Most stars, including the Sun, are born in clusters of varying size.  The most massive of these, globular clusters, with more than a hundred thousand to a million stars, appear to have properties that are distinct from smaller clusters.  In particular, the stars in them have varying elemental abundances, in contrast to the uniform abundances found in less massive clusters. We hypothesized that the varying abundances occur because the most massive clusters form from assembly of multiple subclusters that each evolve independently at early times.

To test this hypothesis, we used a software framework called Torch, built on the Astrophysical Multipurpose Software Environment.  This environment allows multiple simulation codes to be run together and pass needed information to each other on a timestep by timestep basis.  We used this capability to connect a code that models magnetized gas dynamics using an adaptive grid to codes that model stellar dynamics with an N-body algorithm and stellar evolution using scaling relations.  This grant supported modifications to Torch to allow simulation of clouds a million times the mass of the Sun with over a hundred thousand stars.  These included use of an improved N-body code that combines direct gravity solutions at short distances with an approximate tree solution at long distances and an algorithmic slowdown routine to model binaries, as well as restrictions on the mass of stars whose ionizing radiation we model and on the minimum mass of star that we follow.

Thirty-five refereed papers have been supported by this grant, with another one in press, and four more under review.  The most relevant result for this grant is that large star clusters indeed do not form monolithically from spherically symmetric gas clouds.  Instead, turbulent flows driven by the gravitational collapse of gas clouds and by radiative heating and stellar winds from massive stars form regions of higher density.  These high density regions collapse into subclusters, which then fall together to form clusters resembling the ones seen in observations billions of years after their formation.

We find that star formation proceeds in these clusters until heating and winds raise the pressure of the collapsing gas sufficiently to prevent further collapse.  The required pressure depends on the depth of the gravitational potential well of the cloud, and thus the mass of the cloud.  As a result, the smallest clouds that we consider, with masses of around ten thousand solar masses, have star formation efficiencies of around 30%, while the most massive clouds that we simulated reached extremely high star formation efficiencies of more than 80%.  In all cases, subclusters formed and merged to form the final massive cluster, producing observed dynamics such as runaway stars in specific directions.  

We hypothesize that the star formation efficiencies are higher than observed in the most massive clusters because of our assumption of spherical initial conditions.  Therefore we have developed the technology in Torch to import clouds with more realistic filamentary initial conditions from full galaxy simulations to examine the star formation efficiencies of these morphologies, which will be applied in future work.

Ancillary work supported by this grant studied a wide range of topics related to the assembly of cluster-forming clouds in galaxies, as well as the magnetic fields threading them.  Star-by-star models of galaxies from early cosmological history to the present day were also published.

This grant supported work by the PI on planetarium shows at the Hayden Planetarium reaching over a million people per year; teaching by the PI of both numerical astrophysics and space science for high school teachers; international collaborations involving Germany, the Netherlands, China, Finland, Sweden, Kazakhstan, and Canada; and advising of undergraduate research students from underrepresented groups.

Last Modified: 11/16/2024
Modified by: Mordecai-Mark Mac Low