The Statistical Properties of Stars and Their Dependence on Metallicity

Matthew R. Bate

We report the statistical properties of stars and brown dwarfs obtained from four radiation hydrodynamical simulations of star cluster formation, the metallicities of which span a range from 1/100 to 3 times the solar value. Unlike previous similar investigations of the effects of metallicity on stellar properties, these new calculations treat dust and gas temperatures separately and include a thermochemical model of the diffuse interstellar medium. The more advanced treatment of the interstellar medium gives rise to very different gas and dust temperature distributions in the four calculations, with lower metallicities generally resulting in higher temperatures and a delay in the onset of star formation. Despite this, once star formation begins, all four calculations produce stars at similar rates and many of the statistical properties of their stellar populations are difficult to distinguish from each other and from those of observed stellar systems. We do find, however, that the greater cooling rates at high gas densities due to the lower opacities at low metallicities increase the fragmentation on small spatial scales (disc, filament, and core fragmentation). This produces an anti-correlation between the close binary fraction of low-mass stars and metallicity similar to that which is observed, and an increase in the fraction of protostellar mergers at low metallicities. There are also indications that at lower metallicity close binaries may have lower mass ratios and the abundance of brown dwarfs to stars may increase slightly. However, these latter two effects are quite weak and need to be confirmed with larger samples.

Refereed Scientific Papers

"The statistical properties of stars and their dependence on metallicity"
Bate, M. R., 2019, MNRAS, 484, 2341-2361. (Or preprint from astro-ph/1901.03713)

Tables 3 and 4 from the paper are provided electronically in ASCII format. These tables list the stars and brown dwarfs produced by all four of the calculations (their final masses, time of formation, and final accretion rates), and the properties of the multiple systems that exist at the end of the calculations. They can be downloaded as a gzipped tar file.

The dataset consisting of the output and analysis files from the calculations presented in this paper have been placed in the University of Exeter's Open Research Exeter (ORE) repository and can be accessed via the handle: http://hdl.handle.net/10871/35993

Animations

Simulation & visualisation by Matthew Bate.

For each of the four calculations, there are 8 movies.
The first uses my typical red-yellow-white colour scheme to visualise the column density through the star-forming cloud.
Movies 2-4 use a black-blue-red-yellow-white colour scheme to visualise the temperature (mass weighted) through the star-forming cloud. Movie 2 gives gas temperature, Movie 3 gives dust temperature, and Movie 4 gives the temperature of the radiation field generated by the protostars.
Movies 5-7 use the red-yellow-white colour scheme to visualise the mass-weighted chemical abundances of carbon through the clouds. Movie 5 gives the relative abundance of ionised carbon, C+/C. Movie 6 gives the relative abundance of atomic carbon CI/C. Movie 7 gives the relative abundance of gas-phase CO, CO/C, including a prescription for the freeze out of CO at high densities.
Finally, Movie 8 gives a mosaic of panels that show regions 400x400 AU around each protostar that forms in the calculations and survives to the end (i.e. excluding protostars lost in mergers). This type of movie was first published by Bate (2018). These mosaic movies can be used to study the multiple systems that form and are disrupted during the calculations, and the discs that form around the protostars.

On large scales, few differences are apparent in the column density animations (the structure is smoother in clouds with lower metallicity due to the generally warmer gas), but the temperature movies differ substantially from one another.

Click on the images to view the animations (in Quicktime format).

1/100 of solar metallicity (1280x720 pixels)




1/10 of solar metallicity (1280x720 pixels)




Solar metallicity (1280x720 pixels)




3 times solar metallicity (1280x720 pixels)

Copyright: The material on this page is the property of Matthew Bate. Movies and images are released under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Technical Details

The calculations model the collapse and fragmentation of 500 solar mass molecular clouds that are 0.8 pc in diameter (approximately 2.6 light-years). The free-fall time of the cloud is 190,000 years and the simulations cover 228,307 years.

Four calculations were performed which were identical to each other except for their metallicity. The metallicities used were 1/100, 1/10, 1, and 3 times solar metallicity. The calculations employ dust and gas opacities appropriate for their metallicity. They also model gas and dust temperatures separately. A thermochemical model is used that combines radiative transfer with a model for the diffuse interstellar medium (Bate & Keto 2015). The thermochemical model includes heating due to the interstellar radiation field, cosmic rays, and molecular hydrogen formation. It includes cooling due to molecular and atomic line emission, and recombination lines. Collisional thermal coupling between the gas and the dust is also included. The calculations also include a simple chemical model that keeps track of the forms of hydrogen (atomic or molecular) and carbon (carbon monoxide (CO), neutral atomic carbon (CI), and ionised carbon (CII)).

The clouds are 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 lambda^1/2 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 k^11/3. 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 calculations were performed using a parallel three-dimensional smoothed particle hydrodynamics (SPH) code, sphNG, with 35 million particles on the Complexity machine of STFC's DiRAC facility and the University of Exeter Supercomputer. 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 0.03 AU - closer systems are assumed to merge.