From binaries to multiples II: hierarchical multiplicity of F and G   dwarfs
  Statistics of hierarchical multiplicity among solar-type dwarfs are studied using the distance-limited sample of 4847 targets presented in the accompanying Paper I. Known facts about binaries (multiplicity fraction 0.46, log-normal period distribution with median period 100yr and logarithmic dispersion 2.4, and nearly uniform mass-ratio distribution independent of the period) are confirmed with a high statistical significance. The fraction of hierarchies with three or more components is 0.13+-0.01, the fractions of targets with n=1,2,3,... components are 54:33:8:4:1. Sub-systems in the secondary components are almost as frequent as in the primary components, but in half of such cases both inner pairs are present. The high frequency of those 2+2 hierarchies (4%) suggests that both inner pairs were formed by a common process. The statistics of hierarchies can be reproduced by simulations, assuming that the field is a mixture coming from binary-rich and binary-poor environments. Periods of the outer and inner binaries are selected recursively from the same log-normal distribution, subject to the stability constraint and accounting for the correlation between inner sub-systems. The simulator can be used to evaluate the frequency of multiple systems with specified parameters. However, it does not reproduce the observed excess of inner periods shorter than 10d, caused by tidal evolution. 
Andrei Tokovinin
astro-ph.SR