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 _ { turb } \equiv U _ { turb } / | \Omega| = 0 , 0.01 , 0.025 , 0.05 , 0.10 % { and } 0.25 ) and ( b ) , for fixed \alpha _ { turb } , the details of the initial turbulent velocity field ( so as to obtain good statistics ) .

A low level of turbulence ( \alpha _ { turb } \sim 0.05 ) suffices to produce multiple systems , and as \alpha _ { 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 .

The binary statistics reported for field G-dwarfs by Duquennoy & Mayor ( 1991 ) are only reproduced with \alpha _ { turb } \sim 0.05 .
For much lower values of \alpha _ { turb } ( \la 0.025 ) , insufficient binaries are formed .
For higher values of \alpha _ { 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 ) .
It arises because with larger \alpha _ { 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 .