The First Light Curve Modeling and Orbital Period Change Investigation of Nine Contact Binaries around the Short-period Cutoff

In this paper, we present the first light curve synthesis and orbital period change analysis of nine contact binaries around the short-period limit. It is found that all these systems are W-subtype contact binaries. One of them is a medium contact system while the others are shallow contact ones. Four of them manifest obvious O'Connell effect explained by a dark spot or hot spot on one of the component stars. Third light was detected in three systems. By investigating orbital period variations, we found that four of the targets display a secular period decrease while the others exhibit a long-term period increase. The secular period decrease is more likely caused by angular-momentum loss while the long-term period increase is due to mass transfer from the less massive component to the more massive one. Based on the statistic of 19 ultrashort-period contact binaries with known orbital period changes, we found that seven of them display long-term decrease (three of them also exhibit cyclic variations), ten of them manifest long-term increase while two of them only show cyclic variation, and that most of them are shallow contact binaries supporting the long timescale angular-momentum loss theory suggested by Stepien. For the three deep contact systems, we found that they are probably triple systems. The tertiary companion plays an essential role during their formation and evolution.