  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.
