Comparative statistics and origin of triple and quadruple stars
  The statistics of catalogued quadruple stars consisting of two binaries (hierarchy 2+2) is studied in comparison with triple stars, with respective sample sizes of 81 and 724. Seven representative quadruple systems are discussed in greater detail. The properties of multiple stars do not correspond to the products of dynamical decay of small clusters, hence the N-body dynamics is not the dominant process of their formation. On the other hand, rotationally-driven (cascade) fragmentation possibly followed by migration of inner and/or outer orbits to shorter periods is a promising scenario to explain the origin of triple and quadruple stars. Our main results are: (i) Quadruple systems of Epsilon Lyr type with similar masses and inner periods are common. (ii) The distributions of the inner periods in triple and quadruple stars are similar and bimodal. The inner mass ratios do not correlate with the inner periods. (iii) The statistics of outer periods and mass ratios in triples and quadruples are different. The median outer mass ratio in triples is 0.39 independently of the outer period, which has a smooth distribution. In contrast, the outer periods of 25% quadruples concentrate in the narrow range from 10yr to 100yr, the outer mass ratios of these tight quadruples are above 0.6 and their two inner periods are similar to each other. (iv) The outer and inner mass ratios in triple and quadruple stars are not mutually correlated. (v) The inner and outer orbital angular momenta and periods in triple and quadruple systems with inner periods above 30d show some correlation, the ratio of outer-to-inner periods is mostly comprised between 5 and 10^4. In the systems with small period ratios the directions of the orbital spins are correlated, while in the systems with large ratios they are not. 
A. Tokovinin