Ralf S. Klessen

Control of star formation by supersonic turbulence

Understanding the formation of stars in galaxies is central to much of modern astrophysics. However, a quantitative prediction of the star formation rate and the initial distribution of stellar masses remains elusive. For several decades it has been thought that the star formation process is primarily controlled by the interplay between gravity and magnetostatic support, modulated by neutral-ion drift (known as ambipolar diffusion in astrophysics). Recently, however, both observational and numerical work has begun to suggest that supersonic turbulent flows rather than static magnetic fields control star formation. To some extent, this represents a return to ideas popular before the importance of magnetic fields to the interstellar gas was fully appreciated. This review gives a historical overview of the successes and problems of both the classical dynamical theory and the standard theory of magnetostatic support, from both observational and theoretical perspectives. The outline of a new theory relying on control by driven supersonic turbulence is then presented. Numerical models demonstrate that, although supersonic turbulence can provide global support, it nevertheless produces density enhancements that allow local collapse. Inefficient, isolated star formation is a hallmark of turbulent support, while efficient, clustered star formation occurs in its absence. The consequences of this theory are then explored for both local star formation and galactic-scale star formation. It suggests that individual star-forming cores are likely not quasistatic objects, but dynamically collapsing. Accretion onto these objects varies depending on the properties of the surrounding turbulent flow; numerical models agree with observations showing decreasing rates. The initial mass distribution of stars may also be determined by the turbulent flow. Molecular clouds appear to be transient objects forming and dissolving in the larger-scale turbulent flow, or else quickly collapsing into regions of violent star formation. Global star formation in galaxies appears to be controlled by the same balance between gravity and turbulence as small-scale star formation, although modulated by cooling and differential rotation. The dominant driving mechanism in star-forming regions of galaxies appears to be supernovae, while elsewhere coupling of rotation to the gas through magnetic fields or gravity may be important.

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.

Kinetic Energy Decay Rates of Supersonic and Super-Alfvenic Turbulence in Star-Forming Clouds

We compute 3D models of supersonic, sub-Alfvenic, and super-Alfvenic decaying turbulence, with an isothermal equation of state appropriate for star-forming interstellar clouds of molecular gas. We find that in 3D the kinetic energy decays as t-?, with 0.85 < ? < 1.2. In ID magnetized turbulence actually decays faster than unmagnetized turbulence. We compared different algorithms, and performed resolution studies reaching 2563 zones or 703 particles. External driving must produce the observed long lifetimes and supersonic motions in molecular clouds, as undriven turbulence decays too fast.

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.

Gravitational Collapse in Turbulent Molecular Clouds. I. Gasdynamical Turbulence

Observed molecular clouds often appear to have very low star formation efficiencies and lifetimes an order of magnitude longer than their free-fall times. Their support is attributed to the random supersonic motions observed in them. We study the support of molecular clouds against gravitational collapse by supersonic, gasdynamical turbulence using direct numerical simulation. Computations with two different algorithms are compared: a particle-based, Lagrangian method (smoothed particle hydrodynamics [SPH]) and a grid-based, Eulerian, second-order method (ZEUS). The effects of both algorithm and resolution can be studied with this method. We find that, under typical molecular cloud conditions, global collapse can indeed be prevented, but density enhancements caused by strong shocks nevertheless become gravitationally unstable and collapse into dense cores and, presumably, stars. The occurrence and efficiency of local collapse decreases as the driving wavelength decreases and the driving strength increases. It appears that local collapse can be prevented entirely only with unrealistically short wavelength driving, but observed core formation rates can be reproduced with more realistic driving. At high collapse rates, cores are formed on short timescales in coherent structures with high efficiency, while at low collapse rates they are scattered randomly throughout the region and exhibit considerable age spread. We suggest that this naturally explains the observed distinction between isolated and clustered star formation.

THE STAR FORMATION RATE OF TURBULENT MAGNETIZED CLOUDS: COMPARING THEORY, SIMULATIONS, AND OBSERVATIONS

The role of turbulence and magnetic fields is studied for star formation in molecular clouds. We derive and compare six theoretical models for the star formation rate (SFR)—the Krumholz & McKee (KM), Padoan & Nordlund (PN), and Hennebelle & Chabrier (HC) models, and three multi-freefall versions of these, suggested by HC—all based on integrals over the log-normal distribution of turbulent gas. We extend all theories to include magnetic fields and show that the SFR depends on four basic parameters: (1) virial parameter αvir; (2) sonic Mach number ; (3) turbulent forcing parameter b, which is a measure for the fraction of energy driven in compressive modes; and (4) plasma with the Alfven Mach number . We compare all six theories with MHD simulations, covering cloud masses of 300 to 4 × 106 M ☉ and Mach numbers -50 and -∞, with solenoidal (b = 1/3), mixed (b = 0.4), and compressive turbulent (b = 1) forcings. We find that the SFR increases by a factor of four between and 50 for compressive turbulent forcing and αvir ~ 1. Comparing forcing parameters, we see that the SFR is more than 10 times higher with compressive than solenoidal forcing for simulations. The SFR and fragmentation are both reduced by a factor of two in strongly magnetized, trans-Alfvenic turbulence compared to hydrodynamic turbulence. All simulations are fit simultaneously by the multi-freefall KM and multi-freefall PN theories within a factor of two over two orders of magnitude in SFR. The simulated SFRs cover the range and correlation of SFR column density with gas column density observed in Galactic clouds, and agree well for star formation efficiencies SFE = 1%-10% and local efficiencies = 0.3-0.7 due to feedback. We conclude that the SFR is primarily controlled by interstellar turbulence, with a secondary effect coming from magnetic fields.

The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing

The probability density function (PDF) of the gas density in turbulent supersonic flows is investigated with high-resolution numerical simulations. In a systematic study, we compare the density statistics of compressible turbulence driven by the usually adopted solenoidal forcing (divergence-free) and by compressive forcing (curl-free). Our results are in agreement with studies using solenoidal forcing. However, compressive forcing yields a significantly broader density distribution with standard deviation ~3 times larger at the same rms Mach number. The standard deviation-Mach number relation used in analytical models of star formation is reviewed and a modification of the existing expression is proposed, which takes into account the ratio of solenoidal and compressive modes of the turbulence forcing.

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.

Molecular Cloud Evolution. II. From Cloud Formation to the Early Stages of Star Formation in Decaying Conditions

We study the formation of giant dense cloud complexes and of stars within them using SPH numerical simulations of the collision of gas streams (‘‘inflows’’) in the WNM at moderately supersonic velocities. The collisions cause compression,cooling,andturbulencegenerationinthegas,formingacloudthatthenbecomesself-gravitatingandbeginsto collapse globally. Simultaneously, the turbulent, nonlinear density fluctuations induce fast, local collapse events. The simulationsshowthat(1)Thecloudsarenotinastateofequilibrium.Instead,theyundergosecularevolution.Duringits early stages, the cloud’s mass and gravitational energy jEgj increase steadily, while the turbulent energy Ek reaches a plateau.(2)When jEgjbecomescomparabletoEk,globalcollapsebegins,causingasimultaneousincreasein jEgjandEk that maintains a near-equipartition condition jEg j� 2Ek. (3) Longer inflow durations delay the onset of global and local collapsebymaintainingahigherturbulentvelocitydispersioninthecloudoverlongertimes.(4)Thestarformationrate islargefrom the beginning,without any periodofslow and acceleratingstar formation.(5) The column densities of the local star-forming clumps closely resemble reported values of the column density required for molecule formation, suggesting that locally molecular gas and star formation occur nearly simultaneously. The MC formation mechanism discussedherenaturallyexplainstheapparent‘‘virialized’’stateofMCsandtheubiquityofHihalosaroundthem.Also, within their assumptions, our simulations support the scenario of rapid star formation after MCs are formed, although long (k15 Myr) accumulation periods do occur during which the clouds build up their gravitational energy, and which are expected to be spent in the atomic phase.