论文标题
RV方程中$ω$的使用不一致
The Inconsistent use of $ω$ in the RV Equation
论文作者
论文摘要
自从发现第一个轨道行星轨道恒星时，天文学家已经使用恒星径向速度（RV）测量来推断行星的轨道特性。对于由单个行星绕的星星，恒星轨道是扩张和$ 180^\ circ $旋转的行星轨道。因此，恒星的许多开普勒轨道特性与地球的基础相同。但是，有一个值得注意的例外：periastron的$ω$的论点定义为轨道体的脑膜及其上升节点之间的角度。恒星的Periastron（$ω_\ star $）的参数为$ 180^\ circ $偏移，偏移了行星的periastron的参数（$ω_p$）。这种区别很重要，因为RV方程的某些派生使用$ω_\ star $，而另一些则使用$ω_p$。出现这种差异是因为RV方程的常用派生不遵守单个坐标系。结果，在各种RV模型中，开普勒轨道参数的定义存在不一致之处，导致上升节点的值和$ω$的值为$ 180^\ circ $ offset。例如，某些软件包，例如\ texttt {radvel}和\ texttt {exofast}，报告$ω_ {\ star} $的值与其他软件包确定的$ω_p$值相同，例如\ texttt {ttvfast} and \ textttttttt by of trife by of trife by $ nirviation。这种差异突出了RV建模中对标准化的惯例和定义的需求，尤其是当我们进入将RV与Astrestremen结合的时代。
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 $180^\circ$ 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, $ω$, defined as the angle between the periapsis of an orbiting body and its ascending node. The argument of periastron of the star ($ω_\star$) is $180^\circ$ offset from the argument of periastron of the planet ($ω_p$). This distinction is important because some derivations of the RV equation use $ω_\star$, while others use $ω_p$. 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 $ω$ that are $180^\circ$ offset. For instance, some packages, such as \texttt{RadVel} and \texttt{ExoFast}, report values for $ω_{\star}$ that are identical to the $ω_p$ values determined with other packages, such as \texttt{TTVFast} and \texttt{Orvara}, resulting in orbital solutions that differ by $180^\circ$. This discrepancy highlights the need for standardized conventions and definitions in RV modeling, particularly as we enter the era of combining RVs with astrometry.
