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

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.