Simulating star formation in molecular cores

We explore, by means of a large ensemble of SPH simulations, how the level of turbulence affects the collapse and fragmentation of a star-forming core. All our simulated cores have the same mass ( $5.4 ~M_\odot$), the same initial density profile (chosen to fit observations of L1544), and the same barotropic equation of state, but we vary (a) the initial level of turbulence (as measured by the ratio of turbulent to gravitational energy, $\alpha_{\rm turb} \equiv U_{\rm turb}/\vert\Omega\vert = 0,\,0.01,\,0.025,\, 0.05,\,0.10\;{\rm and}\;0.25$ ) and (b), for fixed $\alpha_{\rm turb}$, the details of the initial turbulent velocity field (so as to obtain good statistics).\ud \ud A low level of turbulence ( $\alpha_{\rm turb} \sim 0.05$) suffices to produce multiple systems, and as $\alpha_{\rm turb}$ is increased, the number of objects formed and the companion frequency both increase. The mass function is bimodal, with a flat low-mass segment representing single objects ejected from the core before they can accrete much, and a Gaussian high-mass segment representing objects which because they remain in the core grow by accretion and tend to pair up in multiple systems.\ud \ud The binary statistics reported for field G-dwarfs by Duquennoy & Mayor (1991, A&A, 248, 485) are only reproduced with $\alpha_{\rm turb} \sim 0.05$. For much lower values of $\alpha_{\rm turb}$ ( $\la $0.025), insufficient binaries are formed. For higher values of $\alpha_{\rm turb}$ ( $\ga $0.10), there is a significant sub-population of binaries with small semi-major axis and large mass-ratio (i.e. close binaries with components of comparable mass). This sub-population is not present in Duquennoy & Mayor's sample, although there is some evidence for it in the pre-Main Sequence population of Taurus analyzed by White & Ghez (2001, ApJ, 556, 265). It arises because with larger $\alpha_{\rm turb}$, more low-mass objects are formed, and so there is more scope for the binaries remaining in the core to be hardened by ejecting these low-mass objects. Hard binaries thus formed then tend to grow towards comparable mass by competitive accretion of material with relatively high specific angular momentum.