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How black holes accrete surrounding matter is a fundamental, yet unsolvedquestion in astrophysics. It is generally believed that matter is absorbed intoblack holes via accretion disks, the state of which depends primarily on themass-accretion rate. When this rate approaches the critical rate (the Eddingtonlimit), thermal instability is supposed to occur in the inner disc, causingrepetitive patterns of large-amplitude X-ray variability (oscillations) ontimescales of minutes to hours. In fact, such oscillations have been observedonly in sources with a high mass accretion rate, such as GRS 1915+105. Theselarge-amplitude, relatively slow timescale, phenomena are thought to havephysical origins distinct from X-ray or optical variations with smallamplitudes and fast ($\lesssim$10 sec) timescales often observed in other blackhole binaries (e.g., XTE J1118+480 and GX 339-4). Here we report an extensivemulti-colour optical photometric data set of V404 Cygni, an X-ray transientsource containing a black hole of nine solar masses (and a conpanion star) at adistance of 2.4 kiloparsecs. Our data show that optical oscillations ontimescales of 100 seconds to 2.5 hours can occur at mass-accretion rates morethan ten times lower than previously thought. This suggests that the accretionrate is not the critical parameter for inducing inner-disc instabilities.Instead, we propose that a long orbital period is a key condition for theselarge-amplitude oscillations, because the outer part of the large disc inbinaries with long orbital periods will have surface densities too low tomaintain sustained mass accretion to the inner part of the disc. The lack ofsustained accretion -- not the actual rate -- would then be the critical factorcausing large-amplitude oscillations in long-period systems.

Repetitive Patterns in Rapid Optical Variations in the Nearby Black-hole Binary V404 Cygni