mass stars. Ejections are not required as the brown dwarfs enter the cluster with high relative velocities, suggesting that their disc and binary properties should be similar to that of low-mass stars. This mechanism requires the presence of a strong gravitational potential due to the stellar cluster implying that brown-dwarf formation should be more frequent in stellar clusters than in distributed populations of young stars. Brown dwarfs formed in isolation would require another formation mechanism such as due to turbulent fragmentation.

The SILCC (SImulating the LifeCycle of molecular Clouds) project – I. Chemical evolution of the supernova-driven ISM

The SILCC (SImulating the Life-Cycle of molecular Clouds) project aims to self-consistently understand the small-scale structure of the interstellar medium (ISM) and its link to galaxy evolution. We simulate the evolution of the multiphase ISM in a (500 pc)2 × ±5 kpc region of a galactic disc, with a gas surface density of ΣGAS=10M⊙pc−2. The flash 4 simulations include an external potential, self-gravity, magnetic fields, heating and radiative cooling, time-dependent chemistry of H2 and CO considering (self-) shielding, and supernova (SN) feedback but omit shear due to galactic rotation. We explore SN explosions at different rates in high-density regions (peak), in random locations with a Gaussian distribution in the vertical direction (random), in a combination of both (mixed), or clustered in space and time (clus/clus2). Only models with self-gravity and a significant fraction of SNe that explode in low-density gas are in agreement with observations. Without self-gravity and in models with peak driving the formation of H2 is strongly suppressed. For decreasing SN rates, the H2 mass fraction increases significantly from <10 per cent for high SN rates, i.e. 0.5 dex above Kennicutt–Schmidt, to 70–85 per cent for low SN rates, i.e. 0.5 dex below KS. For an intermediate SN rate, clustered driving results in slightly more H2 than random driving due to the more coherent compression of the gas in larger bubbles. Magnetic fields have little impact on the final disc structure but affect the dense gas (n ≳ 10 cm−3) and delay H2 formation. Most of the volume is filled with hot gas (∼80 per cent within ±150 pc). For all but peak driving a vertically expanding warm component of atomic hydrogen indicates a fountain flow. We highlight that individual chemical species populate different ISM phases and cannot be accurately modelled with temperature-/density-based phase cut-offs.

On the initial mass function of low-metallicity stars: the importance of dust cooling

The first stars to form in the universe are believed to have distribution of masses biased toward massive stars. This contrasts with the present-day initial mass function, which has a predominance of stars with masses lower than 1 M ☉. Therefore, the mode of star formation must have changed as the universe evolved. Such a transition is attributed to a more efficient cooling provided by increasing metallicity. Especially dust cooling can overcome the compressional heating, which lowers the gas temperature thus increasing its instability to fragmentation. The purpose of this paper is to verify if dust cooling can efficiently cool the gas, and enhance the fragmentation of gas clouds at the early stages of the universe. To confirm that, we calculate a set of hydrodynamic simulations that include sink particles, which represent contracting protostars. The thermal evolution of the gas during the collapse is followed by making use of a primordial chemical network and also a recipe for dust cooling. We model four clouds with different amounts of metals (10–4, 10–5, 10–6 Z ☉, and 0), and analyze how this property affect the fragmentation of star-forming clouds. We find evidence for fragmentation in all four cases, and hence conclude that there is no critical metallicity below which fragmentation is impossible. Nevertheless, there is a clear change in the behavior of the clouds at Z <~ 10–5 Z ☉, caused by the fact that at this metallicity, fragmentation takes longer to occur than accretion, leading to a flat mass function at lower metallicities.

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.