Tidal Effects on the Radial Velocities of V723 Mon: Additional Evidence for a Dark $3\,M_\odot$ Companion

Kento Masuda, Teruyuki Hirano

Published 2021-03-09Version 1

Jayasinghe et al. (2021) identified a dark $\approx 3\,M_\odot$ companion on a nearly edge-on $\approx 60\,\mathrm{day}$ orbit around the red giant star V723 Monoceros as a black hole candidate in the mass gap. This scenario was shown to explain most of the data presented by Jayasinghe et al. (2021), except for periodic radial velocity (RV) residuals from the circular Keplerian model. Here we show that the RV residuals are explained by orbital phase-dependent distortion of the absorption line profile associated with changing visible fractions of the approaching and receding sides of the red giant star, whose surface is tidally deformed by and rotating synchronously with the dark companion. Our RV model constrains the companion mass $M_\bullet = 2.95\pm0.17\,M_\odot$ and orbital inclination $i=82.9^{+7.0}_{-3.3}\,\mathrm{deg}$ (medians and 68.3% highest density intervals of the marginal posteriors) adopting the radius of the red giant $24.0\pm0.9\,R_\odot$ as constrained from its SED and distance. The analysis provides independent support for the companion mass from ellipsoidal variations and the limits on the companion's luminosity from the absence of eclipses both derived by Jayasinghe et al. (2021). We also show that a common scheme to evaluate the tidal RV signal as the flux-weighted mean of the surface velocity field can significantly underestimate its amplitude for RVs measured with a cross-correlation technique, and present a modified prescription that directly models the distorted line profile and its effects on the measured RVs. The formulation will be useful for estimating the component masses and inclinations in other similar binaries.