The MACHO project LMC variable star inventory. VI. The second overtone mode of cepheid pulsation from first/second overtone beat cepheids

MACHO Project photometry of 45 LMC first and second overtone (FO and SO, respectively) beat Cepheids that pulsate in the FO and SO has been analyzed to determine the light-curve characteristics for the SO mode of Cepheid pulsation. We predict that singly periodic SO Cepheids will have nearly sinusoidal light curves; that we will only be able to discern SO Cepheids from fundamental (F) and FO Cepheids for P ≲ 1.4 days; and that the SO distribution will overlap the short-period edge of the LMC FO Cepheid period-luminosity relation (when both are plotted as a function of photometric period). We also report the discovery of one SO Cepheid candidate, MACHO*05:03:39.6-70:04:32, with a photometric period of 0.775961 ± 0.000019 days and an instrumental amplitude of 0.047 ± 0.009 mag in V.