Binary asteroid population. 3. Secondary rotations and elongations

•Data on rotations of 46 binary and triple asteroid systems were collected.•An anti-correlation of secondary synchroneity with orbital eccentricity observed.•Libration angles of synchronous secondaries are less than 20° on most epochs.•A paucity of chaotic rotations among asynchronous secondaries is apparent.•An upper limit on the secondary equatorial axis ratios of 1.5 was found. We collected data on rotations and elongations of 46 secondaries of binary and triple systems among near-Earth, Mars-crossing and small main belt asteroids. 24 were found or are strongly suspected to be synchronous (in 1:1 spin–orbit resonance), and the other 22, generally on more distant and/or eccentric orbits, were found or are suggested to have asynchronous rotations. For 18 of the synchronous secondaries, we constrained their librational angles, finding that their long axes pointed to within 20° of the primary on most epochs. The observed anti-correlation of secondary synchroneity with orbital eccentricity and the limited librational angles agree with the theories by Ćuk and Nesvorný (Ćuk, M., Nesvorný, D. [2010]. Icarus 207, 732–743) and Naidu and Margot (Naidu, S.P., Margot, J.-L. [2015]. Astron. J. 149, 80). A reason for the asynchronous secondaries being on wider orbits than synchronous ones may be longer tidal circularization time scales at larger semi-major axes. The asynchronous secondaries show relatively fast spins; their rotation periods are typically