What determines the masses of stars, and why do stars form in clusters?

Stars form in massive molecular clouds. The fundamental problem of star formation is how to break up the cloud into bits that are millions of times smaller. It is thought that part of the answer resides in the turbulent formation of clouds, which naturally give rise to smaller-scale dense fluctuations which can then gravitationally collapse. The way in which this fragmentation actually operates is poorly understood, as it depends sensitively on thermal physics, details of initial conditions, etc.

After a (proto)stellar core forms, it can continue to accrete from its surroundings. This process is shown on the left, where we have simulated the fragmentation and collapse of a sheet of gas (seen face-on). “Sink” particles shown here as circles (“stars”) have formed within a large-scale, complex flow whose motions are driven entirely by gravity. The gas collects into filaments, as frequently seen in real star-forming regions. The sinks (stars) tend to collect together into small groups or mini-clusters, because they tend to form together in regions of high density, and because they also tend to fall in toward each other as they accumulate mass.

In these simulations, the sinks (stars) continue to accumulate mass until their environments are depleted. The more massive stars accumulate more mass at the expense of the low-mass objects. This process, termed “competitive accretion” by Bonnell, Bate, and collaborators, results in the development of a power-law tail at high masses, roughly similar to the standard “Salpeter” mass distribution (dotted line in figure at left).

Our simulations of this process are purposely simplified in order that we can understand exactly what is happening, and so that we can build up sufficient statistics to make quantitatively reliable estimates of the upper mass power law slope by running many cases with random initial positions of the seeds. A typical result is shown on the left, where the mass distribution builds up as a function of time, gradually approaching the Salpeter value. Our results thus suggest that the upper mass “initial mass function” is not invariant but tends toward a limiting value which is slightly flatter than Salpeter; and that the slope should correlate with the maximum stellar masses observed.

Research conducted by graduate student Tina Hsu: Competitive Accretion in Sheet Geometry and the Stellar IMF