Since the discovery of the first exoplanet orbiting a main-sequence star,
astronomers have inferred the orbital properties of planets using stellar
radial velocity (RV) measurements. For a star orbited by a single planet, the
stellar orbit is a dilation and 180β rotation of the planetary orbit.
Thus, many of the Keplerian orbital properties of the star are identical to
those of the planet. However, there is a notable exception: the argument of
periastron, Ο, defined as the angle between the periapsis of an orbiting
body and its ascending node. The argument of periastron of the star
(Οββ) is 180β offset from the argument of periastron of the
planet (Οpβ). This distinction is important because some derivations of
the RV equation use Οββ, while others use Οpβ. This
discrepancy arises because commonly used derivations of the RV equation do not
adhere to a single coordinate system. As a result, there are inconsistencies in
the definitions of the Keplerian orbital parameters in various RV models,
leading to values of the ascending node and Ο that are 180β
offset. For instance, some packages, such as \texttt{RadVel} and
\texttt{ExoFast}, report values for Οββ that are identical to the
Οpβ values determined with other packages, such as \texttt{TTVFast} and
\texttt{Orvara}, resulting in orbital solutions that differ by 180β.
This discrepancy highlights the need for standardized conventions and
definitions in RV modeling, particularly as we enter the era of combining RVs
with astrometry.Comment: 5 pages,2 figures, 1 tabl