Unbiased effective temperatures of red supergiants from iron absorption lines

The Great Dimming of Betelgeuse in 2019/2020 raised the question of how to accurately measure the property of a red supergiant (RSG), for example, effective temperature, star-spot covering fraction, and reddening. Here we focus on the effective temperature, which might be the most representative parameter among them. Among spectroscopic approaches to determine the temperature, the methods using atomic lines in high-resolution spectra have some advantages compared to those using molecular bands; relatively shallow atomic lines are less affected by the uncertain temperature structure in the upper atmosphere of RSGs. A promising approach is the line-depth ratio (LDR) method using ratios of line depths of two atomic absorption lines, which has been successfully applied to various kinds of late-type stars. In this work, we established the relations between effective temperature and LDR of two neutral Fe lines based on calibrating red giant. Our LDR indicators are expected to give the consistent temperature scale both red giants and RSGs because the LDRs of two neutral Fe lines are insensitive to the surface gravity. We then measured the effective temperatures of ten nearby RSGs including Betelgeuse observed with the WINERED near-infrared high-resolution spectrograph (0.97--1.32 micron, R=28,000) to a precision of ~40K. Combining these temperatures with the parallaxes in the Gaia EDR3, we also determined the bolometric luminosities of the RSGs. The resultant effective temperature of Betelgeuse, 3611+-38K, is consistent with those measured with spectro-interferometry by Ohnaka et al. (2011) and Arroyo-Torres et al. (2013), 3690+-54 and 3620+-137K, respectively. Moreover, our effective temperatures and luminosities show good agreements with the Geneva's stellar evolution model.