Competitive Accretion in Clusters and the IMF

Observations have revealed that most stars are born in clusters. As these clusters typically contain more mass in gas than in stars, accretion can play an important role in determining the final stellar masses. Numerical simulations of gas accretion in stellar clusters have found that the stars compete for the available reservoir of gas. The accretion rates are highly nonuniform and are determined primarily by each star's position in the cluster. Stars in the centre accrete more gas, resulting in initial mass segregation. This competitive accretion naturally results in a mass spectrum and is potentially the dominant mechanism for producing the initial mass function. Furthermore, accretion on to the core of a cluster forces it to shrink, which may result in formation of massive stars through collisions.Comment: Proc. of 33rd ESLAB Symp. "Star Formation from the Small to the Large Scale" (F. Favato, A.A. Laas & A. Wilson Eds, ESA SP-445, 2000). 10 pages, incl. 5 figure

The Formation of Massive Stars through Stellar Collisions

In this review, I present the case for how massive stars may form through stellar collisions. This mechanism requires very high stellar densities, up to 4 orders of magnitude higher than are observed in the cores of dense young clusters. In this model, the required stellar densities arise due to gas accretion onto stars in the cluster core, including the precursers of the massive stars. This forces the core to contract until the stellar densities are sufficiently high for collisions to occur. Gas accretion is also likely to play a major role in determining the distribution of stellar masses in the cluster as well as the observed mass segregation. One of the main advantages of this mechanism is that it explicitly relies on the cluster environment in order to produce the massive stars. It is thus in a position to explain the relation between clustered and massive star formation which is not an obvious outcome of an isolated accretion mechanism. A recent numerical simulation supports this model as the cluster core increases its density by $10^5$ during gas accretion. Approximately 15 stellar collisions occur (with $R_{coll}=1$ au) in the cluster core, making a significant contribution to the mass of the most massive star.Comment: 14 pages, 7 figures. in The earliest phase of massive star formation. ASP Conference Series, P. Crowther E

The formation of close binary systems

A viable solution to the origin of close binary systems, unaccounted for in recent theories, is presented. Fragmentation, occurring at the end of the secondary collapse phase (during which molecular hydrogen is dissociating), can form binary systems with separations less than 1 au. Two fragmentation modes are found to occur after the collapse is halted. The first consists of the fragmentation of a protostellar disc due to rotational instabilities in a protostellar core, involving both an $m=1$ and an $m=2$ mode. This fragmentation mechanism is found to be insensitive to the initial density distribution: it can occur in both centrally condensed and uniform initial conditions. The second fragmentation mode involves the formation of a rapidly rotating core at the end of the collapse phase which is unstable to the axisymmetric perturbations. This core bounces into a ring which quickly fragments into several components. The binary systems thus formed contain less than 1 per cent of a solar mass and therefore will need to accrete most of their final mass if they are to form a binary star system. Their orbital properties will thus be determined by the properties of the accreted matter.Comment: 6 pages, uuencoded compressed postscript file (containing 2 figures

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 nine and three, 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.Comment: 22 pages, 14 figures, accepted for publication in MNRAS. Paper with high-resolution figures and animations available from http://www.astro.ex.ac.uk/people/mbate/ Replacement removes inconsistent definitions of base 10 logarithm

Star Formation in Transient Molecular Clouds

We present the results of a numerical simulation in which star formation proceeds from an initially unbound molecular cloud core. The turbulent motions, which dominate the dynamics, dissipate in shocks leaving a quiescent region which becomes gravitationally bound and collapses to form a small multiple system. Meanwhile, the bulk of the cloud escapes due to its initial supersonic velocities. In this simulation, the process naturally results in a star formation efficiency of 50%. The mass involved in star formation depends on the gas fraction that dissipates sufficient kinetic energy in shocks. Thus, clouds with larger turbulent motions will result in lower star formation efficiencies. This implies that globally unbound, and therefore transient giant molecular clouds (GMCs), can account for the low efficiency of star formation observed in our Galaxy without recourse to magnetic fields or feedback processes. Observations of the dynamic stability in molecular regions suggest that GMCs may not be self-gravitating, supporting the ideas presented in this letter.Comment: 5 pages, 3 figures, accepted for MNRAS as a lette

Spiral arm triggering of star formation

We present numerical simulations of the passage of clumpy gas through a galactic spiral shock, the subsequent formation of giant molecular clouds (GMCs) and the triggering of star formation. The spiral shock forms dense clouds while dissipating kinetic energy, producing regions that are locally gravitationally bound and collapse to form stars. In addition to triggering the star formation process, the clumpy gas passing through the shock naturally generates the observed velocity dispersion size relation of molecular clouds. In this scenario, the internal motions of GMCs need not be turbulent in nature. The coupling of the clouds' internal kinematics to their externally triggered formation removes the need for the clouds to be self-gravitating. Globally unbound molecular clouds provides a simple explanation of the low efficiency of star formation. While dense regions in the shock become bound and collapse to form stars, the majority of the gas disperses as it leaves the spiral arm.Comment: 6 pages, 4 figures: IAU 237, Triggering of star formation in turbulent molecular clouds, eds B. Elmegreen and J. Palou

The Formation of Close Binary Systems by Dynamical Interactions and Orbital Decay

We present results from the first hydrodynamical star formation calculation to demonstrate that close binary stellar systems (separations \lsim 10 AU) need not be formed directly by fragmentation. Instead, a high frequency of close binaries can be produced through a combination of dynamical interactions in unstable multiple systems and the orbital decay of initially wider binaries. Orbital decay may occur due to gas accretion and/or the interaction of a binary with its circumbinary disc. These three mechanisms avoid the problems associated with the fragmentation of optically-thick gas to form close systems directly. They also result in a preference for close binaries to have roughly equal-mass components because dynamical exchange interactions and the accretion of gas with high specific angular momentum drive mass ratios towards unity. Furthermore, due to the importance of dynamical interactions, we find that stars with greater masses ought to have a higher frequency of close companions, and that many close binaries ought to have wide companions. These properties are in good agreement with the results of observational surveys.Comment: Published in MNRAS, 10 pages, 6 figures (5 degraded). Paper with high-resolution figures and animations available from http://www.astro.ex.ac.uk/people/mbat

The Origin of the Initial Mass Function

We review recent advances in our understanding of the origin of the initial mass function (IMF). We emphasize the use of numerical simulations to investigate how each physical process involved in star formation affects the resulting IMF. We stress that it is insufficient to just reproduce the IMF, but that any successful model needs to account for the many observed properties of star forming regions including clustering, mass segregation and binarity. Fragmentation involving the interplay of gravity, turbulence, and thermal effects is probably responsible for setting the characteristic stellar mass. Low-mass stars and brown dwarfs can form through the fragmentation of dense filaments and disks, possibly followed by early ejection from these dense environments which truncates their growth in mass. Higher-mass stars and the Salpeter-like slope of the IMF are most likely formed through continued accretion in a clustered environment. The effects of feedback and magnetic fields on the origin of the IMF are still largely unclear. Lastly, we discuss a number of outstanding problems that need to be addressed in order to develop a complete theory for the origin of the IMF.Comment: PPV conference paper, 16 pages, 11 figur

The Formation Mechanism of Brown Dwarfs

We present results from the first hydrodynamical star formation calculation to demonstrate that brown dwarfs are a natural and frequent product of the collapse and fragmentation of a turbulent molecular cloud. The brown dwarfs form via the fragmentation of dense molecular gas in unstable multiple systems and are ejected from the dense gas before they have been able to accrete to stellar masses. Thus, they can be viewed as `failed stars'. Approximately three quarters of the brown dwarfs form in gravitationally-unstable circumstellar discs while the remainder form in collapsing filaments of molecular gas. These formation mechanisms are very efficient, producing roughly the same number of brown dwarfs as stars, in agreement with recent observations. However, because close dynamical interactions are involved in their formation, we find a very low frequency of binary brown dwarf systems (\lsim 5%) and that those binary brown dwarf systems that do exist must be close \lsim 10 AU. Similarly, we find that young brown dwarfs with large circumstellar discs (radii \gsim 10 AU) are rare ($\approx 5$%).Comment: 5 pages, 2 GIF figures, postscript with figures available at http://www.astro.ex.ac.uk/people/mbat