Period-Luminosity Relations Derived From the OGLE-III Fundamental Mode Cepheids II: The Small Magellanic Cloud Cepheids

In this paper we present multi-band period-luminosity (P-L) relations for fundamental mode Cepheids in the SMC. The optical VI-band mean magnitudes for these SMC Cepheids were taken from the third phase of the Optical Gravitational Lensing Experiment (OGLE-III) catalog. We also matched the OGLE-III SMC Cepheids to 2MASS and SAGE-SMC catalog to derive mean magnitudes in the JHK-bands and the four {\it Spitzer} IRAC bands, respectively. All photometry was corrected for extinction by adopting the Zaritsky's extinction map. Cepheids with periods smaller than $\sim2.5$ days were removed from the sample. In addition to the extinction corrected P-L relations in nine filters from optical to infrared, we also derived the extinction-free Wesenheit function for these Cepheids. We tested the nonlinearity of these SMC P-L relations (except the $8.0\mu\mathrm{m}$-band P-L relation) at 10 days: none of the P-L relations show statistically significant evidence of nonlinearity. When compared to the P-L relations in the LMC, the t-test results revealed that there is a difference between the SMC/LMC P-L slopes only in the V- and J-band. Further, we found excellent agreement between the SMC/LMC Wesenheit P-L slope. The difference in LMC and SMC Period-Wesenheit relation LMC and SMC zero points was found to be $\Delta \mu=0.483\pm0.015$ mag. This amounts to a difference in distance modulus between the LMC and SMC.