Red Supergiant Stars in IC 1613 and Metallicity-dependent Mixing Length in the Evolutionary Model

Abstract

We report a spectroscopic study on red supergiant stars (RSGs) in the irregular dwarf galaxy IC 1613 in the Local Group. We derive the effective temperatures (T eff) and metallicities of 14 RSGs by synthetic spectral fitting to the spectra observed with the MMIRS instrument on the MMT telescope for a wavelength range from 1.16 to 1.23 μm. A weak bimodal distribution of the RSG metallicity centered on [Fe/H] = −0.65 is found, which is slightly lower than or comparable to that of the Small Magellanic Cloud (SMC). There is no evidence for spatial segregation between the metal-rich ([Fe/H] > −0.65) and -poor ([Fe/H] < −0.65) RSGs throughout the galaxy. The mean effective temperature of our RSG sample in IC 1613 is higher by about 250 K than that of the SMC. However, no correlation between T eff and metallicity within our RSG sample is found. We calibrate the convective mixing length (α MLT) by comparing stellar evolutionary tracks with the RSG positions on the H-R diagram, finding that models with α MLT = 2.2–2.4H P can best reproduce the effective temperatures of the RSGs in IC 1613 for both Schwarzschild and Ledoux convection criteria. This result supports our previous finding that a metallicity-dependent mixing length is needed to explain the RSG temperatures observed in the Local Group, but we find that this dependence becomes relatively weak for RSGs having a metallicity equal to or less than the SMC metallicity.