The Period-Luminosity Relations of Red Supergiants in M33 and M31

Based on previously selected preliminary samples of Red Supergiants (RSGs) in M33 and M31, the foreground stars and luminous Asymptotic Giant Branch stars (AGBs) are further excluded, which leads to the samples of 717 RSGs in M33 and 420 RSGs in M31. With the time-series data from the iPTF survey spanning nearly 2000 days, the period and amplitude of RSGs are analyzed. According to the lightcurves characteristics, they are classified into four categories in which 84 and 56 objects in M33 and M31 respectively are semi-regular variables. For these semi-regular variables, the pulsation mode is identified by comparing with the theoretical model, which yielded 19 (7) sources in the first overtone mode in M33 (M31), and the other 65 (49) RSGs in M33 (M31) in the fundamental mode. The period-luminosity (P-L) relation is analyzed for the RSGs in the fundamental mode. It is found the P-L relation is tight in the infrared, i.e. the 2MASS $JHK_{\rm S}$ bands and the short-wavelength bands of Spitzer. Meanwhile, the inhomogeneous extinction causes the P-L relation scattering in the $V$ band, and the dust emission causes the less tight P-L relation in the Spitzer/[8.0] and [24] bands. The derived P-L relations in the 2MASS/$K_{\rm S}$ band are in agreement with those of RSGs in SMC, LMC and the Milky Way within the uncertainty range. It is found that the number ratio of RSGs pulsating in the fundamental mode to the first overtone mode increases with metallicity.