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.

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.

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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