We present the results of a multiplicity survey of 126 stars spanning ~0.1-3 solar masses in the ~2-Myr-old Chamaeleon I star-forming region, based on adaptive optics imaging with the ESO Very Large Telescope. Our observations have revealed 30 binaries and 6 triples, of which 19 and 4, respectively, are new discoveries. The overall multiplicity fraction we find for Cha I (~30%) is similar to those reported for other dispersed young associations, but significantly higher than seen in denser clusters and the field, for comparable samples. Both the frequency and the maximum separation of Cha I binaries decline with decreasing mass, while the mass ratios approach unity; conversely, tighter pairs are more likely to be equal mass. We confirm that brown dwarf companions to stars are rare, even at young ages at wide separations. Based on follow-up spectroscopy of two low-mass substellar companion candidates, we conclude that both are likely background stars. The overall multiplicity fraction in Cha I is in rough agreement with numerical simulations of cloud collapse and fragmentation, but its observed mass dependence is less steep than predicted. The paucity of higher-order multiples, in particular, provides a stringent constraint on the simulations, and seems to indicate a low level of turbulence in the prestellar cores in Cha I.
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