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.
