Robi Banerjee

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.

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.

A NEW JEANS RESOLUTION CRITERION FOR (M)HD SIMULATIONS OF SELF-GRAVITATING GAS: APPLICATION TO MAGNETIC FIELD AMPLIFICATION BY GRAVITY-DRIVEN TURBULENCE

Cosmic structure formation is characterized by the complex interplay between gravity, turbulence, and magnetic fields. The processes by which gravitational energy is converted into turbulent and magnetic energies, however, remain poorly understood. Here, we show with high-resolution, adaptive-mesh simulations that MHD turbulence is efficiently driven by extracting energy from the gravitational potential during the collapse of a dense gas cloud. Compressible motions generated during the contraction are converted into solenoidal, turbulent motions, leading to a natural energy ratio of E sol/E tot 2/3. We find that the energy injection scale of gravity-driven turbulence is close to the local Jeans scale. If small seeds of the magnetic field are present, they are amplified exponentially fast via the small-scale dynamo process. The magnetic field grows most efficiently on the smallest scales, for which the stretching, twisting, and folding of field lines, and the turbulent vortices are sufficiently resolved. We find that this scale corresponds to about 30 grid cells in the simulations. We thus suggest a new minimum resolution criterion of 30 cells per Jeans length in (magneto)hydrodynamical simulations of self-gravitating gas, in order to resolve turbulence on the Jeans scale, and to capture minimum dynamo amplification of the magnetic field. Due to numerical diffusion, however, any existing simulation today can at best provide lower limits on the physical growth rates. We conclude that a small, initial magnetic field can grow to dynamically important strength on timescales significantly shorter than the free-fall time of the cloud.

H II REGIONS: WITNESSES TO MASSIVE STAR FORMATION

We describe the first three-dimensional simulation of the gravitational collapse of a massive, rotating molecular cloud that includes heating by both non-ionizing and ionizing radiation. These models were performed with the FLASH code, incorporating a hybrid, long characteristic, ray-tracing technique. We find that as the first protostars gain sufficient mass to ionize the accretion flow, their H II regions are initially gravitationally trapped, but soon begin to rapidly fluctuate between trapped and extended states, in agreement with observations. Over time, the same ultracompact H II region can expand anisotropically, contract again, and take on any of the observed morphological classes. In their extended phases, expanding H II regions drive bipolar neutral outflows characteristic of high-mass star formation. The total lifetime of H II regions is given by the global accretion timescale, rather than their short internal sound-crossing time. This explains the observed number statistics. The pressure of the hot, ionized gas does not terminate accretion. Instead, the final stellar mass is set by fragmentation-induced starvation. Local gravitational instabilities in the accretion flow lead to the build-up of a small cluster of stars, all with relatively high masses due to heating from accretion radiation. These companions subsequently compete with the initial high-mass star for the same common gas reservoir and limit its mass growth. This is in contrast to the classical competitive accretion model, where the massive stars are never hindered in growth by the low-mass stars in the cluster. Our findings show that the most significant differences between the formation of low-mass and high-mass stars are all explained as the result of rapid accretion within a dense, gravitationally unstable, ionized flow.

Outflows and Jets from Collapsing Magnetized Cloud Cores

Star formation is usually accompanied by outflow phenomena. There is strong evidence that these outflows and jets are launched from protostellar disks by magnetorotational processes. Here we report on our three-dimensional, adaptive mesh, magnetohydrodynamic simulations of collapsing, rotating, magnetized Bonnor-Ebert spheres, whose properties are taken directly from observations. In contrast to the pure hydro case, in which no outflows are seen, our present simulations show an outflow from the protodisk surface at ~130 AU and a jet at ~0.07 AU after a strong toroidal magnetic field buildup. The large-scale outflow, which extends up to ~600 AU at the end of our simulation, is driven by toroidal magnetic pressure (spring), whereas the jet is powered by magnetocentrifugal force (fling). At the final stage of our simulation these winds are still confined within two respective shock fronts. Furthermore, we find that the jet-wind and the disk-anchored magnetic field extract a considerable amount of angular momentum from the protostellar disk. The initial spin of our cloud core was chosen high enough to produce a binary system. We indeed find a close binary system (separation ~3 R☉), which results from the fragmentation of an earlier formed ring structure. The magnetic field strength in these protostars reaches ~3 kG and becomes about 3 G at 1 AU from the center, in agreement with recent observational results.

THE INTERPLAY OF MAGNETIC FIELDS, FRAGMENTATION, AND IONIZATION FEEDBACK IN HIGH-MASS STAR FORMATION

Massive stars disproportionately influence their surroundings. How they form has only started to become clear recently through radiation gas dynamical simulations. However, until now, no simulation has simultaneously included both magnetic fields and ionizing radiation. Here we present the results from the first radiation-magnetohydrodynamical (RMHD) simulation including ionization feedback, comparing an RMHD model of a 1000 M ☉ rotating cloud to earlier radiation gas dynamical models with the same initial density and velocity distributions. We find that, despite starting with a strongly supercritical mass-to-flux ratio, the magnetic field has three effects. First, the field offers locally support against gravitational collapse in the accretion flow, substantially reducing the amount of secondary fragmentation in comparison to the gas dynamical case. Second, the field drains angular momentum from the collapsing gas, further increasing the amount of material available for accretion by the central, massive, protostar, and thus increasing its final mass by about 50% from the purely gas dynamical case. Third, the field is wound up by the rotation of the flow, driving a tower flow. However, this flow never achieves the strength seen in low-mass star formation simulations for two reasons: gravitational fragmentation disrupts the circular flow in the central regions where the protostars form, and the expanding H II regions tend to further disrupt the field geometry. Therefore, ionizing radiation is likely to dominate outflow dynamics in regions of massive star formation.

Importance of the initial conditions for star formation – I. Cloud evolution and morphology

We present a detailed parameter study of collapsing turbulent cloud cores, varying the initial density profile and the initial turbulent velocity field. We systematically investigate the influence of different initial conditions on the star formation process, mainly focusing on the fragmentation, the number of formed stars and the resulting mass distributions. Our study compares four different density profiles (uniform, Bonnor-Ebert type, ρ ∝ r ―1.5 and ρ ∝ r ―2 ), combined with six different supersonic turbulent velocity fields (compressive, mixed and solenoidal, initialized with two different random seeds each) in three-dimensional simulations using the adaptive-mesh refinement, hydrodynamics code FLASH. The simulations show that density profiles with flat cores produce hundreds of low-mass stars, either distributed throughout the entire cloud or found in subclusters, depending on the initial turbulence. Concentrated density profiles always lead to the formation of one high-mass star in the centre of the cloud and, if at all, low-mass stars surrounding the central one. In uniform and Bonnor-Ebert type density distributions, compressive initial turbulence leads to local collapse about 25 per cent earlier than solenoidal turbulence. However, central collapse in the steep power-law profiles is too fast for the turbulence to have any significant influence. We conclude that (i) the initial density profile and turbulence mainly determine the cloud evolution and the formation of clusters, (ii) the initial mass function (IMF) is not universal for all setups and (iii) that massive stars are much less likely to form in flat density distributions. The IMFs obtained in the uniform and Bonnor-Ebert type density profiles are more consistent with the observed IMF, but shifted to lower masses.

LIMITING ACCRETION ONTO MASSIVE STARS BY FRAGMENTATION-INDUCED STARVATION

Massive stars influence their surroundings through radiation, winds, and supernova explosions far out of proportion to their small numbers. However, the physical processes that initiate and govern the birth of massive stars remain poorly understood. Two widely discussed models are monolithic collapse of molecular cloud cores and competitive accretion. To learn more about massive star formation, we perform and analyze simulations of the collapse of rotating, massive, cloud cores including radiative heating by both non-ionizing and ionizing radiation using the FLASH adaptive-mesh refinement code. These simulations show fragmentation from gravitational instability in the enormously dense accretion flows required to build up massive stars. Secondary stars form rapidly in these flows and accrete mass that would have otherwise been consumed by the massive star in the center, in a process that we term fragmentation-induced starvation. This explains why massive stars are usually found as members of high-order stellar systems that themselves belong to large clusters containing stars of all masses. The radiative heating does not prevent fragmentation, but does lead to a higher Jeans mass, resulting in fewer and more massive stars than would form without the heating. This mechanism reproduces the observed relation between the total stellar mass in the cluster and the mass of the largest star. It predicts strong clumping and filamentary structure in the center of collapsing cores, as has recently been observed. We speculate that a similar mechanism will act during primordial star formation.

Small-scale dynamo action during the formation of the first stars and galaxies. I. The ideal MHD limit

We explore the amplification of magnetic seeds during the formation of the first stars and galaxies. During gravitational collapse, turbulence is created from accretion shocks, which may act to amplify weak magnetic fields in the protostellar cloud. Numerical simulations showed that such turbulence is sub-sonic in the first star-forming minihalos, and highly supersonic in the first galaxies with virial temperatures larger than 10(4) K. We investigate the magnetic field amplification during the collapse both for Kolmogorov and Burgers-type turbulence with a semi-analytic model that incorporates the effects of gravitational compression and small-scale dynamo amplification. We find that the magnetic field may be substantially amplified before the formation of a disk. On scales of 1/10 of the Jeans length, saturation occurs after similar to 10(8) yr. Although the saturation behaviour of the small-scale dynamo is still somewhat uncertain, we expect a saturation field strength of the order similar to 10 (7)n(0.5) G in the first star-forming halos, with n the number density in cgs units. In the first galaxies with higher turbulent velocities, the magnetic field strength may be increased by an order of magnitude, and saturation may occur after 10(6)-10(7) yr. In the Kolmogorov case, the magnetic field strength on the integral scale (i.e. the scale with most magnetic power) is higher due to the characteristic power-law indices, but the difference is less than a factor of 2 in the saturated phase. Our results thus indicate that the precise scaling of the turbulent velocity with length scale is of minor importance. They further imply that magnetic fields will be significantly enhanced before the formation of a protostellar disk, where they may change the fragmentation properties of the gas and the accretion rate.

Mach number dependence of turbulent magnetic field amplification: solenoidal versus compressive flows.

We study the growth rate and saturation level of the turbulent dynamo in magnetohydrodynamical simulations of turbulence, driven with solenoidal (divergence-free) or compressive (curl-free) forcing. For models with Mach numbers ranging from 0.02 to 20, we find significantly different magnetic field geometries, amplification rates, and saturation levels, decreasing strongly at the transition from subsonic to supersonic flows, due to the development of shocks. Both extreme types of turbulent forcing drive the dynamo, but solenoidal forcing is more efficient, because it produces more vorticity.