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 ( 1-2400 AU ) and G ( 28-1590 AU ) primaries in the field and intermediate mass primary binaries in Sco OB2 ( 29-1612 AU ) for mass ratios , q = M _ { 2 } / M _ { 1 } , 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 .
Finally we note that the KS test gives a \sim 1 % probability of the observed CMRD in the Pleiades and Taurus being consistent with that observed for solar type primaries in the field over comparable primary mass range .
This highlights the value of using CMRDs to understand which star formation events contribute most to the field .