The mass-radius relationship of M dwarf stars from Kepler eclipsing binaries
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M dwarf stars make up over 70% of stars by number in the Milky Way Galaxy and are known to host at least two exoplanets per star on average. Using mutually eclipsing double-lined spectroscopic binary stars (SB2 EBs), astronomers can empirically measure stellar properties of M dwarf stars including mass and radius. However, empirical measurements systematically differ from the predictions of stellar evolutionary models and show large scatter. Some M dwarf stars are outliers, with radii that are a factor of 2-to-3 larger than model predictions, assuming they were measured accurately. In this dissertation, I investigated whether the outliers, systematic offset, and the scatter seen in the mass-radius diagram are physical, using SB2 EBs with photometry from NASA's Kepler Mission and high-resolution near-infrared ground-based spectroscopy. Empirical measurements using space-based photometry and high-resolution near-infrared ground-based spectroscopy, together with Bayesian model-fitting techniques, provide significant advancements over previous measurements. For this dissertation work, a sample of Kepler EBs were carefully chosen to be detached and non-interacting. I conducted a radial velocity survey of the sample using Immersion GRating INfrared Spectrometer (IGRINS) with the Discovery Channel Telescope (DCT) and iSHELL with NASA's Infrared Telescope Facility (IRTF). Combined with high-precision Kepler data, I determined the masses and radii of the component stars in the sample. I also determined a new mass-radius relationship of M dwarf stars using the sample of Kepler EB systems. My investigation showed that the outliers in the mass-radius diagram of M dwarf stars are not physical and they are due to the quality of data and from analysis using different pipelines. I also showed that the offset and scatter in the mass-radius diagram are persistent, which are not from the measurement uncertainties. This suggests the need for an extra degree of freedom to accurately capture the discrepancies between the empirical measurements and model predictions. Lastly, I showed that reduced convective heat flow due to enhanced magnetic fields from rapid stellar rotation can account for the offset and scatter in the measurements.