The Period-Luminosity Relation of Red Supergiant Stars in the Small Magellanic Cloud

The characteristics of light variation of RSGs in SMC are analyzed based on the nearly 8-10 year long data collected by the ASAS and MACHO projects. The identified 126 RSGs are classified into five categories accordingly: 20 with poor photometry, 55 with no reliable period, 6 with semi-regular variation, 15 with Long Secondary Period (LSP) and distinguishable short period and 30 with only LSP. For the semi-regular variables and the LSP variables with distinguishable short period, the Ks band period-luminosity (P-L) relation is analyzed and compared with that of the Galaxy, LMC and M33. It is found that the RSGs in these galaxies obey similar P-L relation except the Galaxy. In addition, the P-L relations in the infrared bands, namely the 2MASS JHKs, Spitzer/IRAC and Spitzer/MIPS 24 {\mu}m bands, are derived with high reliability. The best P-L relation occurs in the Spitzer/IRAC [3.6] and [4.5] bands. Based on the comparison with the theoretical calculation of the P-L relation, the mode of pulsation of RSGs in SMC is suggested to be the first overtone radial mode.