The Optical Gravitational Lensing Experiment. Cepheids in the Magellanic Clouds. III. Period-Luminosity-Color and Period-Luminosity Relations of Classical Cepheids

We present Period-Luminosity-Color and Period-Luminosity relations of classical Cepheids constructed for about 1280 Cepheids from the LMC and 2140 from the SMC. High quality BVI observations (120-360 epochs in the I-band and 15-40 in the BV-bands) were collected during the OGLE-II microlensing experiment. The I-band diagrams of the LMC show very small scatter, \sigma=0.074 mag, indicating that Cepheid variables can potentially be a very good standard candle. We compare relations of fundamental mode Cepheids from the LMC and SMC and we do not find significant differences of slopes of the Period-Luminosity- Color and Period-Luminosity relations in these galaxies. For the first overtone Cepheids a small change of the slope of Period-Luminosity relation is possible. We determine the difference of distance moduli between the SMC and LMC with Cepheid relations and compare the result with difference obtained with other standard candles: RR Lyr and red clump stars. Results are very consistent and indicate that the values of zero points of the fundamental mode Cepheid relations are similar in these galaxies. The mean difference of distance moduli between the SMC and LMC is equal to \mu_SMC-\mu_LMC=0.51\pm0.03 mag. We calibrate the Period-Luminosity-Color and Period-Luminosity relations for classical, fundamental mode Cepheids using the observed LMC relations and adopting the short LMC distance modulus, \mu_LMC=18.22\pm0.05 mag, resulting from the recent determination with eclipsing system HV2274, RR Lyr and red clump stars and consistent with observations of Cepheids in NGC4258 galaxy, to which precise geometric distance is known. Finally, we determine a constraint on the absolute magnitude of Cepheids by comparison of their mean V-band magnitude with that of RR Lyr stars in both Magellanic Clouds.