How black holes accrete surrounding matter is a fundamental yet unsolved question in astrophysics. It is generally believed that matter is absorbed into black holes via accretion disks, the state of which depends primarily on the mass-accretion rate. When this rate approaches the critical rate (the Eddington limit), thermal instability is supposed to occur in the inner disk, causing repetitive patterns of large-amplitude X-ray variability (oscillations) on timescales of minutes to hours. In fact, such oscillations have been observed only in sources with a high mass-accretion rate, such as GRS 1915+105 (refs 2, 3). These large-amplitude, relatively slow timescale, phenomena are thought to have physical origins distinct from those of X-ray or optical variations with small amplitudes and fast timescales (less than about 10 seconds) often observed in other black-hole binaries-for example, XTE J1118+480 (ref. 4) and GX 339-4 (ref. 5). Here we report an extensive multi-colour optical photometric data set of V404 Cygni, an X-ray transient source containing a black hole of nine solar masses (and a companion star) at a distance of 2.4 kiloparsecs (ref. 8). Our data show that optical oscillations on timescales of 100 seconds to 2.5 hours can occur at mass-accretion rates more than ten times lower than previously thought. This suggests that the accretion rate is not the critical parameter for inducing inner-disk instabilities. Instead, we propose that a long orbital period is a key condition for these large-amplitude oscillations, because the outer part of the large disk in binaries with long orbital periods will have surface densities too low to maintain sustained mass accretion to the inner part of the disk. The lack of sustained accretion--not the actual rate--would then be the critical factor causing large-amplitude oscillations in long-period systems.

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, M., Nesvorný, D. [2010].

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We studied a sample of 93 asteroid pairs, i.e., pairs of genetically related asteroids that are on highly similar heliocentric orbits. We estimated times elapsed since separation of pair members (i.e., pair age) that are between 7 × 10 3 yr and a few 10 6 yr. With photometric observations, we derived the rotation periods P 1 for all the primaries (i.e., the larger members of asteroid pairs) and a sample of secondaries (the smaller pair members). We derived the absolute magnitude differences of the studied asteroid pairs that provide their mass ratios q. For a part of the studied pairs, we refined their WISE geometric albedos and collected or estimated their taxonomic classifications. For 17 asteroid pairs, we also determined their pole positions. In two pairs where we obtained the spin poles for both pair components, we saw the same sense of rotation for both components and constrained the angles between their original spin vectors at the time of their separation. We found that the primaries of 13 asteroid pairs in our sample are actually binary or triple systems, i.e., they have one or two bound, orbiting secondaries (satellites). As a by-product, we found also 3 new young asteroid clusters (each of them consisting of three known asteroids on highly similar heliocentric orbits). We compared the obtained asteroid pair data with theoretical predictions and discussed their implications. We found that 86 of the 93 studied asteroid pairs follow the trend of primary rotation period vs mass ratio that was found by Pravec et al. (2010). Of the 7 outliers, 3 appear insignificant (may be due to our uncertain or incomplete knowledge of the three pairs), but 4 are high mass ratio pairs that were unpredicted by the theory of asteroid pair formation by rotational fission. We discuss a (remotely) possible way that they could be created by rotational fission of flattened parent bodies followed by re-shaping of the formed components. The 13 asteroid pairs with binary primaries are particularly interesting systems that place important constraints on formation and evolution of asteroid pairs. We present two hypotheses for their formation: The asteroid pairs having both bound and unbound secondaries could be "failed asteroid clusters", or they could be formed by a cascade primary spin fission process. Further studies are needed to reveal which of these two hypotheses for formation of the paired binary systems is real.

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