Comments on Gravoturbulent Star Formation

Understanding the star formation process is central to much of modern astrophysics. Stellar birth is intimately linked to the dynamical behavior of the parental gas cloud. Gravoturbulent fragmentation determines where and when protostellar cores form, and how they contract and grow in mass via accretion from the surrounding cloud material to build up stars. Supersonic turbulence can provide support against gravitational collapse on global scales, whereas at the same time it produces localized density enhancements that allow for collapse on small scales. The efficiency and timescale of stellar birth in Galactic molecular clouds strongly depend on the properties of the interstellar turbulent velocity field, with slow, inefficient, isolated star formation being a hallmark of turbulent support, and fast, efficient, clustered star formation occurring in its absence.     

Hot stars in old stellar populations: a continuing need for intermediate ages

We present numerical investigations into the formation of massive stars from turbulent cores of density structure  ρ∝ r ^−1.5  . The results of five hydrodynamical simulations are described, following the collapse of the core, fragmentation and the formation of small clusters of protostars. We generate two different initial turbulent velocity fields corresponding to power-law spectra   P ∝ k ⁻⁴  and   P ∝ k ^−3.5  , and we apply two different initial core radii. Calculations are included for both completely isothermal collapse, and a non-isothermal equation of state above a critical density  (10⁻¹⁴ g cm⁻³)  . Our calculations reveal the preference of fragmentation over monolithic star formation in turbulent cores. Fragmentation was prevalent in all the isothermal cases. Although disc fragmentation was largely suppressed in the non-isothermal runs due to the small dynamic range between the initial density and the critical density, our results show that some fragmentation still persisted. This is inconsistent with previous suggestions that turbulent cores result in the formation of a single massive star. We conclude that turbulence cannot be measured as an isotropic pressure term.     

Fragmentation and Structure Formation

I present an overview of the hierarchy of structures existing in the interstellar medium (ISM) and the possible mechanisms that cause the fragmentation of one level into the next, with the formation of stars as its last step. Within this framework, I then give an overview of the contributions to this session. Numerical work addresses, at the largest scales, the shaping and formation of structures in the ISM through turbulence driven by stellar energy injection, and the resulting star formation rate as a function of mean density. At the scales of molecular clouds, results comparing observational and numerical data on the density and velocity structure of turbulence-produced cores, as well as their mass spectra, are summarized, together with existing theories of core and star formation controlled by the turbulence. Observationally, an attempt to discriminate between the standard and turbulent models of star formation is presented, finding inconclusive results, but suggesting that both turbulence and the magnetic field are dynamically important in molecular clouds and their cores. Finally, various determinations of the magnetic field strength and geometry are also presented.     

Random fragmentation of turbulent molecular clouds lying in the central region of giant galaxies

A stochastic model of fragmentation of molecular clouds has been developed for studying the resulting Initial Mass Function (IMF) where the number of fragments, inter-occurrence time of fragmentation, masses and velocities of the fragments are random variables. Here two turbulent patterns of the velocities of the fragments have been considered, namely, Gaussian and Gamma distributions. It is found that for Gaussian distribution of the turbulent velocity, the IMFs are shallower in general compared to Salpeter mass function. On the contrary, a skewed distribution for turbulent velocity leads to an IMF which is much closer to Salpeter mass function. The above result might be due to the fact that strong driving mechanisms e.g. shocks, arising out of a big explosion occurring at the centre of the galaxy or due to big number of supernova explosions occurring simultaneously in massive parent clouds during the evolution of star clusters embedded into them are responsible for stripping out most of the gas from the clouds. This inhibits formation of massive stars in large numbers making the mass function a steeper one.     

The formation of brown dwarfs

We review four mechanisms for forming brown dwarfs: (i) turbulent fragmentation (producing very low‐mass prestellar cores); (ii) gravitational instabilities in discs; (iii) dynamical ejection of stellar embryos from their placental cores; and (iv) photo‐erosion of pre‐existing cores in HII regions. We argue (a) that these are simply the mechanisms of low‐mass star formation , and (b) that they are not mutually exclusive. If, as seems possible, all four mechanisms operate in nature, their relative importance may eventually be constrained by their ability to reproduce the binary statistics of brown dwarfs, but this will require fully 3‐D radiative magneto‐hydrodynamic simulations. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Photoionizing feedback in star cluster formation

We present the first ever hydrodynamic calculations of star cluster formation that incorporate the effect of feedback from ionizing radiation. In our simulations, the ionizing source forms in the cluster core at the intersection of several dense filaments of inflowing gas. We show that these filaments collimate ionized outflows and suggest such an environmental origin for at least some observed outflows in regions of massive star formation. Our simulations show both positive feedback (i.e. promotion of star formation in neutral gas compressed by expanding H  ii regions) and negative feedback (i.e. suppression of the accretion flow in to the central regions). We show that the volume filling factor of ionized gas is very different in our simulations from the result from the case where the central source interacted with an azimuthally smoothed gas density distribution. As expected, gas density is the key parameter in determining whether or not clusters are unbound by photoionizing radiation. Nevertheless, we find – on account of the acceleration of a small fraction of the gas to high velocities in the outflows – that the deposition in the gas of an energy that exceeds the binding energy of the cluster is not a sufficient criterion for unbinding the bulk of the cluster mass.     

Star formation in galaxies along the Pisces-Cetus Supercluster filaments

We investigate the variation of current star formation in galaxies as a function of distance along three supercluster filaments, each joining pairs of rich clusters, in the Pisces-Cetus supercluster, which is part of the two-degree Field Galaxy Redshift Survey (2dFGRS). We find that even though there is a steady decline in the rate of star formation, as well as in the fraction of star-forming galaxies, as one approaches the core of a cluster at an extremity of such a filament, there is an increased activity of star formation in a narrow distance range between 3 and  4  h ⁻¹₇₀ Mpc  , which is 1.5–2 times the virial radius of the clusters involved. This peak in star formation is seen to be entirely due to the dwarf galaxies  (−20 < M _B ≤−17.5)  . The position of the peak does not seem to depend on the velocity dispersion of the nearest cluster, undermining the importance of the gravitational effect of the clusters involved. We find that this enhancement in star formation occurs at the same place for galaxies which belong to groups within these filaments, while group members elsewhere in the 2dFGRS do not show this effect. We conclude that the most likely mechanism for this enhanced star formation is galaxy–galaxy harassment, in the crowded infalling region of rich clusters at the extremities of filaments, which induces a burst of star formation in galaxies, before they have been stripped of their gas in the denser cores of clusters. The effects of strangulation in the cores of clusters, as well as excess star formation in the infalling regions along the filaments, are more pronounced in dwarfs since they more vulnerable to the effects of strangulation and harassment than giant galaxies.     

Fragmentation in molecular clouds and its connection to the IMF

We present an analysis of star-forming gas cores in a smooth particle hydrodynamics simulation of a giant molecular cloud. We identify cores using their deep potential wells. This yields a smoother distribution with clearer boundaries than density. Additionally, this gives an indication of future collapse, as bound potential cores (p-cores) represent the earliest stages of fragmentation in molecular clouds. We find that the mass function of the p-cores resembles the stellar initial mass function and the observed clump mass function, although p-core masses  (∼0.7 M_⊙)  are smaller than typical density clumps. The bound p-cores are generally subsonic, have internal substructure and are only quasi-spherical. We see no evidence of massive bound cores supported by turbulence. We trace the evolution of the p-cores forward in time, and investigate the connection between the original p-core mass and the stellar mass that formed from it. We find that there is a poor correlation, with considerable scatter suggesting accretion on to the core is dependent on more factors than just the initial core mass. During the accretion process the p-cores accrete from beyond the region first bound, highlighting the importance of the core environment to its subsequent evolution.     

Collapsing index: a new method to identify star-forming cores based on ALMA images

Stars form through the gravitational collapse of molecular cloud cores.Before collapsing,the cores are supported by thermal pressure and turbulent motions.A question of critical importance for the understanding of star formation is how to observationally discern whether a core has already initiated gravitational collapse or is still in hydrostatic balance.The canonical method to identify gravitational collapse is based on the observed radial density profile,which would change from Bonnor-Ebert type toward power laws as the core collapses.In practice,due to the projection effect,the resolution limit and other caveats,it has been difficult to directly reveal the dynamical status of cores,particularly in massive star forming regions.We here propose a novel,straightforward diagnostic,namely,the collapsing index(CI),which can be modeled and calculated based on the radial profile of the line width of dense gas.A meaningful measurement of CI requires spatially and spectrally resolved images of optically thin and chemically stable dense gas tracers.ALMA observations are making such data sets increasingly available for massive star forming regions.Applying our method to one of the deepest dense-gas spectral images ever taken toward such a region,namely,the Orion molecular cloud,we detect the dynamical status of selected cores.We observationally distinguished a collapsing core in a massive star forming region from a hydrostatical one.Our approach would help significantly improve our understanding of the interaction between gravity and turbulence within molecular cloud cores in the process of star formation.     

A pressure dependence for bound and unbound clusters

Hierarchical structure in gas and young stars produces clusters in high-density regions where the individual stellar orbits rapidly mix. For a fixed density at the onset of gas collapse (e.g. determined by changes in the ionization equilibrium and grain properties), the efficiency of star formation is automatically high in the high-density regions of giant molecular clouds. Thus, bound cluster formation follows somewhat trivially from hierarchical structure. The density where the efficiency is high enough to produce a bound cluster depends on the dispersion of the density probability distribution function (pdf), decreasing for higher dispersions and making bound cluster formation more likely. Similarly, the mass fraction of star formation in the form of bound clusters increases with the pdf dispersion. Because this dispersion is related to the turbulent Mach number, and also to the interstellar medium pressure and star-formation rate per unit volume, it follows that high-pressure or highly active regions tend to produce bound clusters, while low-pressure and inactive regions tend to produce stars in unbound associations.     

Gas phase processes affecting galactic evolution

Gas processes affecting star formation are reviewed with an emphasis on gravitational and magnetic instabilities as a source of turbulence. Gravitational instabilities are pervasive in a multi-phase medium, even for sub-threshold column densities, suggesting that only an ISM with a pure-warm phase can stop star formation. The instabilities generate turbulence, and this turbulence influences the structure and timing of star formation through its effect on the gas distribution and density. The final trigger for star formation is usually direct compression by another star or cluster. The star formation rate is apparently independent of the detailed mechanisms for star formation, and determined primarily by the total mass of gas in a dense form. If the density distribution function is a log-normal, as suggested by turbulence simulations, then this dense gas mass can be calculated and the star formation rate determined from first principles. The results suggest that only 10^-4 of the ISM mass actively participates in the star formation process and that this fraction does so because its density is larger than 10⁵ cm^-3, at which point several key processes affecting dynamical equilibrium begin to break down. This revised version was published online in August 2006 with corrections to the Cover Date.     

Gas removal and the initial mass function of star clusters

We explore how the expulsion of gas from star-forming cores due to supernova explosions affects the shape of the initial cluster mass function, that is, the mass function of star clusters when cluster infant weight-loss triggered by gas expulsion is over. We demonstrate that if the radii of cluster-forming gas ‘cores’ are roughly constant over the core mass range, as supported by observations, then more massive cores undergo slower gas expulsion. Therefore, for a given star-formation efficiency, more massive cores retain a larger fraction of stars after gas expulsion. The initial cluster mass function may thus substantially differ from the core mass function, with the final shape depending on the star-formation efficiency. A mass-independent star-formation efficiency of about 20% turns a power-law core mass function into a bell-shaped initial cluster mass function, while mass-independent efficiencies of order 40% preserve the shape of the core mass function.     

Oligarchic growth with migration and fragmentation

In the core-accretion model, giant-planet cores form by oligarchic growth from a population of planetesimals prior to the dispersal of the disk gas. Once a core reaches a critical mass of roughly 10 Earth masses, it begins to accrete a gaseous envelope, forming a giant planet. Collisions between planetesimals cause fragmentation. Planetesimal fragments are more easily captured by cores, speeding up growth, but fragments are also lost by radial drift, reducing the total solid mass in the disk. Interaction with the gas causes cores to undergo inward type-I migration. Migration allows a core to accrete planetesimals from a larger region, but migrating cores may be lost if they reach the star. Thus, migration and fragmentation have both a positive and a negative impact on core formation. Here we describe results of new simulations of oligarchic growth that include fragmentation and/or migration. In the absence of migration, cores grow until they reach their isolation mass, which increases with distance from the star, or until the disk gas disperses. Fragmentation increases the maximum core mass by increasing growth rates in the outer disk, allowing objects to reach their isolation mass during the disk lifetime. When migration is present, cores migrate inwards rapidly when they approach 1 Earth mass. Most migrating cores are lost. Migrating cores gain little extra mass since they are passing through regions that have been depleted by earlier generations of cores. For a disk viscosity parameter alpha=1e−3 and planetesimal radius = 10 km, the maximum core mass is roughly 4 and 0.5 Earth masses with/without fragmentation, respectively, with little dependence on the disk mass. Formation and survival of 10-Earth-mass cores, in the presence of migration, requires large alpha (1e−2) and a massive disk (0.1 solar masses). When alpha is large, type-I migration rates decrease rapidly with time, allowing large, late-forming cores to survive. The addition of a stochastic (random-walk) migration component makes little difference to the outcome, provided that stochastic migration affects only cores larger than 0.01 Earth masses. Stochastic migration becomes increasingly important if it also affects lower-mass objects.     

A turbulent MHD model for molecular clouds and a new method of accretion on to star-forming cores

We describe the results of a sequence of simulations of gravitational collapse in a turbulent magnetized region. The parameters are chosen to be representative of molecular cloud material. We find that several protostellar cores and filamentary structures of higher than average density form. The filaments inter connect the high-density cores. Furthermore, the magnetic field strengths are found to correlate positively with the density, in agreement with recent observations. We make synthetic channel maps of the simulations, and show that material accreting on to the cores is channelled along the magnetized filamentary structures. This is compared with recent observations of S106, and shown to be consistent with these data. We postulate that this mechanism of accretion along filaments may provide a means for molecular cloud cores to grow to the point where they become gravitationally unstable and collapse to form stars.     

The formation of galaxy discs

Galaxy disc formation must incorporate the multiphase nature of the interstellar medium. The resulting two-phase structure is generated and maintained by gravitational instability and supernova energy input, which yield a source of turbulent viscosity that is able to compete effectively in the protodisc phase with early angular momentum loss of the baryonic component via dynamical friction in the dark halo. Provided that star formation occurs on the viscous drag time-scale, this mechanism provides a means of accounting for disc sizes and radial profiles. The star formation feedback is self-regulated by turbulent gas pressure limited percolation of the supernova remnant heated hot phase, but can run away in gas-rich protodiscs to generate compact starbursts. A simple analytic model is derived for a Schmidt-like global star formation law in terms of the cold gas volume density.     

Spectral energy distribution modelling of southern candidate massive protostars using the Bayesian inference method

Concatenating data from the millimetre regime to the infrared, we have performed spectral energy distribution (SED) modelling for 227 of the 405 millimetre continuum sources of Hill et al. which are thought to contain young massive stars in the earliest stages of their formation. Three main parameters are extracted from the fits: temperature, mass and luminosity. The method employed was the Bayesian inference, which allows a statistically probable range of suitable values for each parameter to be drawn for each individual protostellar candidate. This is the first application of this method to massive star formation.
The cumulative distribution plots of the SED modelled parameters in this work indicate that collectively, the sources without methanol maser and/or radio continuum associations (MM-only cores) display similar characteristics to those of high-mass star formation regions. Attributing significance to the marginal distinctions between the MM-only cores and the high-mass star formation sample, we draw hypotheses regarding the nature of the MM-only cores, including the possibility that the population itself comprises different types of source, and discuss their role in the formation scenarios of massive star formation. In addition, we discuss the usefulness and limitations of SED modelling and its application to the field. From this work, it is clear that within the valid parameter ranges, SEDs utilising current far-infrared data cannot be used to determine the evolution of massive protostars or massive young stellar objects.     

Predicting the properties of binary stellar systems: the evolution of accreting protobinary systems

We investigate the formation of binary stellar systems. We consider a model where a 'seed' protobinary system forms, via fragmentation, within a collapsing molecular cloud core and evolves to its final mass by accreting material from an infalling gaseous envelope. This accretion alters the mass ratio and orbit of the binary, and is largely responsible for forming the circumstellar and/or circumbinary discs.
Given this model for binary formation, we predict the properties of binary systems and how they depend on the initial conditions within the molecular cloud core. We predict that there should be a continuous trend such that closer binaries are more likely to have equal-mass components and are more likely to have circumbinary discs than wider systems. Comparing our results with observations, we find that the observed mass-ratio distributions of binaries and the frequency of circumbinary discs as a function of separation are most easily reproduced if the progenitor molecular cloud cores have radial density profiles between uniform and 1/ r (e.g., Gaussian) with near-uniform rotation. This is in good agreement with the observed properties of pre-stellar cores. Conversely, we find that the observed properties of binaries cannot be reproduced if the cloud cores are in solid-body rotation and have initial density profiles which are strongly centrally condensed. Finally, in agreement with the radial-velocity searches for extrasolar planets, we find that it is very difficult to form a brown dwarf companion to a solar-type star with a separation ≲10 au, but that the frequency of brown dwarf companions should increase with larger separations or lower mass primaries.     

The dependence of star formation on initial conditions and molecular cloud structure

We investigate the dependence of stellar properties on the initial kinematic structure of the gas in star-forming molecular clouds. We compare the results from two large-scale hydrodynamical simulations of star cluster formation that resolve the fragmentation process down to the opacity limit, the first of which was reported by Bate, Bonnell & Bromm. The initial conditions of the two calculations are identical, but in the new simulation the power spectrum of the velocity field imposed on the cloud initially and allowed to decay is biased in favour of large-scale motions. Whereas the calculation of Bate et al. began with a power spectrum   P ( k ) ∝ k ⁻⁴  to match the Larson scaling relations for the turbulent motions observed in molecular clouds, the new calculation begins with a power spectrum   P ( k ) ∝ k ⁻⁶  .
Despite this change to the initial motions in the cloud and the resulting density structure of the molecular cloud, the stellar properties resulting from the two calculations are indistinguishable. This demonstrates that the results of such hydrodynamical calculations of star cluster formation are relatively insensitive to the initial conditions. It is also consistent with the fact that the statistical properties of stars and brown dwarfs (e.g. the stellar initial mass function) are observed to be relatively invariant within our Galaxy and do not appear to depend on environment.     

On the formation of massive stars

We present a model for the formation of massive ( M ≳10 M⊙) stars through accretion-induced collisions in the cores of embedded dense stellar clusters. This model circumvents the problem of accreting on to a star whose luminosity is sufficient to reverse the infall of gas. Instead, the central core of the cluster accretes from the surrounding gas, thereby decreasing its radius until collisions between individual components become sufficient. These components are, in general, intermediate-mass stars that have formed through accretion on to low-mass protostars. Once a sufficiently massive star has formed to expel the remaining gas, the cluster expands in accordance with this loss of mass, halting further collisions. This process implies a critical stellar density for the formation of massive stars, and a high rate of binaries formed by tidal capture.     

The unusual distribution of molecular gas and star formation in Arp 140

We investigate the atomic and molecular interstellar medium and star formation of NGC 275, the late-type spiral galaxy in Arp 140, which is interacting with NGC 274, an early-type system. The atomic gas (H  i ) observations reveal a tidal tail from NGC 275 which extends many optical radii beyond the interacting pair. The H  i morphology implies a prograde encounter between the galaxy pair approximately ∼1.5 × 10⁸ yr ago. The Hα emission from NGC 275 indicates clumpy irregular star formation, clumpiness which is mirrored by the underlying mass distribution as traced by the K _s-band emission. The molecular gas distribution is striking in its anticorrelation with the H  ii regions. Despite the evolved nature of NGC 275's interaction and its barred potential, neither the molecular gas nor the star formation is centrally concentrated. We suggest that this structure results from stochastic star formation leading to preferential consumption of the gas in certain regions of the galaxy. In contrast to the often-assumed picture of interacting galaxies, NGC 275, which appears to be close to merger, does not display enhanced or centrally concentrated star formation. If the eventual merger is to lead to a significant burst of star formation it must be preceded by a significant conversion of atomic to molecular gas as at the current rate of star formation all the molecular gas will be exhausted by the time the merger is complete.