  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.
