The exotic range of known planetary systems has provoked an equally exotic range of physical explanations for their diverse architectures. However, constraining formation processes requires mapping the observed exoplanet population to that which initially formed in the protoplanetary disc. Numerous results suggest that (internal or external) dynamical perturbation alters the architectures of some exoplanetary systems. Isolating planets that have evolved without any perturbation can help constrain formation processes. We consider the Kepler multiples, which have low mutual inclinations and are unlikely to have been dynamically perturbed. We apply an adaption of previous modelling efforts, accounting for the two-dimensionality of the radius ($R_\mathrm{pl} =0.3\!-\!20\, R_\oplus$) and period (Porb = 0.5–730 d) distribution. We find that an upper limit in planet mass of the form $M_\mathrm{lim} \propto a_\mathrm{pl}^{\beta } \exp (-a_\mathrm{in}/a_\mathrm{pl})$, for semimajor axis apl and a broad range of ain and β, can reproduce a distribution of Porb, Rpl that is indistinguishable from the observed distribution by our comparison metric. The index is consistent with β = 1.5, expected if growth is limited by accretion within the Hill radius. This model is favoured over models assuming a separable PDF in Porb, Rpl. The limit, extrapolated to longer periods, is coincident with the orbits of RV-discovered planets (apl > 0.2 au, $M_\mathrm{pl}\gt 1\, M_\mathrm{J}$) around recently identified low density host stars, hinting at isolation mass limited growth. We discuss the necessary circumstances for a coincidental age-related bias as the origin of this result; such a bias is possible but unlikely. We conclude that, in light of the evidence suggesting that some planetary systems have been dynamically perturbed, simple models for planet growth during the formation stage are worth revisiting.

中文翻译：

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内行星生长的上限？

已知行星系统的奇异范围引发了对其多样化结构的同样奇异的物理解释。然而，限制形成过程需要将观察到的系外行星种群映射到最初在原行星盘中形成的种群。许多结果表明（内部或外部）动态扰动改变了一些系外行星系统的架构。隔离在没有任何扰动的情况下进化的行星可以帮助限制形成过程。我们考虑开普勒倍数，它们相互倾角低，不太可能受到动态扰动。我们应用了对先前建模工作的调整，考虑了半径的二维（$R_\mathrm{pl} =0.3\!-\!20\, R_\oplus$）和周期（Porb = 0.5–730 d ） 分配。我们发现行星质量的上限形式为 $M_\mathrm{lim} \propto a_\mathrm{pl}^{\beta } \exp (-a_\mathrm{in}/a_\mathrm{pl}) $，对于半长轴 apl 和广泛的 ain 和 β，可以重现 Porb、Rpl 的分布，这与我们的比较度量观察到的分布无法区分。该指数与 β = 1.5 一致，如果增长受到希尔半径内的增长限制，则可以预期。该模型优于假设 Porb, Rpl 中的可分离 PDF 的模型。外推到更长周期的极限与最近发现的低密度附近的 RV 发现的行星（apl > 0.2 au, $M_\mathrm{pl}\gt 1\, M_\mathrm{J}$）的轨道一致宿主恒星，暗示孤立质量限制了增长。我们讨论了巧合的与年龄相关的偏见的必要情况，作为这一结果的起源；这种偏见是可能的，但不太可能。我们得出的结论是，鉴于有证据表明某些行星系统已受到动态扰动，因此值得重新审视形成阶段行星生长的简单模型。