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How a black hole accretes matter and how this process is regulated are fundamental but unsolved questions in astrophysics. In transient black-hole binaries, a lot of mass stored in an accretion disk is suddenly drained to the central black hole because of thermal-viscous instability. This phenomenon is called an outburst and is observable at various wavelengths (Frank et al., 2002). During the outburst, the accretion structure in the vicinity of a black hole shows dramatical transitions from a geometrically-thick hot accretion flow to a geometrically-thin disk, and the transition is observed at X-ray wavelengths (Remillard, McClintock, 2006; Done et al., 2007). However, how that X-ray transition occurs remains a major unsolved problem (Dunn et al., 2008). Here we report extensive optical photometry during the 2018 outburst of ASASSN-18ey (MAXI J1820$+$070), a black-hole binary at a distance of 3.06 kpc (Tucker et al., 2018; Torres et al., 2019) containing a black hole and a donor star of less than one solar mass. We found optical large-amplitude periodic variations similar to superhumps which are well observed in a subclass of white-dwarf binaries (Kato et al., 2009). In addition, the start of the stage transition of the optical variations was observed 5 days earlier than the X-ray transition. This is naturally explained on the basis of our knowledge regarding white dwarf binaries as follows: propagation of the eccentricity inward in the disk makes an increase of the accretion rate in the outer disk, resulting in huge mass accretion to the black hole. Moreover, we provide the dynamical estimate of the binary mass ratio by using the optical periodic variations for the first time in transient black-hole binaries. This paper opens a new window to measure black-hole masses accurately by systematic optical time-series observations which can be performed even by amateur observers., Comment: VSOLJ Variable Star Bulletin submitted

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., Comment: Published in Nature on January 7th, 2016