Emerging ordinary superhumps as the standard candle for WZ Sge stars

Abstract: In Kato (2015, arXiv:1507.07659), I suggested that the magnitude when ordinary superhumps appear can be a standard candle for WZ Sge stars. Using Gaia EDR3 parallaxes, I studied 53 WZ Sge stars to examine this suggestion. The analysis indicated that the absolute magnitudes when ordinary superhumps appear are strongly dependent on orbital inclinations, which is consistent with what is expected for the projected area for optical thick accretion disks. I showed that there is a linear relation between these absolute magnitudes and logarithmic amplitudes of early superhumps, which are also dependent on the inclinations. I confirmed that the magnitude when ordinary superhumps appear can be used as the standard candle for WZ Sge stars particularly when the amplitude of early superhumps is observationally known. The resultant median absolute magnitude when ordinary superhumps appear was $+$5.4 (for an average inclination of 1 radian). A few objects with multiple rebrightenings, which are good candidates for period bouncers, showed slightly fainter absolute magnitudes, although the majority of the same class of objects follows the relation. Using the relation, I derived an empirical relation between the inclination and the amplitude of early superhumps. I applied the relation to MASTER OT J030227.28$+$191754.5, which was initially considered as a possible optical counterpart of the high-energy neutrino event IceCube-211125A, and concluded that this WZ Sge star was one of the faintest before the outburst and one of the brightest around the optical peak in terms of absolute magnitudes.