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 disc, 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. These large-amplitude, relatively slow timescale, phenomena are thought to have physical origins distinct from X-ray or optical variations with small amplitudes and fast ($lesssim$10 sec) timescales often observed in other black hole binaries (e.g., XTE J1118+480 and GX 339-4). 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 conpanion star) at a distance of 2.4 kiloparsecs. 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-disc 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 disc in binaries with long orbital periods will have surface densities too low to maintain sustained mass accretion to the inner part of the disc. The lack of sustained accretion -- not the actual rate -- would then be the critical factor causing large-amplitude oscillations in long-period systems.
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