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 $M_1 = 0.31 \pm 0.01 M_{\odot}$ and its radius as $R_1 = 0.414 \pm 0.004 R_{\odot}$. By fitting the double-peaked H${\rm \alpha}$ emission, we derived the mass ratio of $q = 1.76 \pm 0.04$, indicating a compact star mass of $M_2 = 0.54 \pm 0.01 M_{\odot}$. Using Phoebe to model the light curve and radial velocity curve for the detached binary system, we obtained a red dwarf star mass of $M_1 = 0.29 \pm 0.02 M_{\odot}$, a radius of $R_1 = 0.39 \pm 0.04 R_{\odot}$, and a Roche-lobe filling factor of $f = 0.995\pm0.129$, which is close to the $f=1$ expected for a semi-detached system. The Phoebe model gives a compact star mass $M_2 = 0.53 \pm 0.05 M_{\odot}$. Constraining the system to be semidetached gives $M_1 = 0.34 \pm 0.02 M_{\odot}$, $R_1 = 0.41 \pm 0.01 R_{\odot}$, and $M_2 = 0.62 \pm 0.03 M_{\odot}$. 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.