Developing a Novel Method by Integrating the Monte-Carlos Solver into Cross-Correlation Fitting to Efficiently Discover a New Mass-Radius Relation with More Precision

When will Earth be destroyed? Where did we come from? How do stars form? These are all fundamental questions which the study of astronomy and stellar evolution and formation can answer. However, there is an obstacle; there is a significant lack of research about stars with masses below around 0.8 solar masses, with inconsistencies as large as 30%. In this research, stellar parameters of low-mass eclipsing binaries were extracted using the space Kepler data and ground-based MARVELS radial velocity data from the Sloan Digital Sky Survey III program. Eight eclipsing binaries (radial velocities already extracted) were selected and their transits were fit using Python code to derive the primary and secondary radii along with their periods. Through my findings, stellar masses and orbital parameters such as the period, eccentricity were extracted through the MCMC solver and cross-correlation fitting to MARVELS RV data. For targets unable to fit as double-line spectroscopic binary, their single-line spectroscopic binary radial velocities were still extracted and plotted. My measurements are the first report of data to further investigate the fundamental stellar mass-radius relation at low stellar masses (< 0.8 solar masses) and their dependence on other physical parameters such as age, mass, stellar magnetic activity and orbital period. The mass-radius relation of stars is the fundamental law of the universe to understand the universe’s building block: stars. The method developed in this research will have significant implementations in stellar evolution and formation, enhancing our ability to answer important questions about our universe.