Simon C. O. Glover

The Formation of Supermassive Black Holes in the First Galaxies

We discuss the formation of supermassive black holes in the early universe, and how to probe their subsequent evolution with the upcoming mm/sub‐mm telescope ALMA. We first focus on the chemical and radiative conditions for black hole formation, in particular considering radiation trapping and molecular dissociation effects. We then turn our attention towards the magnetic properties in the halos where the first black holes form, and show that the presence of turbulence may lead to a magnetic dynamo, which could support the black hole formation process by providing an efficient means of transporting the angular momentum. We finally focus on observable properties of high‐redshift black holes with respect to ALMA, and discuss how to distinguish between chemistry driven by the starburst and chemistry driven by X‐rays from the black hole.

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 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.

Modelling CO formation in the turbulent interstellar medium

We present results from high-resolution three-dimensional simulations of turbulent interstellar gas that self-consistently follow its coupled thermal, chemical and dynamical evolution, with a particular focus on the formation and destruction of H 2 and CO. We quantify the formation time-scales for H 2 and CO in physical conditions corresponding to those found in nearby giant molecular clouds, and show that both species form rapidly, with chemical time-scales that are comparable to the dynamical time-scale of the gas. We also investigate the spatial distributions of H 2 and CO, and how they relate to the underlying gas distribution. We show that H 2 is a good tracer of the gas distribution, but that the relationship between CO abundance and gas density is more complex. The CO abundance is not well-correlated with either the gas number density n or the visual extinction Av : both have a large influence on the CO abundance, but the inhomogeneous nature of the density field produced by the turbulence means that n and A v are only poorly correlated. There is a large scatter in A v , and hence CO abundance, for gas with any particular density, and similarly a large scatter in density and CO abundance for gas with any particular visual extinction. This will have important consequences for the interpretation of the CO emission observed from real molecular clouds. Finally, we also examine the temperature structure of the simulated gas. We show that the molecular gas is not isothermal. Most of it has a temperature in the range of 10-20 K, but there is also a significant fraction of warmer gas, located in low-extinction regions where photoelectric heating remains effective.

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.

Simulating the Formation of Molecular Clouds. II. Rapid Formation from Turbulent Initial Conditions

In this paper we present results from a large set of numerical simulations that demonstrate that H2 formation occurs rapidly in turbulent gas. Starting with purely atomic hydrogen, large quantities of molecular hydrogen can be produced on timescales of 1-2 Myr, given turbulent velocity dispersions and magnetic field strengths consistent with observations. Moreover, as our simulations underestimate the effectiveness of H2 self-shielding and dust absorption, we can be confident that the molecular fractions that we compute are strong lower limits on the true values. The formation of large quantities of molecular gas on the timescale required by rapid cloud formation models therefore appears to be entirely plausible. We also investigate the density and temperature distributions of gas in our model clouds. We show that the density probability distribution function is approximately lognormal, with a dispersion that agrees well with the prediction of Padoan and coworkers. The temperature distribution is similar to that of a polytrope, with an effective polytropic index γeff 0.8, although at low gas densities, the scatter of the actual gas temperature around this mean value is considerable, and the polytropic approximation does not capture the full range of behavior of the gas.

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.

On the relationship between molecular hydrogen and carbon monoxide abundances in molecular clouds

The most usual tracer of molecular gas is line emission from CO. However, the reliability of this tracer has long been questioned in environments different from the Milky Way. We study the relationship between H2 and CO abundances using a fully dynamical model of magnetized turbulence coupled to a chemical network simplified to follow only the dominant pathways for H2 and CO formation and destruction, and including photodissociation using a six-ray approximation. We find that the abundance of H2 is primarily determined by the amount of time available for its formation, which is proportional to the product of the density and the metallicity, but insensitive to photodissociation. Photodissociation only becomes important at extinctions under a few tenths of a visual magnitude, in agreement with both observational and prior theoretical work. On the other hand, CO forms quickly, within a dynamical time, but its abundance depends primarily on photodissociation, with only a weak secondary dependence on H2 abundance. As a result, there is a sharp cut-off in CO abundance at mean visual extinctions AV 3. At lower values of AV, we find that the ratio of H2 column density to CO emissivity XCO ∝ A −3.5 V . This explains the discrepancy observed in low metallicity systems between cloud masses derived from CO observations and other techniques such as infrared emission. Our work predicts that CO-bright clouds in low metallicity systems should be systematically larger or denser than Milky Way clouds, or both. Our results further explain the narrow range of observed molecular cloud column densities as a threshold effect, without requiring the assumption of virial equilibrium.

Simulating the Formation of Molecular Clouds. I. Slow Formation by Gravitational Collapse from Static Initial Conditions

We study the formation of H2 in the ISM, using a modified version of the astrophysical magnetohydrodynamical code ZEUS-MP that includes a nonequilibrium treatment of the formation and destruction of H2. We examine two different approximations to treat the shielding of H2 against photodissociation: a local approximation, which gives us a solid lower bound on the amount of shielding, and a method based on ray-tracing that is considerably more accurate in some circumstances but that produces results that are harder to clearly interpret. In both cases, the computational cost of determining H2 photodissociation rates is reduced by enough to make three-dimensional high-resolution simulations of cloud formation feasible with modest computational resources. Our modification to ZEUS-MP also includes a detailed treatment of the thermal behavior of the gas. In this paper, we focus on the problem of molecular cloud formation in gravitationally unstable, initially static gas. (In a subsequent paper, we consider turbulent flow.) We show that in these conditions, and for initial densities consistent with those observed in the cold, neutral atomic phase of the interstellar medium, H2 formation occurs on a timescale t ≥ 10 Myr, comparable to or longer than the gravitational free-fall timescale of the cloud. We also show that the collapsing gas very quickly reaches thermal equilibrium and that the equation of state of the thermal equilibrium gas is generally softer than isothermal. Finally, we demonstrate that although these results show little sensitivity to variations in most of our simulation parameters, they are highly sensitive to the assumed initial density ni. Reducing ni significantly increases the cloud formation timescale and decreases the amount of hydrogen ultimately converted to H2.

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.