Large Star Cluster Formation with Radiative Feedback

Matthew R. Bate

This calculation is a repeat of my 2008 star cluster calculation (published in January 2009) but this time including a realistic equation of state and radiative transfer. The calculation models the collapse and fragmentation of a 500 solar mass cloud, but resolves the opacity limit for fragmentation, discs with radii as small as 1 AU, and binary and multiple star systems. The calculation produces a cluster containing 183 stars and brown dwarfs, including 40 multiple stellar systems (i.e. binaries, triples and quadruples) to allow comparison with stellar observations.

Refereed Scientific Papers

"Stellar, brown dwarf, and multiple star properties from a radiation hydrodynamical simulation of star cluster formation"
Bate, M. R., 2012, MNRAS, 419, 3115-3146. (Or preprint from astro-ph/1110.1092)


Simulation & visualisation by Matthew Bate, University of Exeter unless stated otherwise.

There are two versions of the movie. One uses my typical red-yellow-white colour scheme to visualise the column density through the star-forming cloud. The other uses a black-blue-red-yellow-white colour scheme to visualise the temperature (mass weighted) through the star-forming cloud.

  Column density through the star cluster formation calculation.

Available formats for 33 second animation (15 frames/sec):

Quicktime (10MB, 1280x800, high quality)

  Temperature in the star cluster formation calculation.

Available formats for 33 second animation (15 frames/sec):

Quicktime (3.2MB, 1280x800, high quality)

Copyright: The material on this page is the property of Matthew Bate. Any of my pictures and animations may be used freely for non-profit purposes (such as during scientific talks) as long as appropriate credit is given wherever they appear. Permission must be obtained from me before using them for any other purpose (e.g. pictures for publication in books).

Notes on formats:
Quicktime: Plays directly in Powerpoint on an Apple computer. Can be played under Windows by downloading the FREE Quicktime player from Apple. Some version can be played under Unix/Linux using xanim.

Technical Details

The calculation models the collapse and fragmentation of a 500 solar mass molecular cloud that is 0.8 pc in diameter (approximately 2.6 light-years). At the initial temperature of 10 K with a mean molecular weight of 2.38, this results in an thermal Jeans mass of 1 solar mass. The free-fall time of the cloud is 190,000 years and the simulation covers 285,000 years.

The cloud is given an initial supersonic `turbulent' velocity field in the same manner as Ostriker, Stone & Gammie (2001). We generate a divergence-free random Gaussian velocity field with a power spectrum P(k) \propto k-4, where k is the wave-number. In three-dimensions, this results in a velocity dispersion that varies with distance, lambda, as sigma(lambda) \propto lambda1/2 in agreement with the observed Larson scaling relations for molecular clouds (Larson 1981). This power spectrum is slighly steeper than the Kolmogorov spectrum, P(k)\propto k11/3. Rather, it matches the amplitude scaling of Burgers supersonic turbulence associated with an ensemble of shocks (but differs from Burgers turbulence in that the initial phases are uncorrelated).

The calculation was performed using a parallel three-dimensional smoothed particle hydrodynamics (SPH) code with 35 million particles on the University of Exeter Supercomputer. It took approximately 6,000,000 core-hours running on up to 256 compute cores (16 compute nodes). The SPH code was parallelised using both MPI and OpenMP by M. Bate. The code uses sink particles (Bate, Bonnell & Price 1995) to model condensed objects (i.e. the stars and brown dwarfs). Sink particles are point masses that accrete bound gas that comes within a specified radius of them. This accretion radius is to set 0.5 AU. Binary systems are followed to separations as small as 0.01 AU - closer systems are assumed to merge (but no mergers occur in the calculation here).

High Resolution Still Images and Commentary

High resolution, unannotated (1800x1800 pixel) versions that are suitable for publication are available on request by emailing Matthew Bate at: mbate @

Click on the images below to view medium resolution, annotated (600x600 pixel) versions.

Copyright: Matthew Bate, University of Exeter.