The Minimum Jeans Mass, Brown Dwarf Companion IMF, and Predictions for   Detection of Y-type Dwarfs
  Cool L- and T-type objects were discovered first as companions to stars in 1988 and 1995, respectively. A certain example of the yet cooler Y-type spectral class (Teff <~ 500K?) has not been seen. Recent infrared imaging observations of stars and brown dwarfs indicate that substellar companions with large semi-major axes and with masses less than the brown dwarf/giant planet dividing line (~13.5 Mj) are rare. Theoretical considerations of Jeans mass fragmentation of molecular clouds are consistent with this minimum mass cutoff and also with the semi-major axis (hundreds of AU) characteristic of the lowest mass imaged companions. As a consequence, Y-class companions with large semi-major axes should be scarce around stars <2Gyr old, and also around substellar primaries of all ages. By focusing on brown dwarf companions to young stellar primaries, it is possible to derive a first estimate of the brown dwarf IMF over the entire range of brown dwarf masses (13 Mj to 79 Mj) -- the number of companion brown dwarfs is proportional to mass to the -1.2+-0.2 power. 
Ben Zuckerman and Inseok Song