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We observed RZ LMi, which is renowned for its extremely short (∼19 d) supercycle and is a member of a small, unusual class of cataclysmic variables called ER UMa-type dwarf novae, in 2013 and 2016. In 2016, the supercycles of this object substantially lengthened in comparison to the previous measurements to 35, 32, and 60 d for three consecutive superoutbursts. We consider that the object virtually experienced a transition to the nova-like state (permanent superhumper). This observed behavior reproduced the prediction of the thermal-tidal instability model extremely well. We detected a precursor in the 2016 superoutburst and detected growing (stage A) superhumps with a mean period of 0.0602(1) d in 2016 and in 2013. Combined with the period of superhumps immediately after the superoutburst, the mass ratio is not as small as in WZ Sge-type dwarf novae, having orbital periods similar to RZ LMi. By using least absolute shrinkage and selection operator (Lasso) two-dimensional power spectra, we detected possible negative superhumps with a period of 0.05710(1) d. We estimated an orbital period of 0.05792 d, which suggests a mass ratio of 0.105(5). This relatively large mass ratio is even above that of ordinary SU UMa-type dwarf novae, and it is also possible that the exceptionally high mass-transfer rate in RZ LMi may be a result of a stripped secondary with an evolved core in a system evolving toward an AM CVn-type object.

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.

Continued from Kato et al. (2009, PASJ, 61, S395), we collected the times of superhump maxima for 68 SU UMa-type dwarf novae, mainly observed during the 2009–2010 season. The newly obtained data confirmed the basic findings reported in Kato et al. (ibid.): the presence of stages A–C and the predominance of positive period derivatives during stage B in systems with superhump periods shorter than 0.07 d. There was a systematic difference in the period derivatives for the systems with superhump periods longer than 0.075 d between this study and Kato et al. (ibid.). We suggest that this difference was possibly caused by a relative lack of frequently outbursting SU UMa-type dwarf novae in this period regime in the present study. We recorded a strong beat phenomenon during the 2009 superoutburst of IY UMa. A close correlation between the beat period and the superhump period suggests that the changing angular velocity of the apsidal motion of the elliptical disk is responsible for the variation of the superhump periods. We also described three new WZ Sge-type objects with established early superhumps and one with likely early superhumps. We suggest that two systems, VX For and EL UMa, are WZ Sge-type dwarf novae with multiple rebrightenings. The $O-C$variation in OT J213806.6$+$261957 suggests that the frequent absence of rebrightenings in very short-$P_{\rm orb}$objects can be the result of a sustained superoutburst plateau at the epoch when usual SU UMa-type dwarf novae return to quiescence, preceding a rebrightening. We also present a formulation for a variety of Bayesian extensions to traditional period analyses.

We systematically surveyed period variations of superhumps in SU UMa-type dwarf novae based on newly obtained data and past publications. In many systems, the evolution of the superhump period is found to be composed of three distinct stages: an early evolutionary stage with a longer superhump period, a middle stage with systematically varying periods, and a final stage with a shorter, stable superhump period. During the middle stage, many systems with superhump periods of less than 0.08 d show positive period derivatives. We present observational characteristics of these stages and give greatly improved statistics. Contrary to an earlier claim, we found no clear evidence for a variation of period derivatives among different superoutbursts of the same object. We present an interpretation that the lengthening of the superhump period is a result of the outward propagation of an eccentricity wave, which is limited by the radius near the tidal truncation. We interpret that late-stage superhumps are rejuvenated excitation of a 3:1 resonance when superhumps in the outer disk are effectively quenched. The general behavior of the period variation, particularly in systems with short orbital periods, appears to follow a scenario proposed in Kato, Maehara, and Monard (2008, PASJ, 60, L23). We also present an observational summary of WZ Sge-type dwarf novae. Many of them have shown long-enduring superhumps during a post-superoutburst stage having longer periods than those during the main superoutburst. The period derivatives in WZ Sge-type dwarf novae are found to be strongly correlated with the fractional superhump excess, or consequently with the mass ratio. WZ Sge-type dwarf novae with a long-lasting rebrightening or with multiple rebrightenings tend to have smaller period derivatives, and are excellent candidates for those systems around or after the period minimum of evolution of cataclysmic variables.

We report on photometric and spectroscopic observations and analysis of the 2019 superoutburst of TCP J21040470+4631129. This object showed a 9 mag superoutburst with early superhumps and ordinary superhumps, which are the features of WZ Sge-type dwarf novae. Five rebrightenings were observed after the main superoutburst. The spectra during the post-superoutburst stage showed Balmer, He i, and possible sodium doublet features. The mass ratio is derived as 0.0880(9) from the period of the superhump. During the third and fifth rebrightenings, growing superhumps and superoutbursts were observed, which have never been detected during a rebrightening phase among WZ Sge-type dwarf novae with multiple rebrightenings. To induce a superoutburst during the brightening phase, the accretion disk needs to have expanded beyond the 3 : 1 resonance radius of the system again after the main superoutburst. These peculiar phenomena can be explained by the enhanced viscosity and large radius of the accretion disk suggested by the higher luminosity and the presence of late-stage superhumps during the post-superoutburst stage, plus by more mass supply from the cool mass reservoir and/or from the secondary because of the enhanced mass transfer than those of other WZ Sge-type dwarf novae.

Continuing the project described by Kato et al. (2009, PASJ, 61, S395), we collected times of superhump maxima for 102 SU UMa-type dwarf novae observed mainly during the 2017 season, and characterized these objects. WZ Sge-type stars identified in this study are PT And, ASASSN-17ei, ASASSN-17el, ASASSN-17es, ASASSN-17fn, ASASSN-17fz, ASASSN-17hw, ASASSN-17kd, ASASSN-17la, PNV J20205397$+$2508145, and TCP J00332502$-$3518565. We obtained new mass ratios for seven objects using growing superhumps (stage A). ASASSN-17gf is an EI Psc-type object below the period minimum. CRTS J080941.3$+$171528 and DDE 51 are objects in the period gap, and both showed a long-lasting phase of stage A superhumps. We also summarize the recent advances in understanding of SU UMa-type and WZ Sge-type dwarf novae.

We found that the SU UMa-type dwarf nova NY Ser in the period gap [orbital period 0.097558(6) d] showed standstills twice in 2018. This is the first clear demonstration of a standstill occurring between superoutbursts of an SU UMa-type dwarf nova. There was no sign of superhumps during the standstill, and at least one superoutburst directly started from the standstill. This provides strong evidence that the 3:1 resonance was excited during standstills. This phenomenon indicates that the disk radius can grow during standstills. We also deduce that the condition close to the limit of the tidal instability caused early quenching of superoutbursts, which resulted in a substantial amount of matter left in the disk after the superoutburst. We think that substantial matter in the disk in a condition close to the limit of the tidal instability is responsible for standstills (as in the high-mass-transfer system NY Ser) or multiple rebrightenings (as in the low-mass-transfer system V1006 Cyg).

There are several peculiar long-period dwarf-nova-like objects that show rare, low-amplitude outbursts with highly ionized emission lines; 1SWASP J162117+441254, BD Pav, and V364 Lib are among them. Some researchers even doubt whether 1SWASP J1621 and V364 Lib have the same nature as normal dwarf novae. We studied the peculiar outbursts in these three objects via our optical photometry and spectroscopy, and performed numerical modeling of their orbital variations to investigate their properties. We found that their outbursts lasted for a long interval (a few tens of days), and that slow rises in brightness were commonly observed during the early stage of their outbursts. Our analyses and numerical modeling suggest that 1SWASP J1621 has a very high inclination, close to 90°, plus a faint hot spot. Although BD Pav seems to have a slightly lower inclination (∼75°), the other properties are similar to those in 1SWASP J1621. On the other hand, V364 Lib appears to have a massive white dwarf, a hot companion star, and a low inclination (∼35°). In addition, these three objects possibly have a low transfer rate and/or large disks originating from the long orbital periods. We found that these properties of the three objects can explain their infrequent and low-amplitude outbursts within the context of the disk instability model in normal dwarf novae without a strong magnetic field. In addition, we suggest that the highly ionized emission lines in outburst are observed due to a high inclination and/or a massive white dwarf. More instances of this class of object may be unrecognized, since their unremarkable outbursts can be easily overlooked.

We report on our photometric observations of the 2016 superoutburst of ASASSN-16eg. This object showed a WZ Sge-type superoutburst with prominent early superhumps with a period of 0.075478(8) d and a post-superoutburst rebrightening. During the superoutburst plateau, it showed ordinary superhumps with a period of 0.077880(3) d and a period derivative of 10.6(1.1) × 10−5in stage B. The orbital period (Porb), which is almost identical with the period of the early superhumps, is exceptionally long for a WZ Sge-type dwarf nova. The mass ratio (q= M2/M1) estimated from the period of developing (stage A) superhumps is 0.166(2), which is also too large for a WZ Sge-type dwarf nova. This suggests that the 2 : 1 resonance can be reached in such high-qsystems, contrary to our expectation. Such conditions are considered to be achieved if the mass-transfer rate is much lower than those in typical SU UMa-type dwarf novae that have comparable orbital periods to ASASSN-16eg, and a resultant accumulation of a large amount of matter on the disk is realized at the onset of an outburst. We examined other candidates for long-period WZ Sge-type dwarf novae for their supercycles, which are considered to reflect the mass-transfer rate, and found that V1251 Cyg and RZ Leo have longer supercycles than those of other WZ Sge-type dwarf novae. This result indicates that these long-period objects including ASASSN-16eg have a low mass-transfer rate in comparison to other WZ Sge-type dwarf novae.

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.

We report on time-resolved photometry of the 2015 February–March superoutburst of QZ Virginis. The superoutburst consisted of a separated precursor, main superoutburst, and rebrightening. We detected superhumps with a period of 0.061181(42) d between the precursor and main superoutburst. Based on analyses of period changes and amplitudes of superhumps, the observed superhumps were identified as growing superhumps (stage A superhumps). The duration of the stage A superhumps was about 5 d, unusually long for SU UMa-type dwarf novae. Using the obtained stage A superhump period, we estimated the mass ratio of QZ Vir to be 0.108(3). This value suggests that QZ Vir is an SU UMa-type dwarf nova evolving toward the period minimum. Based on the present and previous observations regarding long-lasting stage A superhumps, the time scale for stage A superhumps is likely to be determined by the mass ratio of the system and the temperature of the accretion disk.

We observed the 2016 outburst of OT J002656.6+284933 (CSS101212:002657+284933) and found that it has the longest recorded [0.13225(1) d on average] superhumps among SU UMa-type dwarf novae. The object is the third known SU UMa-type dwarf nova above the period gap. The outburst, however, was unlike ordinary long-period SU UMa-type dwarf novae in that it showed two post-outburst rebrightenings. It showed superhump evolution similar to short-period SU UMa-type dwarf novae. We could constrain the mass ratio to less than 0.15 (most likely between 0.10 and 0.15) by using superhump periods in the early and post-superoutburst stages. These results suggest the possibility that OT J002656.6+284933 has an anomalously undermassive secondary and it should have followed a different evolutionary track from the standard one.

Continuing the project described by Kato et al. (2009, PASJ, 61, S395), 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, and 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, and 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 future observations will be more astrophysically beneficial and rewarding to observers, we propose guidelines on how to organize observations of various superoutbursts.

We present optical photometry of a WZ Sge-type dwarf nova (DN), ASASSN-15jd. Its light curve showed a small dip in the middle of the superoutburst in 2015 for the first time among WZ Sge-type DNe. The unusual light curve implies a delay in the growth of the 3 : 1 resonance tidal instability. Also, the light curve is similar to those of two other WZ Sge-type stars, SSS J122221.7−311523 and OT J184228.1+483742, which are believed to be the best candidates for period bouncers on the basis of their small values of the mass ratio (q≡ M2/M1). Additionally, the small mean superhump amplitude (<0.1 mag) and the long duration of no ordinary superhumps at the early stage of its superoutburst are common to the best candidates for period bouncers. Its average superhump period was Psh= 0.0649810(78) d and no early superhumps were detected. Although we could not estimate a mass ratio of ASASSN-15jd with high accuracy, this object is expected to be a candidate for a period bouncer—a binary accounting for the missing population of post-period minimum cataclysmic variables—based on the above characteristics.

We observed the first-ever recorded outburst of PM J03338+3320, the cataclysmic variable selected by proper-motion survey. The outburst was composed of a precursor and the main superoutburst. The precursor outburst occurred at least 5 d before the maximum of the main superoutburst. Despite this separation, long-period superhumps were continuously seen between the precursor and main superoutburst. The period of these superhumps is longer than its orbital period by 6.0(1)% and can be interpreted to reflect the dynamical precession rate at the 3 : 1 resonance for a mass ratio of 0.172(4). These superhumps smoothly evolved into those in the main superoutburst. These observations provide the clearest evidence that the 3 : 1 resonance is triggered by the precursor outburst, even if it is well separated, and the resonance eventually causes the main superoutburst as predicted by the thermaltidal instability model. The presence of superhumps well before the superoutburst cannot be explained by alternative models (the enhanced mass-transfer model and the pure thermal instability one) and the present observations clearly support the thermaltidal instability model.

We observed the 2015 July–August long outburst of V1006 Cyg and established this object to be an SU UMa-type dwarf nova in the period gap. Our observations have confirmed that V1006 Cyg is the second established object showing three types of outbursts (normal, long normal, and superoutbursts) after TU Men. We have succeeded in recording the growing stage of superhumps (stage A superhumps) and obtained a mass ratio of 0.26–0.33, which is close to the stability limit of tidal instability. This identification of stage A superhumps demonstrates that superhumps indeed slowly grow in systems near the stability limit, the idea first introduced by Kato et al. (2014, PASJ, 66, 90). The superoutburst showed a temporary dip followed by a rebrightening. The moment of the dip coincided with the stage transition of superhumps, and we suggest that stage C superhumps are related to the start of the cooling wave in the accretion disk. We interpret that the tidal instability was not strong enough to maintain the disk in the hot state when the cooling wave started. We propose that the properties commonly seen in the extreme ends of mass ratios (WZ Sge-type objects and long-period systems) can be understood as a result of weak tidal effect.

In 2015 March, the notable WZ Sge-type dwarf nova AL Com exhibited an unusual outburst with a recurrence time of ∼ 1.5 yr, which is the shortest interval of superoutbursts among WZ Sge-type dwarf novae. Early superhumps in the superoutburst light curve were absent, and a precursor was observed at the onset of the superoutburst for the first time in WZ Sge-type dwarf novae. The present superoutburst can be interpreted as a result of the condition that the disk radius barely reached the 3:1 resonance radius, but did not reach the 2:1 resonance one. Ordinary superhumps immediately grew following the precursor. The initial part of the outburst is indistinguishable from those of superoutbursts of ordinary SU UMa-type dwarf novae. This observation supports the interpretation that the 2:1 resonance suppresses a growth of ordinary superhumps. The estimated superhump period and superhump period derivative are Psh= 0.0573185(11) d and Pdot= +1.5(3.1) × 10−5, respectively. These values indicate that the evolution of ordinary superhumps is the same as that in past superoutbursts with much larger extent. Although the light curve during the plateau stage was typical for an SU UMa-type dwarf nova, this superoutburst showed a rebrightening, together with a regrowth of the superhumps. The overall light curve of the rebrightening was the almost the same as those observed in previous rebrightenings. This implies that the rebrightening type is inherent in the system.

Continuing the project described by Kato et al. (2009, PASJ, 61, S395), we collected times of superhump maxima for 102 SU UMa-type dwarf novae, observed mainly during the 2014–2015 season, and characterized these objects. Our project has greatly improved the statistics of the distribution of orbital periods, which is a good approximation of the distribution of cataclysmic variables at the terminal evolutionary stage, and has confirmed the presence of a period minimum at a period of 0.053 d and a period spike just above this period. The number density monotonically decreased toward the longer period and there was no strong indication of a period gap. We detected possible negative superhumps in Z Cha. It is possible that normal outbursts are also suppressed by the presence of a disk tilt in this system. There was no indication of enhanced orbital humps just preceding the superoutburst, and this result favors the thermal–tidal disk instability as the origin of superoutbursts. We detected superhumps in three AM CVn-type dwarf novae. Our observations and recent other detections suggest that 8% of objects showing dwarf nova-type outbursts are AM CVn-type objects. AM CVn-type objects and EI Psc-type objects may be more abundant than previously recognized. OT J213806, a WZ Sge-type object, exhibited remarkably different features between the 2010 and 2014 superoutbursts. Although the 2014 superoutburst was much fainter, the plateau phase was shorter than the 2010 one, and the course of the rebrightening phase was similar. This object indicates that the O− Cdiagrams of superhumps can indeed be variable, at least in WZ Sge-type objects. Four deeply eclipsing SU UMa-type dwarf novae (ASASSN-13cx, ASASSN-14ag, ASASSN-15bu, and NSV 4618) were identified. We studied long-term trends in supercycles in MM Hya and CY UMa and found systematic variations of supercycles of ∼20%.

Continuing the project undertaken by Kato et al. (2009), we collected times of superhump maxima for 56 SU UMa-type dwarf novae mainly observed during the 2013–2014 season and characterized these objects. We detected negative superhumps in VW Hyi and indicated that the low number of normal outbursts in some supercycles can be interpreted as a result of disk tilt. This finding, combined with the Kepler observation of V1504 Cyg and V344 Lyr, suggests that disk tilt is responsible for modulating the outburst pattern in SU UMa-type dwarf novae. We also studied the deeply eclipsing WZ Sge-type dwarf nova MASTER OT J005740.99+443101.5 and found evidence of a sharp eclipse during the phase of early superhumps. The profile can be reproduced by a combination of the eclipse of the axisymmetric disk and the uneclipsed light source of early superhumps. This finding shows the lack of evidence for a greatly enhanced hot spot during the early stage of WZ Sge-type outburst. We detected growing (stage A) superhumps in MN Dra and give a suggestion that some of SU UMa-type dwarf novae situated near the critical condition of tidal instability may show long-lasting stage A superhumps. The large negative period derivatives reported in such systems can be understood as a result of the combination of stage A and B superhumps. Two WZ Sge-type dwarf novae, AL Com and ASASSN-13ck, showed a long-lasting (plateau-type) rebrightening. In the early phase of their rebrightenings, both objects showed a precursor-like outburst, suggesting that the long-lasting rebrightening is triggered by a precursor outburst.

We report on a superoutburst of the AM CVn-type object SDSS J090221.35+381941.9 [J0902; orbital period 0.03355(6) d] in 2014 March–April. The entire superoutburst consisted of a precursor outburst and the main superoutburst, followed by a short rebrightening. During the rising phase of the main superoutburst, we detected growing superhumps (stage A superhumps) with a period of 0.03409(1) d. During the plateau phase of the superoutburst, superhumps with a shorter period (stage B superhumps) were observed. Using the orbital period and the period of stage A superhumps, we were able to measure the dynamical precession rate of the accretion disk at the 3:1 resonance, and obtained a mass ratio (q) of 0.041(7). This is the first successful measurement of the mass ratio in an AM CVn-type object accomplished by the recently developed stage A superhump method. The value is generally in agreement with that based on the theoretical evolutionary model. The orbital period of J0902 is the longest among those of the outbursting AM CVn-type objects, and a period on the borderline between the outbursting system and the system with a stable cool disk appears to be longer than one supposed.

Continuing the project described in Kato et al. (2009, PASJ, 61, S395), we collected times of superhump maxima for SU UMa-type dwarf novae mainly observed during the 2012–2013 season. We found three objects (V444 Peg, CSS J203937, and MASTER J212624) having strongly positive period derivatives despite the long orbital period (Porb). By using the period of growing stage (stage A) superhumps, we obtained mass ratios for six objects. We characterized nine new WZ Sge-type dwarf novae. We made a pilot survey of the decline rate in the slowly fading parts of SU UMa-type and WZ Sge-type outbursts. The decline time scale was found to generally follow an expected $P_{\rm orb}^{1/4}$dependence, and WZ Sge-type outbursts also generally follow this trend. There are some objects which show slower decline rates, and we consider these objects good candidates for period bouncers. We also studied unusual behavior in some objects, including BK Lyn which made a transition from an ER UMa-type state to a novalike (standstill) state in 2013, and unusually frequent occurrences of superoutbursts in NY Ser and CR Boo. We applied the least absolute shrinkage and selection operator (Lasso) power spectral analysis, which has been proven to be very effective in analyzing the Kepler data, to the ground-based photometry of BK Lyn, and detected a dramatic disappearance of the signal of negative superhumps in 2013. We suggested that the mass-transfer rates did not strongly vary between the ER UMa-type state and novalike state in BK Lyn, and this transition was less likely caused by a systematic variation of the mass-transfer rate.

We report on photometric observations of two WZ Sge-type dwarf novae, MASTER OT J211258.65+242145.4 and MASTER OT J203749.39+552210.3, which underwent outbursts in 2012. Early superhumps were recorded in both systems. During the superoutburst plateau, ordinary superhumps with a period of 0.060291(4) d (MASTER J211258) and with 0.061368(11) d (MASTER J203749) on average were observed. MASTERJ211258 and MASTERJ203749 exhibited eight post-superoutburst rebrightenings and more than four, respectively. In the final part of the superoutburst, an increase in superhump period was seen in both systems. We made a survey of WZSge-type dwarf novae with multiple rebrightenings, and confirmed that the superhump periods of WZSge-type dwarf novae with multiple rebrightenings were longer than those of WZSge-type dwarf novae without a rebrightening. Although WZSge-type dwarf novae with multiple rebrightenings have been thought to be likely candidates for period bouncers based on their low mass ratio (q), inferred from the period of fully grown (stage B) superhumps, our new method of using the period of growing superhumps (stage A superhumps), however, implies higher q's than those expected from stage B superhumps. These qvalues appear to be consistent with the duration of the stage A superoutbursts, which likely reflects the growth time of the 3W1 resonance. We present a working hypothesis that the small fractional superhump excesses for stage B superhumps in these systems may be explained by a gas pressure effect that works more efficiently in these systems than in ordinary SU UMa-type dwarf novae. This result forms a new picture that WZSge-type dwarf novae with multiple rebrightenings and SU UMa-type ones without a rebrightening (they are not period bouncers) are located in the same place on the evolutionary track.

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.

Continuing the project described by Kato et al. (2009, PASJ, 61, S395), we collected the times of superhump maxima for 51 SU UMa-type dwarf novae, mainly observed during the 2010–2011 season. Although most of the new data for systems with short superhump periods basically confirmed the findings by Kato et al. (ibid.) and Kato et al. (2010, PASJ, 62, 1525), the long-period system GX Cas showed an exceptionally large positive-period derivative. An analysis of public Kepler data of V344 Lyr and V1504 Cyg yielded less-striking stage transitions. In V344 Lyr, there was a prominent secondary component growing during the late stage of superoutbursts, and this component persisted for at least two more cycles of successive normal outbursts. We also investigated the superoutburst of two conspicuous eclipsing objects: HT Cas and the WZ Sge-type object SDSS J080434.20$+$510349.2. Strong beat phenomena were detected in both objects, and late-stage superhumps in the latter object had an almost constant luminosity during repeated rebrightenings. The WZ Sge-type object SDSS J133941.11$+$484727.5 showed a phase reversal around the rapid fading from the superoutburst. The object showed a prominent beat phenomenon, even after the end of the superoutburst. A pilot study of superhump amplitudes indicated that the amplitude of superhumps is strongly correlated with the orbital period, and the dependence on the inclination is weak in systems with inclinations smaller than 80$^{\circ}$.