The variable stars of the young LMC cluster NGC 2164

The young, populous Large Magellanic Cloud (LMC) cluster NGC 2164 has been searched for variable stars. From (up to) 64 epochs of new BV CCD photometry obtained between December 1989 and December 1991 we have discovered one new member (overtone) classical Cepheid variable with a period of 3.772 days. We also present photometry for a previously unknown field overtone Cepheid variable with a period of 3.4626 days and the longer-period HV 12078 which has a period of 10.6878 days. It is suggested that HV 12078 may be a member of the nearby, young cluster NGC 2156 which is also contained within our field on most frames. We have investigated the lightcurve shape of the NGC 2164 member and find that its Fourier phase φ₂₁ = 3.1 which is in agreement with the sequence of longer-period s-Cepheids suggested by Antonello et al. [A&A, 236, 138 (1990)]. The clear separation of fundamental and overtone pulsators in the period-luminosity-color relation of known LMC cluster Cepheids leaves no doubt that the NGC 2164 member is a true overtone. Our best images of NGC 2164 (with the smallest FWHM) reveal the superluminous giant candidates of Flower & Hodge (1975) to have double or multiple components, suggesting that (in this cluster, at least) these objects can be accounted for by near-superpositions of ordinary stars. We discuss a possible origin for their appearance in earlier color-magnitude diagrams. We speculate that the increased dispersion observed in the Small Magellanic Cloud infrared period-luminosity (P-L) and period-luminosity-color (P-L-C) relations, relative to those of the LMC, may be due to a different long-period cutoff in the period distribution of overtone pulsators.