  Abridged: Alpha Virginis is a binary system whose proximity and brightness
allow detailed investigations of the internal structure and evolution of stars
undergoing time-variable tidal interactions. Previous studies have led to the
conclusion that the internal structure of Spica's primary star may be more
centrally condensed than predicted by theoretical models of single stars,
raising the possibility that the interactions could lead to effects that are
currently neglected in structure and evolution calculations. The key parameters
in confirming this result are the values of the orbital eccentricity $e$, the
apsidal period $U$, and the primary star's radius, R_1. We analyze the impact
that line profile variability has on the derivation of its orbital elements and
R_1. We use high SNR observations obtained in 2000, 2008, and 2013 to derive
the orbital elements from fits to the radial velocity curves. We produce
synthetic line profiles using an ab initio tidal interaction model. Results:
The variations in the line profiles can be understood in terms of the tidal
flows, whose large-scale structure is relatively fixed in the rotating binary
system reference frame. Fits to the radial velocity curves yield
$e$=0.108$\pm$0.014. However, the analogous RV curves from theoretical line
profiles indicate that the distortion in the lines causes the fitted value of
$e$ to depend on the argument of periastron; i.e., on the epoch of observation.
As a result, the actual value of $e$ may be as high as 0.125. We find that
$U$=117.9$\pm$1.8, which is in agreement with previous determinations. Using
the value $R_1=6.8 R_\odot$ derived by Palate et al. (2013) the value of the
observational internal structure constant $k_{2,obs}$ is consistent with
theory. We confirm the presence of variability in the line profiles of the
secondary star.
