We present the results of a search for additional exoplanets in all multiplanetary systems discovered to date, employing a logarithmic spacing between planets in our Solar System known as the Titius–Bode (TB) relation. We use the Markov Chain Monte Carlo method and separately analyse 229 multiplanetary systems that house at least three or more confirmed planets. We find that the planets in $\sim 53\%$ of these systems adhere to a logarithmic spacing relation remarkably better than the Solar System planets. Using the TB relation, we predict the presence of 426 additional exoplanets in 229 multiplanetary systems, of which 197 candidates are discovered by interpolation and 229 by extrapolation. Altogether, 47 predicted planets are located within the habitable zone of their host stars, and 5 of the 47 planets have a maximum mass limit of 0.1–2 ${\rm M}_{\oplus}$ and a maximum radius lower than 1.25 ${\rm R}_{\oplus}$ . Our results and prediction of additional planets agree with previous studies’ predictions; however, we improve the uncertainties in the orbital period measurement for the predicted planets significantly.

中文翻译：

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多行星系统中的系外行星预测

我们展示了在迄今为止发现的所有多行星系统中寻找额外系外行星的结果，采用了我们太阳系中行星之间的对数间距，称为 Titius-Bode (TB) 关系。我们使用马尔可夫链蒙特卡罗方法，分别分析了 229 个多行星系统，这些系统至少包含三个或更多已确认的行星。我们发现行星在 $\sim 53\%$ 这些系统中的一些遵循比太阳系行星明显更好的对数间距关系。使用 TB 关系，我们预测在 229 个多行星系统中存在 426 个额外的系外行星，其中 197 个候选是通过插值发现的，229 个是通过外推发现的。总共有 47 颗预测行星位于其宿主恒星的宜居带内，47 颗行星中有 5 颗的最大质量限制为 0.1-2 ${\rm M}_{\oplus}$ 最大半径小于 1.25 ${\rm R}_{\oplus}$ . 我们对其他行星的结果和预测与先前研究的预测一致；然而，我们显着改善了预测行星轨道周期测量的不确定性。