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We present a comprehensive study of the star cluster population and the hierarchical structure in the clustering of blue stars with ages [?]500 Myr in the Local Group dwarf irregular galaxy NGC 6822. Our observational material comprises the most complete optical stellar catalog of the galaxy from imaging with the Suprime-Cam at the 8.2 m Subaru Telescope. We identify 47 distinct star clusters with the application of the nearest-neighbor density method to this catalog for a detection threshold of 3s above the average stellar density. The size distribution of the detected clusters can be very well approximated by a Gaussian with a peak at [?]68 pc. The total stellar masses of the clusters are estimated by extrapolating the cumulative observed stellar mass function of all clusters to be in the range 103-104 M . Their number distribution is fitted very well by a power law with index a [?] 1.5 +- 0.7, which is consistent with the cluster mass functions of other Local Group galaxies and the cluster initial mass function. In addition to the detected star clusters of the galaxy, the application of the nearest-neighbor density method for various density thresholds, other than 3s, enabled the identification of stellar concentrations in various lengthscales. The stellar density maps constructed with this technique provide a direct proof of hierarchically structured stellar concentrations in NGC 6822, in the sense that smaller dense stellar concentrations are located inside larger and looser ones. We illustrate this hierarchy by the so-called dendrogram, or structure tree of the detected stellar structures, which demonstrates that most of the detected structures split up into several substructures over at least three levels. We quantify the hierarchy of these structures with the use of the minimum spanning tree method. We find that structures detected at 1, 2, and 3s density thresholds are hierarchically constructed with a fractal dimension of D [?] 1.8. Some of the larger stellar concentrations, particularly in the northern part of the central star-forming portion of the galaxy, coincide with IR-bright complexes previously identified with Spitzer and associated with high column density neutral gas, indicating structures that currently form stars. The morphological hierarchy in stellar clustering, which we observe in NGC 6822, resembles that of the turbulent interstellar matter, suggesting that turbulence on pc and kpc scales has been probably the major agent that regulated clustered star formation in NGC 6822.

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.

The spatial morphology, spectral characteristics, and time variability of ultracompact (UC) H II regions provide strong constraints on the process of massive star formation. We have performed simulations of the gravitational collapse of rotating molecular cloud cores, including treatments of the propagation of ionizing and non-ionizing radiation. We here present synthetic radio continuum observations of H II regions from our collapse simulations, to investigate how well they agree with observation, and what we can learn about how massive star formation proceeds. We find that intermittent shielding by dense filaments in the gravitationally unstable accretion flow around the massive star leads to highly variable H II regions that do not grow monotonically, but rather flicker, growing and shrinking repeatedly. This behavior appears to be able to resolve the well-known lifetime problem. We find that multiple ionizing sources generally form, resulting in groups of UC H II regions, consistent with observations. We confirm that our model reproduces the qualitative H II region morphologies found in surveys, with generally consistent relative frequencies. We also find that simulated spectral energy distributions (SEDs) from our model are consistent with the range of observed H II region SEDs, including both regions showing a normal transition from optically thick to optically thin emission, and those with intermediate spectral slopes. In our models, anomalous slopes are solely produced by inhomogeneities in the H II region, with no contribution from dust emission at millimeter or submillimeter wavelengths. We conclude that many observed characteristics of UC H II regions appear consistent with massive star formation in fast, gravitationally unstable, accretion flows.

Using three-dimensional cosmological simulations, we study the assembly process of one of the first galaxies, with a total mass of [?]108 M , collapsing at z [?] 10. Our main goal is to trace the transport of the heavy chemical elements produced and dispersed by a pair-instability supernova exploding in one of the minihalo progenitors. To this extent, we incorporate an efficient algorithm into our smoothed particle hydrodynamics code that approximately models turbulent mixing as a diffusion process. We study this mixing with and without the radiative feedback from Population III (Pop III) stars that subsequently form in neighboring minihalos. Our simulations allow us to constrain the initial conditions for second-generation star formation, within the first galaxy itself, and inside of minihalos that virialize after the supernova explosion. We find that most minihalos remain unscathed by ionizing radiation or the supernova remnant, while some are substantially photoheated and enriched to supercritical levels, likely resulting in the formation of low-mass Pop III or even Population II (Pop II) stars. At the center of the newly formed galaxy, [?]105 M of cold, dense gas uniformly enriched to [?]10-3 Z is in a state of collapse, suggesting that a cluster of Pop II stars will form. The first galaxies, as may be detected by the James Webb Space Telescope, would therefore already contain stellar populations familiar from lower redshifts.

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.

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.

We investigate the properties of "star-forming regions" in a previously published numerical simulation of molecular cloud formation out of compressive motions in the warm neutral atomic interstellar medium, neglecting magnetic fields and stellar feedback. We study the properties (density, total gas + stars mass, stellar mass, velocity dispersion, and star formation rate (SFR)) of the cloud hosting the first local, isolated "star formation" event and compare them with those of the cloud formed by the central, global collapse event. In this simulation, the velocity dispersions at all scales are caused primarily by infall motions rather than by random turbulence. We suggest that the small-scale isolated collapses may be representative of low- to intermediate-mass star-forming regions, with gas masses (M gas) of hundreds of solar masses, velocity dispersions s v [?] 0.7 km s-1, and SFRs [?]3 x 10-5 M yr-1, while the large-scale, massive ones may be representative of massive star-forming regions, with M gas of thousands of solar masses, s v [?] a few km s-1, and SFRs [?]3 x 10-4 M yr-1. We also compare the statistical distributions of the physical properties of the dense cores appearing in the central region of massive collapse with those from a recent survey of the massive star-forming region in the Cygnus X molecular cloud, finding that the observed and simulated distributions are in general very similar. However, we find that the star formation efficiency per free-fall time (SFEff) of the high mass region, similar to that of OMC-1, is low, [?]0.04. In the simulated cloud, this is not a consequence of a "slow" SFR in a nearly hydrostatic cloud supported by turbulence, but rather of the region accreting mass at a high rate. Thus, we find that measuring a low SFEff may be incorrectly interpreted as implying a lifetime much longer than the core's local free-fall time, and an SFR much slower than that given by the free-fall rate, if the accretion is not accounted for. We suggest that rather than requiring a low value of the SFEff everywhere in the Galaxy, attaining a globally low specific SFR requires star formation to be a spatially intermittent process, so that most of the mass in a giant molecular cloud (GMC) is not participating in the SF process at any given time. Locally, the specific SFR of a star-forming region can be much larger than the global GMC's average.

We explore the effects of magnetic energy dissipation on the formation of the first stars. For this purpose, we follow the evolution of primordial chemistry in the presence of magnetic fields in the post-recombination universe until the formation of the first virialized halos. From the point of virialization, we follow the protostellar collapse up to densities of [?]1012 cm-3 in a one-zone model. In the intergalactic medium (IGM), comoving field strengths of [?]0.1 nG lead to Jeans masses of 108 M or more and thus delay gravitational collapse in the first halos until they are sufficiently massive. During protostellar collapse, we find that the temperature minimum at densities of [?]103 cm-3 does not change significantly, such that the characteristic mass scale for fragmentation is not affected. However, we find a significant temperature increase at higher densities for comoving field strengths of [?] 0.1 nG. This may delay gravitational collapse, in particular at densities of [?]109 cm-3, where the proton abundance drops rapidly and the main contribution to the ambipolar diffusion resistivity is due to collisions with Li+. We further explore how the thermal evolution depends on the scaling relation of magnetic field strength with density. While the effects are already significant for our fiducial model with B [?] r0.5-0.57, the temperature may increase even further for steeper relations and lead to the complete dissociation of H2 at densities of [?]1011 cm-3 for a scaling with B [?] r0.6. The correct modeling of this relation is therefore very important, as the increase in temperature enhances the subsequent accretion rate onto the protostar. Our model confirms that initial weak magnetic fields may be amplified considerably during gravitational collapse and become dynamically relevant. For instance, a comoving field strength above 10-5 nG will be amplified above the critical value for the onset of jets which can magnetize the IGM.

Primordial star formation appears to result in stars at least an order of magnitude more massive than modern star formation. It has been proposed that the transition from primordial to modern initial mass functions occurs due to the onset of effective metal-line cooling at a metallicity Z/Z = 10-3.5. However, these simulations neglected molecular hydrogen cooling. We perform simulations using the same initial conditions, but including molecular cooling, using a complex network that follows molecular hydrogen formation and also directly follows carbon monoxide and water. We find that molecular hydrogen cooling allows roughly equivalent fragmentation to proceed even at zero metallicity for these initial conditions. The apparent transition just represents the point where metal-line cooling becomes more important than molecular cooling. In all cases, the fragments are massive enough to be consistent with models of primordial stellar masses, suggesting that the transition to the modern initial mass function may be determined by other physics such as dust formation. We conclude that such additional cooling mechanisms, combined with the exact initial conditions produced by cosmological collapse are likely more important than metal-line cooling in determining the initial mass function, and thus that there is unlikely to be a sharp transition in the initial mass function at Z/Z = 10-3.5.

The formation of the first stars out of metal-free gas appears to result in stars at least an order of magnitude more massive than in the present-day case. We here consider what controls the transition from a primordial to a modern initial mass function. It has been proposed that this occurs when effective metal line cooling occurs at a metallicity threshold of Z/Z > 10-3.5. We study the influence of low levels of metal enrichment on the cooling and collapse of initially ionized gas in small protogalactic halos using three-dimensional, smoothed particle hydrodynamics simulations with particle splitting. Our initial conditions represent protogalaxies forming within a previously ionized H II region that has not yet had time to cool and recombine. These differ considerably from those used in simulations predicting a metallicity threshold, where the gas was initially cold and only partially ionized. In the centrally condensed potential that we study here, a wide variety of initial conditions for the gas yields a monolithic central collapse. Our models show no fragmentation during collapse to number densities as high as 105 cm-3, for metallicities reaching as high as 10-1 Z , far above the threshold suggested by previous work. Rotation allows for the formation of gravitationally stable gas disks over large fractions of the local Hubble time. Turbulence slows the growth of the central density slightly, but both spherically symmetric and turbulent initial conditions collapse and form a single sink particle. We therefore argue that fragmentation at moderate density depends on the initial conditions for star formation more than on the metal abundances present. The actual initial conditions to be considered still need to be determined in detail by observation and modeling of galaxy formation. Metal abundance may still drive fragmentation at very high densities due to dust cooling, perhaps giving an alternative metallicity threshold.

We present evidence that the star-forming region NGC 346/N66 in the Small Magellanic Cloud is the product of hierarchical star formation, probably from more than one star formation event. We investigate the spatial distribution and clustering behavior of the pre-main-sequence (PMS) stellar population in the region, using data obtained with Hubble Space Telescope's Advanced Camera for Surveys. By applying the nearest neighbor and minimum spanning tree methods on the rich sample of PMS stars previously discovered in the region, we identify 10 individual PMS clusters in the area and quantify their structures. The clusters show a wide range of morphologies from hierarchical multipeak configurations to centrally condensed clusters. However, only about 40% of the PMS stars belong to the identified clusters. The central association NGC 346 is identified as the largest stellar concentration, which cannot be resolved into subclusters. Several PMS clusters are aligned along filaments of higher stellar density pointing away from the central part of the region. The PMS density peaks in the association coincide with the peaks of [O III] and 8 mm emission. While more massive stars seem to be concentrated in the central association when considering the entire area, we find no evidence for mass segregation within the system itself.

In a systematic study, we compare the density statistics in high-resolution numerical experiments of supersonic isothermal turbulence, driven by the usually adopted solenoidal (divergence-free) forcing and by compressive (curl-free) forcing. We find that for the same rms Mach number, compressive forcing produces much stronger density enhancements and larger voids compared to solenoidal forcing. Consequently, the Fourier spectra of density fluctuations are significantly steeper. This result is confirmed using the D-variance analysis, which yields power-law exponents b [?] 3.4 for compressive forcing and b [?] 2.8 for solenoidal forcing. We obtain fractal dimension estimates from the density spectra and D-variance scaling, and by using the box counting, mass size, and perimeter area methods applied to the volumetric data, projections, and slices of our turbulent density fields. Our results suggest that compressive forcing yields fractal dimensions significantly smaller compared to solenoidal forcing. However, the actual values depend sensitively on the adopted method, with the most reliable estimates based on the D-variance, or equivalently, on Fourier spectra. Using these methods, we obtain D [?] 2.3 for compressive and D [?] 2.6 for solenoidal forcing, which is within the range of fractal dimension estimates inferred from observations (D [?] 2.0-2.7). The velocity dispersion to size relations for both solenoidal and compressive forcings obtained from velocity spectra follow a power law with exponents in the range 0.4-0.5, in good agreement with previous studies.

Magnetic fields in the early universe can significantly alter the thermal evolution and the ionization history during the dark ages. This is reflected in the 21 cm line of atomic hydrogen, which is coupled to the gas temperature through collisions at high redshifts, and through the Wouthuysen-Field effect at low redshifts. We present a semianalytic model for star formation and the build-up of a Lyman-a background in the presence of magnetic fields, and calculate the evolution of the mean 21 cm brightness temperature and its frequency gradient as a function of redshift. We further discuss the evolution of linear fluctuations in temperature and ionization in the presence of magnetic fields and calculate the effect on the 21 cm power spectrum. At high redshifts, the signal is increased compared to the nonmagnetic case due to the additional heat input into the intergalactic medium from ambipolar diffusion and the decay of MHD turbulence. At lower redshifts, the formation of luminous objects and the build-up of a Lyman-a background can be delayed by a redshift interval of 10 due to the strong increase of the filtering mass scale in the presence of magnetic fields. This tends to decrease the 21 cm signal compared to the zero-field case. In summary, we find that 21 cm observations may become a promising tool to constrain primordial magnetic fields.

The characteristic mass Mc in the stellar initial mass function (IMF) is about constant for most star-forming regions. Numerical simulations consistently show a proportionality between Mc and the thermal Jeans mass MJ at the time of cloud fragmentation, but no models have explained how it can be the same in diverse conditions. Here we show that MJ depends weakly on density, temperature, metallicity, and radiation field in three environments: the dense cores where stars form, larger star-forming regions ranging from GMCs to galactic disks, and the interiors of H II regions and super star clusters. In dense cores, the quantity T3/2n[?]1/2 that appears in MJ scales with core density as n0.25 or with radiation density as U0.1 at the density where dust and gas come into thermal equilibrium. On larger scales, this quantity varies with ambient density as n[?]0.05 and ambient radiation field as U[?]0.033 when the Kennicutt-Schmidt law of star formation determines U(n) . In super star clusters with ionization and compression of prestellar globules, MJ varies as the 0.13 power of the cluster column density. These weak dependencies on n, U, and column density imply that most environmental variations affect the thermal Jeans mass by at most a factor of ~2. Cosmological increases in MJ, which have been suggested by observations, may be explained if the star formation efficiency is systematically higher at high redshift for a given density and pressure, if dust grains are smaller at lower metallicity, and so hotter for a given radiation field, or if small prestellar cores are more severely ionized in extreme starburst conditions.

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 g [?] 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.

We perform three-dimensional smoothed particle hydrodynamics simulations in a realistic cosmological setting to investigate the expansion, feedback, and chemical enrichment properties of a 200 M pair-instability supernova in the high-redshift universe. We find that the SN remnant propagates for a Hubble time at z [?] 20 to a final mass-weighted mean shock radius of 2.5 kpc (proper), roughly half the size of the H II region, and in this process sweeps up a total gas mass of 2.5 x 105 M. The morphology of the shock becomes highly anisotropic once it leaves the host halo and encounters filaments and neighboring minihalos, while the bulk of the shock propagates into the voids of the intergalactic medium. The SN entirely disrupts the host halo and terminates further star formation for at least 200 Myr, while in our specific case it exerts positive mechanical feedback on neighboring minihalos by shock-compressing their cores. In contrast, we do not observe secondary star formation in the dense shell via gravitational fragmentation, due to the previous photoheating by the progenitor star. We find that cooling by metal lines is unimportant for the entire evolution of the SN remnant, while the metal-enriched, interior bubble expands adiabatically into the cavities created by the shock, and ultimately into the voids with a maximum extent similar to the final mass-weighted mean shock radius. Finally, we conclude that dark matter halos of at least Mvir [?] 108 M must be assembled to recollect all components of the swept-up gas.

Jets and outflows from young stellar objects have been proposed as candidates to drive supersonic turbulence in molecular clouds. Here we present the results from multidimensional jet simulations where we investigate in detail the energy and momentum deposition from jets into their surrounding environment and quantify the character of the excited turbulence with velocity probability density functions. Our study includes jet-clump interaction, transient jets, and magnetized jets. We find that collimated supersonic jets do not excite supersonic motions far from the vicinity of the jet. Supersonic fluctuations are damped quickly and do not spread into the parent cloud. Instead, subsonic, noncompressional modes occupy most of the excited volume. This is a generic feature that cannot be fully circumvented with overdense jets or magnetic fields. Nevertheless, jets are able to leave strong imprints in the cloud structure and can disrupt dense clumps. Our results question the ability of collimated jets to sustain supersonic turbulence in molecular clouds.

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, and turbulence generation in the gas, forming a cloud that then becomes self-gravitating and begins to collapse globally. Simultaneously, the turbulent, nonlinear density fluctuations induce fast, local collapse events. The simulations show that (1) The clouds are not in a state of equilibrium. Instead, they undergo secular evolution. During its early stages, the cloud's mass and gravitational energy |Eg| increase steadily, while the turbulent energy Ek reaches a plateau. (2) When |Eg| becomes comparable to Ek, global collapse begins, causing a simultaneous increase in |Eg| and Ek that maintains a near-equipartition condition |Eg| ~ 2Ek. (3) Longer inflow durations delay the onset of global and local collapse by maintaining a higher turbulent velocity dispersion in the cloud over longer times. (4) The star formation rate is large from the beginning, without any period of slow and accelerating star 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 discussed here naturally explains the apparent ``virialized'' state of MCs and the ubiquity of H I halos around them. Also, within their assumptions, our simulations support the scenario of rapid star formation after MCs are formed, although long ([?]15 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.

We model gravitational instability in a wide range of isolated disk galaxies, using GADGET, a three-dimensional, smoothed particle hydrodynamics code. The model galaxies include a dark matter halo and a disk of stars and isothermal gas. Absorbing sink particles are used to directly measure the mass of gravitationally collapsing gas. Below the density at which they are inserted, the collapsing gas is fully resolved. We make the assumption that stars and molecular gas form within the sink particle once it is created and that the star formation rate is the gravitational collapse rate times a constant efficiency factor. In our models, the derived star formation rate declines exponentially with time, and radial profiles of atomic and molecular gas and star formation rate reproduce observed behavior. We derive from our models and discuss both the global and local Schmidt laws for star formation: power-law relations between surface densities of gas and star formation rate. The global Schmidt law observed in disk galaxies is quantitatively reproduced by our models. We find that the surface density of star formation rate directly correlates with the strength of local gravitational instability. The local Schmidt laws of individual galaxies in our models show clear evidence of star formation thresholds. The variations in both the slope and the normalization of the local Schmidt laws cover the observed range. The averaged values agree well with the observed average and with the global law. Our results suggest that the nonlinear development of gravitational instability determines the local and global Schmidt laws and the star formation thresholds. We derive from our models the quantitative dependence of the global star formation efficiency on the initial gravitational instability of galaxies. The more unstable a galaxy is, the quicker and more efficiently its gas collapses gravitationally and forms stars.

We investigate the core mass distribution (CMD) resulting from numerical models of turbulent fragmentation of molecular clouds. In particular we study its dependence on the sonic rms Mach number Ms. We analyze simulations with Ms ranging from 1 to 15 to show that, as Ms increases, the number of cores increases as well, while their average mass decreases. This stems from the fact that high Mach number flows produce many and strong shocks on intermediate to small spatial scales, leading to a highly fragmented density structure. We also show that the CMD from purely turbulent fragmentation does not follow a single power law, but can be described by a function that changes its shape continuously, probably similar to a lognormal function. The CMD in supersonic turbulent flows does not have a universal slope, which casts some doubt on attempts to directly relate the CMD to a universal initial mass function.

We model gravitational collapse leading to star formation in a wide range of isolated disk galaxies using a three-dimensional, smoothed particle hydrodynamics code. The model galaxies include a dark matter halo and a disk of stars and isothermal gas. Absorbing sink particles are used to directly measure the mass of gravitationally collapsing gas. They reach masses characteristic of stellar clusters. In this paper we describe our galaxy models and numerical methods, followed by an investigation of the gravitational instability in these galaxies. Gravitational collapse forms star clusters with correlated positions and ages, as observed, for example, in the Large Magellanic Cloud. Gravitational instability alone acting in unperturbed galaxies appears sufficient to produce flocculent spiral arms, although not more organized patterns. Unstable galaxies show collapse in thin layers in the galactic plane; associated dust will form thin dust lanes in those galaxies, in agreement with observations. We find an exponential relationship between the global collapse timescale and the minimum value in a galaxy of the Toomre instability parameter for a combination of stars and gas Qsg. Furthermore, collapse occurs only in regions with Qsg < 1.6. Our results suggest that vigorous starbursts occur where Qsg [?] 1, while slow star formation takes place at higher values of Qsg below 1.6. A massive, or gas-rich, galaxy has low initial Qsg, giving it a high star formation rate, while a low-mass, or gas-poor, galaxy has a high initial Qsg, giving it a low star formation rate.

We investigate the velocity structure of protostellar cores that result from nonmagnetic numerical models of the gravoturbulent fragmentation of molecular cloud material. A large fraction of the cores analyzed are "quiescent"; i.e., they have nonthermal line widths smaller or equal to the thermal line width. Specifically, about 23% of the cores have subsonic turbulent line-of-sight velocity dispersions sturb [?] cs. A total of 46% are "transonic," with cs < sturb [?] 2cs. More than half of our sample cores are identified as "coherent," i.e., with sturb roughly independent of column density. Of these, about 40% are quiescent, 40% are transonic, and 20% are supersonic. The fact that dynamically evolving cores in highly supersonic turbulent flows can be quiescent may be understood because cores lie at the stagnation points of convergent turbulent flows, where compression is at a maximum and relative velocity differences are at a minimum. The apparent coherence may be due, at least in part, to an observational effect related to the length and concentration of the material contributing to the line. In our simulated cores, sturb often has its local maximum at small but finite offsets from the column density maximum, suggesting that the core is the dense region behind a shock. Such a configuration is often found in observations of nearby molecular cloud cores and argues in favor of the gravoturbulent scenario of stellar birth as it is not expected in star formation models based on magnetic mediation. A comparison between the virial estimate Mvir for the mass of a core based on sturb and its actual value M shows that cores with collapsed objects tend to be near equipartition between their gravitational and kinetic energies, while cores without collapsed objects tend to be gravitationally unbound, suggesting that gravitational collapse occurs immediately after gravity becomes dominant. Finally, cores in simulations driven at large scales are more frequently quiescent and coherent and have more realistic ratios of Mvir/M, supporting the notion that molecular cloud turbulence is driven at large scales.

D01 The Supernova Rate-velocity Dispersion Relation in the Interstellar MediumD02 Mesoturbulence and the Physical Parameters of the Bok Globules CB 24, CB 25, CB 202, CB 213, and CB 231D03 Turbulent Ambipolar Diffusion: Numerical Studies in 2DD04 The EncounterWith Small Scale Turbulence in Substellar ObjectsD05 Star Formation from Gravoturbulent FragmentationD06 The Physical and Chemical Structure of Galactic Photon Dominated RegionsD07 Measuring the Velocity Structure in Turbulent CloudsD08 Impact of Turbulence Induced Temperature Fluctuations on Astrophysical Condensation ProcessesD09 Star Formation in Turbulent Molecular Clouds: Mass Accretion and Evolution of ProtostarsD10 Modelling of Turbulence in Simulations of Type Ia Supernova ExplosionsD11 Stars: Twisting Exteriors – Turbulent Interiors

We study the effect of varying the equation of state on the formation of stellar clusters in turbulent molecular clouds using three-dimensional, smoothed particle hydrodynamics simulations. Our results show that the equation of state helps determine how strongly self-gravitating gas fragments. The degree of fragmentation decreases with increasing polytropic exponent g in the range 0.2 < g < 1.4, although the total amount of mass accreted onto collapsed fragments appears to remain roughly constant through that range. Low values of g are expected to lead to the formation of dense clusters of low-mass stars, while g > 1 probably results in the formation of isolated and massive stars. Fragmentation and collapse ceases entirely for g > 1.4, as expected from analytic arguments. The mass spectrum of overdense gas clumps is roughly lognormal for non-self-gravitating turbulent gas, but changes to a power law under the action of gravity. The spectrum of collapsed cores, on the other hand, remains lognormal for g [?] 1 but flattens markedly for g > 1. The density probability function approaches lognormal, with widths that decrease with increasing g. Primordial gas may have effective g > 1, in which case these results could help explain why models of the formation of the first stars tend to produce isolated, massive objects.

We discuss the column density profiles of "cores" in three-dimensional smoothed particle hydrodynamics (SPH) numerical simulations of turbulent molecular clouds. The SPH scheme allows us to perform a high spatial resolution analysis of the density maxima (cores) at scales between ~0.003 and 0.3 pc. We analyze simulations in three different physical conditions: large-scale driving (LSD), small-scale driving (SSD), and random Gaussian initial conditions without driving (GC), each one at two different time steps: just before self-gravity is turned on (t0) and when gravity has been operating such that 5% of the total mass in the box has been accreted into cores (t1). For this data set, we perform Bonnor-Ebert fits to the column density profiles of cores found by a clump-finding algorithm. We find that, for the particular fitting procedure we use, 65% of the cores can be matched to Bonnor-Ebert (BE) profiles, and of these, 47% correspond to stable equilibrium configurations with xmax < 6.5, even though the cores analyzed in the simulations are not in equilibrium but instead are dynamically evolving. The temperatures obtained with the fitting procedure vary between 5 and 60 K (in spite of the simulations being isothermal, with T = 11.3 K), with the peak of the distribution being at T = 11 K and most clumps having fitted temperatures between 5 and 30 K. Central densities obtained with the BE fit tend to be smaller than the actual central densities of the cores. We also find that for the LSD and GC cases, there are more BE-like cores at t0 than at t1 with xmax [?] 20, while in the case of SSD, there are more such cores at t1 than at t0. We interpret this as a consequence of the stronger turbulence present in the cores of run SSD, which prevents good BE fits in the absence of gravity, and delays collapse in its presence. Finally, in some cases we find substantial superposition effects when we analyze the projection of the density structures, even though the scales over which we project are small ([?]0.18 pc). As a consequence, different projections of the same core may give very different values of the BE fits. Finally, we briefly discuss recent results claiming that Bok globule B68 is in hydrostatic equilibrium, stressing that they imply that this core is unstable by a wide margin. We conclude that fitting BE profiles to observed cores is not an unambiguous test of hydrostatic equilibrium and that fit-estimated parameters such as mass, central density, density contrast, temperature, or radial profile of the BE sphere may differ significantly from the actual values in the cores.

We test whether the structural properties of the nearby dwarf spheroidal (dSph) galaxy Draco, a well-studied Milky Way companion, can be reconciled with the suggestion that dSphs are unbound tidal remnants with a large depth extent along the line of sight. In order to apply the observational test of this hypothesis, suggested by Klessen & Zhao, we use public photometric data from the Sloan Digital Sky Survey (SDSS) to explore the width of Draco's blue horizontal branch over a range of areas covering 0.06-6.25 deg2 centered on Draco. The SDSS database is the only currently existing database with sufficient depth and area coverage to permit a stringent test of the tidal models. Blue horizontal branch stars were chosen as tracers of Draco's spatial extent and depth because of their low contamination by Galactic foreground stars and since they have a spatially more extended distribution than the more centrally concentrated red horizontal branch stars. Indeed, we show that blue horizontal branch stars extend beyond the previously inferred limiting radii of Draco, consistent with the observed absence of a truncated stellar surface density profile of this dSph (Odenkirchen et al.). Following the method of Klessen & Kroupa, we calculate new models for a galaxy without dark matter, using Draco's morphological properties as constraints. The resulting models are unable to reproduce the narrow observed horizontal branch width of Draco, which stays roughly constant regardless of the field of view. We conclude that Draco cannot be the remnant of a tidally disrupted satellite but is probably strongly dark matter-dominated, as suggested independently by the structural analysis conducted by Odenkirchen et al. and by the kinematic analysis of Kleyna et al.

The failure of standard cosmological models in accounting for the statistics of dwarf satellites and the rotation curve of gas-rich dwarf galaxies in detail has led us to examine whether earlier nonequilibrium models of dwarf spheroidal satellites without any dark matter should be reconsidered in more detail. Such models can explain the high dispersion of the dwarf spheroids by the projection of disrupted tidal debris. We show in the case of Milky Way satellites that these models predict a significant spread in the apparent magnitude of horizontal-branch (HB) stars that is correlated with sky position and velocity. In particular, the models produce a strong correlation of radial velocity with the long axis of the dwarf. Current data do not set strong enough constraints on models, but we suggest that photometric and spectroscopic surveys of extratidal stars of nearby dwarf spheroids in the Milky Way and Andromeda galaxies can falsify these models without dark matter.

Star formation is intimately linked to the dynamical evolution of molecular clouds. Turbulent fragmentation determines where and when protostellar cores form, and how they contract and grow in mass via competitive accretion from the surrounding cloud material. This process is investigated using numerical models of self-gravitating molecular cloud dynamics, where no turbulent support is included, where turbulence is allowed to decay freely, and where it is continuously replenished on large, intermediate, and small scales, respectively. Molecular cloud regions without turbulent driving sources, or where turbulence is driven on large scales, exhibit rapid and efficient star formation in a clustered mode, whereas interstellar turbulence that carries most energy on small scales results in isolated star formation with low efficiency. The clump-mass spectrum of shock-generated density fluctuations in non-self-gravitating hydrodynamic supersonic turbulence is not well fit by a power law, and it is too steep at the high-mass end to be in agreement with the observational data. When gravity is included in the turbulence models, local collapse occurs, and the spectrum extends toward larger masses as clumps merge together; then a power-law description dN/dM [?] Mn becomes possible with slope n [?] -2. In the case of pure gravitational contraction, i.e., in regions without turbulent support, the clump-mass spectrum is shallower with n [?] -3/2. The mass spectrum of protostellar cores in regions with no turbulent support and where turbulence is replenished on large scales, however, is well described by a lognormal or by multiple power laws, similar to the stellar initial mass function (IMF) at low and intermediate masses. The model clusters are not massive enough to allow for comparison with the high-mass part of the IMF. In the case of small-scale turbulence, the core mass spectrum is too flat compared to the IMF for all masses.

Using hydrodynamic simulations, we investigate the time evolution and fragmentation of regions within molecular clouds that have lost their turbulent support, leading to gravitational contraction. The initial density distributions are described by random Gaussian fluctuations with varying slopes ? of the power spectrum P(k) k-?, covering the range from flat (? = 0) to very steep (? = 3) spectra. We consider molecular cloud volumes containing different masses relative to the average Jeans mass MJ, from 1MJto 222MJ. This parameter study extends a previous detailed analysis of systems with, initially, P(k) k-2and mass 222MJ. The dynamical evolution of the simulated molecular cloud regions is insensitive to the slope of the initial density fluctuation spectrum. The system evolves into a complex network of intersecting filaments and collapsing clumps, leading to the formation of a compact cluster of accreting and interacting embedded protostellar cores. The cluster builds up as a bound entity but dissolves later due to collisional effects. In all simulations, the mass spectrum of collapsed cores is very broad, has approximately log-normal shape, and peaks roughly at the average Jeans mass. This supports the hypothesis that the average Jeans mass is the main parameter determining the peak in the stellar spectrum and suggests that the interplay between self-gravity on the one side and thermal and turbulent pressure on the other side is the dominant process that regulates the formation of stellar clusters.

Hydrodynamic supersonic turbulence can only prevent local gravitational collapse if the turbulence is driven on scales smaller than the local Jeans lengths in the densest regions, which is a very severe requirement (see Paper I). Magnetic fields have been suggested to support molecular clouds either magnetostatically or via magnetohydrodynamic (MHD) waves. Whereas the first mechanism would form sheetlike clouds, the second mechanism not only could exert a pressure onto the gas counteracting the gravitational forces but could lead to a transfer of turbulent kinetic energy down to smaller spatial scales via MHD wave interactions. This turbulent magnetic cascade might provide sufficient energy at small scales to halt local collapse. We test this hypothesis with MHD simulations at resolutions up to 2563zones done with ZEUS-3D. We first derive a resolution criterion for self-gravitating, magnetized gas: to prevent collapse of magnetostatically supported regions caused by numerical diffusion, the minimum Jeans length must be resolved by four zones. Resolution of MHD waves increases this requirement to roughly six zones. We then find that magnetic fields cannot prevent local collapse unless they provide magnetostatic support. Weaker magnetic fields do somewhat delay collapse and cause it to occur more uniformly across the supported region in comparison to the hydrodynamical case. However, they still cannot prevent local collapse for much longer than a global free-fall time.

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.

Turbulence is essential for understanding the structure and dynamics of molecular clouds and star-forming regions. There is a need for adequate tools to describe and characterize the properties of turbulent flows. One-point probability distribution functions (PDFs) of dynamical variables have been suggested as appropriate statistical measures and applied to several observed molecular clouds. However, the interpretation of these data requires comparison with numerical simulations. To address this issue, smoothed particle hydrodynamics (SPH) simulations of driven and decaying, supersonic, turbulent flows with and without self-gravity are presented. In addition, random Gaussian velocity fields are analyzed to estimate the influence of variance effects. To characterize the flow properties, the PDFs of the density, of the line-of-sight velocity centroids, and of the line centroid increments are studied. This is supplemented by a discussion of the dispersion and the kurtosis of the increment PDFs, as well as the spatial distribution of velocity increments for small spatial lags. From the comparison between different models of interstellar turbulence, it follows that the inclusion of self-gravity leads to better agreement with the observed PDFs in molecular clouds. The increment PDFs for small spatial lags become exponential for all considered velocities. However, all the processes considered here lead to non-Gaussian signatures, differences are only gradual, and the analyzed PDFs are in addition projection dependent. It appears therefore very difficult to distinguish between different physical processes on the basis of PDFs only, which limits their applicability for adequately characterizing interstellar turbulence.

Self-consistent simulations of the dynamical evolution of a low-mass satellite galaxy without dark matter are reported. The orbits have eccentricities of 0.41 [?] e [?] 0.96 in a Galactic dark halo with a mass of 2.85 x 1012 M and 4.5 x 1011 M. A particle-mesh code with nested subgrids and a direct-summation N-body code running with the special-purpose hardware device GRAPE are used for the simulations. Initially, the satellite is spherical with an isotropic velocity distribution and a mass of 107 M. Simulations with 1.3 x 105 up to 2 x 106 satellite particles are performed. The calculations proceed for many orbital periods, until well after the satellite disrupts. In all cases, the dynamical evolution converges to a remnant that contains roughly 1% of the initial satellite mass. The stable remnant results from severe tidal shaping of the initial satellite. To an observer from Earth, these remnants appear strikingly similar to the Galactic dwarf spheroidal satellite galaxies. Their apparent mass-to-light ratios are very large, despite the fact that they contain no dark matter. These computations show that a remnant without dark matter displays larger line-of-sight velocity dispersions, s, for more eccentric orbits, as a result of projection onto the observational plane. Assuming that they are not dark matter dominated, it follows that the Galactic dSph satellites with s > 6 km s-1 should have orbital eccentricities of e > 0.5. Some remnants have substructure along the line of sight that may be apparent in the morphology of the horizontal branch.

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.

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.

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.