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.