论文标题
一些改良的重力模型对二元系统的径向速度的影响
Effect of some modified models of gravity on the radial velocity of binary systems
论文作者
论文摘要
对于许多类别的天文学和天体物理二进制系统，可以使用其径向速度$ V $的长期观察记录，这是它们直接可观察的数量。对于靠近母星的系外行星，它们涵盖了几种完整的轨道旋转，而对于诸如Proxima/$α$ CENTAURI AB系统之类的广泛二进制文件，只有相对较短的轨道弧是由现有的径向速度测量来取样的。在这里，通过分析计算了一些长期修改的重力模型，在二进制的径向速度上引起的变化$ΔV$。特别是，考虑到与$ r^{ - n}，\，n = 2，\，3 $和$ r^2 $成比例的超电势；宇宙常数$λ$属于后一组。每个轨道的净偏移均为每个模型明确计算。 The Cosmological Constant induces a shift in the radial velocity of the Proxima/$α$ Centauri AB binary as little as $\left|ΔV\right|\lesssim 10^{-7}\,\mathrm{m\,s}^{-1}$, while the present-day accuracy in measuring its radial velocity is $σ_V\simeq 30 \，\ Mathrm {m \，s}^{ - 1} $。此处介绍的计算方案非常通用，并且可以直接扩展到任何其他修改的重力。
For many classes of astronomical and astrophysical binary systems, long observational records of their radial velocity $V$, which is their directly observable quantity, are available. For exoplanets close to their parent stars, they cover several full orbital revolutions, while for wide binaries like, e.g., the Proxima/$α$ Centauri AB system, only relatively short orbital arcs are sampled by existing radial velocity measurements. Here, the changes $ΔV$ induced on a binary's radial velocity by some long-range modified models of gravity are analytically calculated. In particular, extra-potentials proportional to $r^{-N},\,N=2,\,3$ and $r^2$ are considered; the Cosmological Constant $Λ$ belongs to the latter group. Both the net shift per orbit and the instantaneous one are explicitly calculated for each model. The Cosmological Constant induces a shift in the radial velocity of the Proxima/$α$ Centauri AB binary as little as $\left|ΔV\right|\lesssim 10^{-7}\,\mathrm{m\,s}^{-1}$, while the present-day accuracy in measuring its radial velocity is $σ_V\simeq 30\,\mathrm{m\,s}^{-1}$. The calculational scheme presented here is quite general, and can be straightforwardly extended to any other modified gravity.
