We conducted a survey of nearby binary systems composed of main sequence stars of spectral types F and G in order to improve our understanding of the hierarchical nature of multiple star systems .
Using Robo-AO , the first robotic adaptive optics instrument , we collected high angular resolution images with deep and well-defined detection limits in the SDSS i ^ { \prime } band .
A total of 695 components belonging to 595 systems were observed .
We prioritized observations of faint secondary components with separations over 10 ^ { \prime \prime } to quantify the still poorly constrained frequency of their sub-systems .
Of the 214 secondaries observed , 39 contain such subsystems ; 19 of those were discovered with Robo-AO .
The selection-corrected frequency of secondary sub-systems with periods from 10 ^ { 3.5 } to 10 ^ { 5 } days is 0.12 \pm 0.03 , the same as the frequency of such companions to the primary .
Half of the secondary pairs belong to quadruple systems where the primary is also a close pair , showing that the presence of sub-systems in both components of the outer binary is correlated .
The relatively large abundance of 2+2 quadruple systems is a new finding , and will require more exploration of the formation mechanism of multiple star systems .
We also targeted close binaries with periods less than 100Â yr , searching for their distant tertiary components , and discovered 17 certain and 2 potential new triples .
In a sub-sample of 241 close binaries , 71 have additional outer companions .
The overall frequency of tertiary components is not enhanced , compared to all ( non-binary ) targets , but in the range of outer periods from 10 ^ { 6 } to 10 ^ { 7.5 } days ( separations on the order of 500Â AU ) , the frequency of tertiary components is 0.16 \pm 0.03 , exceeding by almost a factor of two the frequency of similar systems among all targets ( 0.09 ) .
Measurements of binary stars with Robo-AO allowed us to compute first orbits for 9 pairs and to improve orbits of another 11 pairs .