Fundamental Parameters of a Binary System Consisting of a Red Dwarf and a Compact Star

TIC 157365951 has been classified as a $\delta$ Scuti type by the International Variable Star Index (VSX). Through the spectra from Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) and its light curve, we further discovered that it is a binary system. This binary system comprises a red dwarf star and a compact star. Through the spectral energy distribution (SED) fitting, we determined the mass of the red dwarf star as $M_1=0.31\pm 0.01M_{\odot }$ and its radius as $R_1=0.414\pm 0.004R_{\odot }$. By fitting the double-peaked H$\alpha$ emission, we derived the mass ratio of $q=1.76\pm 0.04$, indicating a compact star mass of $M_2=0.54\pm 0.01M_{\odot }$. Using Phoebe to model the light curve and radial velocity curve for the detached binary system, we obtained a red dwarf star mass of $M_1=0.29\pm 0.02M_{\odot }$, a radius of $R_1=0.39\pm 0.04R_{\odot }$, and a Roche-lobe filling factor of $f=0.995\pm 0.129$, which is close to the $f=1$ expected for a semi-detached system. The Phoebe model gives a compact star mass $M_2=0.53\pm 0.05M_{\odot }$. Constraining the system to be semidetached gives $M_1=0.34\pm 0.02M_{\odot }$, $R_1=0.41\pm 0.01R_{\odot }$, and $M_2=0.62\pm 0.03M_{\odot }$. The consistency of the models is encouraging. The value of the Roche-lobe filling factor suggests that there might be ongoing mass transfer. The compact star mass is as massive as a typical white dwarf.