Binary Formation Mechanisms: Constraints from the Companion Mass Ratio
  Distribution
  We present a statistical comparison of the mass ratio distribution of
companions, as observed in different multiplicity surveys, to the most recent
estimate of the single object mass function (Bochanski et al. 2010). The main
goal of our analysis is to test whether or not the observed companion mass
ratio distribution (CMRD) as a function of primary star mass and star formation
environment is consistent with having been drawn from the field star IMF. We
consider samples of companions for M dwarfs, solar type and intermediate mass
stars, both in the field as well as clusters or associations, and compare them
with populations of binaries generated by random pairing from the assumed IMF
for a fixed primary mass. With regard to the field we can reject the hypothesis
that the CMRD was drawn from the IMF for different primary mass ranges: the
observed CMRDs show a larger number of equal-mass systems than predicted by the
IMF. This is in agreement with fragmentation theories of binary formation. For
the open clusters {\alpha} Persei and the Pleiades we also reject the IMF
random- pairing hypothesis. Concerning young star-forming regions, currently we
can rule out a connection between the CMRD and the field IMF in Taurus but not
in Chamaeleon I. Larger and different samples are needed to better constrain
the result as a function of the environment. We also consider other companion
mass functions (CMF) and we compare them with observations. Moreover the CMRD
both in the field and clusters or associations appears to be independent of
separation in the range covered by the observations. Combining therefore the
CMRDs of M and G primaries in the field and intermediate mass primary binaries
in Sco OB2 for mass ratios, q = M2/M1, from 0.2 to 1, we find that the best
chi-square fit follows a power law dN/dq \propto q^{\beta}, with {\beta} =
-0.50 \pm 0.29, consistent with previous results.
