Estimating Mass and Luminosity of Spectroscopic Binary Stars Using a Python-Based Computational Approach

Abstract

Spectroscopic binary stars provide crucial insights into stellar masses, orbital dynamics, and evolutionary processes. This study presents a computational approach to analyzing spectroscopic binary systems using Python by developing an algorithm to estimate their mass and luminosity. In our study, the algorithm processes the spectral data, particularly variations in the Hydrogen-alpha line over time (in Modified Julian Date), to compute radial velocities by incorporating Doppler shifts and applying barycentric corrections. A sinusoidal function is then fitted to the velocity variations to determine the orbital period. The stellar masses are derived using the radial velocity curve with the inclination angle and orbital parameters. Given the mass-luminosity relation, the luminosities of the stars are estimated. Since the derived mass of the system ranges between 2 and 55 times the mass of the sun, the luminosity can be calculated based on the mass-luminosity relation, where luminosity is proportional to the stellar mass raised to the power of 3.5. This computational method offers an efficient and accurate technique for studying spectroscopic binaries, which can be extended to analyze large datasets from astronomical surveys, enhancing our understanding of binary star evolution.