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.

Continuing the project described by Kato et al. (2009), we collected times of superhump maxima for 128 SU UMa-type dwarf novae observed mainly during the 2015-2016 season and characterized these objects. The data have improved the distribution of orbital periods, the relation between the orbital period and the variation of superhumps, the relation between period variations and the rebrightening type in WZ Sge-type objects. Coupled with new measurements of mass ratios using growing stages of superhumps, we now have a clearer and statistically greatly improved evolutionary path near the terminal stage of evolution of cataclysmic variables. Three objects (V452 Cas, KK Tel, ASASSN-15cl) appear to have slowly growing superhumps, which is proposed to reflect the slow growth of the 3:1 resonance near the stability border. ASASSN-15sl, ASASSN-15ux, SDSS J074859.55+312512.6 and CRTS J200331.3−284941 are newly identified eclipsing SU UMa-type (or WZ Sge-type) dwarf novae. ASASSN-15cy has a short (∼0.050 d) superhump period and appears to belong to EI Psc-type objects with compact secondaries having an evolved core. ASASSN-15gn, ASASSN-15hn, ASASSN-15kh and ASASSN-16bu are candidate period bouncers with superhump periods longer than 0.06 d. We have newly obtained superhump periods for 79 objects and 13 orbital periods, including periods from early superhumps. In order that the future observations will be more astrophysically beneficial and rewarding to observers, we propose guidelines how to organize observations of various superoutbursts.

Continuing the project described by Kato et al. (2009, PASJ, 61, S395), we collected times of superhump maxima for 86 SU UMa-type dwarf novae, mainly observed during the 2011–2012 season. We confirmed general trends recorded in our previous studies, such as the relation between period derivatives and orbital periods. There are some systems showing positive period derivatives despite the long orbital period. We observed the 2011 outburst of the WZ Sge-type dwarf nova BW Scl, and recorded an $ O$$-$$ C$ diagram similar to those of previously known WZ Sge-type dwarf novae. The WZ Sge-type dwarf nova OT J184228.1$ +$ 483742 showed an unusual pattern of double outbursts composed of an outburst with early superhumps and one with ordinary superhumps. We propose an interpretation that a very small growth rate of the 3:1 resonance due to an extremely low mass-ratio led to quenching the superoutburst before the ordinary superhump appeared. We systematically studied ER UMa-type dwarf novae, and found that V1159 Ori showed positive superhumps similar to ER UMa in the 1990s. The recently recognized ER UMa-type object BK Lyn dominantly showed negative superhumps, and its behavior was very similar to the present-day state of ER UMa. The pattern of period variations in AM CVn-type objects was very similar to that of short-period hydrogen-rich SU UMa-type dwarf novae, making them a helium analogue of hydrogen-rich SU UMa-type dwarf novae. SBS 1108$ +$ 574, a peculiar hydrogen-rich dwarf nova below the period minimum, showed a very similar pattern of period variations to those of short-period SU UMa-type dwarf novae. The mass-ratio derived from the detected orbital period suggests that this secondary is a somewhat evolved star whose hydrogen envelope was mostly stripped during the mass-exchange. CC Scl, MASTER OT J072948.66$ +$ 593824.4, and OT J173516.9$ +$ 154708 showed only low-amplitude superhumps with complex profiles. These superhumps are likely to be a combination of two closely separated periods.

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Continuing the project described by Kato et al. (2009, PASJ, 61, S395), we collected times of superhump maxima for 127 SU UMa-type dwarf novae observed mainly during the 2016–2017 season and characterized these objects. We provide updated statistics of the relation between the orbital period and the variation of superhumps, the relation between period variations and the rebrightening type in WZ Sge-type objects. We obtained the period minimum of 0.05290(2) d and confirmed the presence of the period gap above the orbital period ∼0.09 d. We note that four objects (NY Her, 1RXS J161659.5+620014, CRTS J033349.8−282244, and SDSS J153015.04+094946.3) have supercycles shorter than 100 d but show infrequent normal outbursts. We consider that these objects are similar to V503 Cyg, whose normal outbursts are likely suppressed by a disk tilt. These four objects are excellent candidates to search for negative superhumps. DDE 48 appears to be a member of ER UMa-type dwarf novae. We identified a new eclipsing SU UMa-type object, MASTER OT J220559.40−341434.9. We observed 21 WZ Sge-type dwarf novae during this interval and report 18 of them in this paper. Among them, ASASSN-16js is a good candidate for a period bouncer. ASASSN-16ia showed a precursor outburst for the first time in a WZ Sge-type superoutburst. ASASSN-16kg, CRTS J000130.5+050624, and SDSS J113551.09+532246.2 are located in the period gap. We have newly obtained 15 orbital periods, including periods from early superhumps.