A multitransition molecular line study of inward motions towards massive star-forming cores

A multitransition 3-mm molecular line single pointing and mapping survey was carried out towards 29 massive star-forming cores in order to search for the signature of inward motions. Up to seven different transitions, optically thick lines HCO⁺(1-0), CS(2-1), HNC(1-0), HCN(1-0) and ¹²CO(1-0), and optically thin lines C¹⁸O(1-0) and ¹³CO(1-0) were observed towards each source. The normalized velocity differences (     ) between the peak velocities of optically thick lines and optically thin line C¹⁸O(1-0) for each source were derived. Prominent inward motions are probably present in either HCO⁺(1-0) or CS(2-1) or HNC(1-0) observations in most sources. Our observations show that there is a significant difference in the incidence of blueshifted asymmetric line profiles between CS(2-1) and HCO⁺(1-0). The HCO⁺(1-0) shows the highest occurrence of obvious asymmetric features, perhaps owing to different optical depth between CS(2-1) and HCO⁺(1-0). HCO⁺(1-0) appears to be the best inward motion tracer. The mapping observations of multiple line transitions enable us to identify six strong infall candidates: G123.07-6.31, W75(OH), S235N, CEP-A, W3(OH) and NGC 7538. The infall signature is extended up to a linear scale  >0.2 pc  .     

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.     

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.     

The approach to collapse of molecular clouds

The dense molecular cloud cores that form stars, like other self-gravitating objects, undergo bulk oscillations. Just at the point of gravitational instability, their fundamental oscillation mode has zero frequency. We study, using perturbation theory, the evolution of a spherical cloud that possesses such a frozen mode. We find that the cloud undergoes a prolonged epoch of subsonic, accelerating contraction. This slow contraction occurs whether the cloud is initially inflated or compressed by the oscillation. The subsonic motion described here could underlie the spectral infall signature observed in many starless dense cores.     

The origin of the initial mass function and its dependence on the mean Jeans mass in molecular clouds

We investigate the dependence of stellar properties on the mean thermal Jeans mass in molecular clouds. We compare the results from the two largest hydrodynamical simulations of star formation to 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 except for the radii of the clouds, which are chosen so that the mean densities and mean thermal Jeans masses of the clouds differ by factors of 9 and 3, respectively.
We find that the denser cloud, with the lower mean thermal Jeans mass, produces a higher proportion of brown dwarfs and has a lower characteristic (median) mass of the stars and brown dwarfs. This dependence of the initial mass function (IMF) on the density of the cloud may explain the observation that the Taurus star-forming region appears to be deficient in brown dwarfs when compared with the Orion Trapezium cluster. The new calculation also produces wide binaries (separations >20 au), one of which is a wide binary brown dwarf system.
Based on the hydrodynamical calculations, we develop a simple accretion/ejection model for the origin of the IMF. In the model, all stars and brown dwarfs begin with the same mass (set by the opacity limit for fragmentation) and grow in mass until their accretion is terminated stochastically by their ejection from the cloud through dynamically interactions. The model predicts that the main variation of the IMF in different star-forming environments should be in the location of the peak (due to variations in the mean thermal Jeans mass of the cloud) and in the substellar regime. However, the slope of the IMF at high masses may depend on the dispersion in the accretion rates of protostars.     

Accretion and dynamical interactions in small-N star-forming clusters: N= 5

We present results from high-resolution hydrodynamical simulations that explore the effects of small-scale clustering in star-forming regions. A large ensemble of small- N clusters with five stellar seeds have been modelled and the resulting properties of stars and brown dwarfs statistically derived and compared with observational data.
Close dynamical interactions between the protostars and competitive accretion driven by the cloud collapse are shown to produce a distribution of final masses that is bimodal, with most of the mass residing in the binary components. When convolved with a suitable core mass function, the final distribution of masses resembles the observed initial mass function, in both the stellar and substellar regimes. Binaries and single stars are found to constitute two kinematically distinct populations, with about half of the singles attaining velocities ≥2 km s⁻¹, which might deprive low-mass star-forming regions of their lightest members in a few crossing times. The eccentricity distribution of binaries and multiples is found to follow a distribution similar to that of observed long-period (uncircularized) binaries.
The results obtained support a mechanism in which a significant fraction of brown dwarfs form under similar circumstances as those of normal stars but are ejected from the common envelope of unstable multiple systems before their masses exceed the hydrogen burning limit. We predict that many close binary stars should have wide brown dwarf companions. Brown dwarfs, and, in general, very low-mass stars, would be rare as pure binary companions. The binary fraction should be a decreasing function of primary mass, with low-mass or substellar primaries being scarce. Where such binaries exist, they are expected either to be close enough (semimajor axis ∼10 au) to survive strong interactions with more massive binaries or to be born in very small molecular cloud cores.     

Star formation in unbound giant molecular clouds: the origin of OB associations?

We investigate the formation of star clusters in an unbound giant molecular cloud, where the supporting kinetic energy is twice as large as the cloud's self-gravity. This cloud manages to form a series of star clusters and disperse, all within roughly two crossing times (10 Myr), supporting recent claims that star formation is a rapid process. Simple assumptions about the nature of the star formation occurring in the clusters allows us to place an estimate for the star formation efficiency at about 5–10 per cent, consistent with observations. We also propose that unbound clouds can act as a mechanism for forming OB associations. The clusters that form in the cloud behave as OB subgroups. These clusters are naturally expanding from one another due to the unbound nature of the flows that create them. The properties of the cloud we present here are consistent with those of classic OB associations.     

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.     

Dust dynamics in dense molecular cores

We show that in a quiescent, dense pre-stellar core, exposed to the average interstellar radiation field, radiation pressure can cause the dust to migrate inwards, relative to the gas, on a time-scale of a few megayears – and faster if the radiation field is stronger than average. This has two potentially important effects.
First, there is an increase in the abundance of dust relative to gas in the inner parts of the core, and hence also in the efficiency of gas-cooling by dust. The increased cooling efficiency predisposes these regions to dynamical collapse and star formation. Additionally, it predisposes them to fragmentation, particularly if – as seems likely – the dust enhancements are stochastic and inhomogeneous, due to anisotropy of the incident radiation field and/or to directing of the migration by the local magnetic field. It also increases the metallicities of the resulting stars, and hence presumably the likelihood of planet formation in their accretion discs.
Secondly, there is a steepening of the optical-depth profile, especially at those impact parameters b where the visual optical depth through the core   τ _t∼1  . Since the observational evidence for steep optical-depth profiles in the outer envelopes of some pre-stellar cores (specifically   τ _t∝ b ^{- β}   , with   β ≳2)  constrains only the dust column density, this leaves open the possibility that the gas has a shallower column-density profile.