To date, only 18 exoplanets with radial velocity (RV) semi-amplitude <2 m s−1 have had their masses directly constrained. The biggest obstacle to RV detection of such exoplanets is variability intrinsic to stars themselves, e.g. nuisance signals arising from surface magnetic activity such as rotating spots and plages, which can drown out or even mimic planetary RV signals. We use Kepler-37 – known to host three transiting planets, one of which, Kepler-37d, should be on the cusp of RV detectability with modern spectrographs – as a case study in disentangling planetary and stellar activity signals. We show how two different statistical techniques – one seeking to identify activity signals in stellar spectra, and another to model activity signals in extracted RVs and activity indicators – can each enable a detection of the hitherto elusive Kepler-37d. Moreover, we show that these two approaches can be complementary, and in combination, facilitate a definitive detection and precise characterization of Kepler-37d. Its RV semi-amplitude of 1.22 ± 0.31 m s−1 (mass 5.4 ± 1.4 M⊕) is formally consistent with TOI-178b’s $1.05^{+0.25}_{-0.30}$ m s−1, the latter being the smallest detected RV signal of any transiting planet to date, though dynamical simulations suggest Kepler-37d’s mass may be on the lower end of our 1σ credible interval. Its consequent density is consistent with either a water-world or that of a gaseous envelope ($\sim 0.4{{\ \rm per\ cent}}$ by mass) surrounding a rocky core. Based on RV modelling and a re-analysis of Kepler-37 TTVs, we also suggest that the putative (non-transiting) planet Kepler-37e should be stripped of its ‘confirmed’ status.

中文翻译：

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难以捉摸的 Kepler-37d 的 HARPS-N 质量：解开恒星活动和行星信号的案例研究

迄今为止，只有 18 颗径向速度 (RV) 半振幅 <2 ms-1 的系外行星的质量受到直接约束。对此类系外行星进行 RV 检测的最大障碍是恒星本身固有的可变性，例如由表面磁活动（如旋转点和斑块）产生的有害信号，这些信号可能会淹没甚至模仿行星 RV 信号。我们使用 Kepler-37 - 已知拥有三颗过境行星，其中之一 Kepler-37d 应该处于现代光谱仪可探测到 RV 的风口浪尖 - 作为解开行星和恒星活动信号的案例研究。我们展示了两种不同的统计技术——一种试图识别恒星光谱中的活动信号，另一个用于模拟提取的 RV 和活动指标中的活动信号 - 每个都可以检测迄今为止难以捉摸的 Kepler-37d。此外，我们表明这两种方法可以互补，并且结合起来，有助于明确检测和精确表征 Kepler-37d。其 RV 半振幅 1.22 ± 0.31 ms−1（质量 5.4 ± 1.4 M⊕）与 TOI-178b 的 $1.05^{+0.25}_{-0.30}$ ms−1 一致，后者是检测到的最小 RV迄今为止，任何凌日行星的信号，尽管动力学模拟表明 Kepler-37d 的质量可能位于我们 1σ 可信区间的下端。其结果密度与水世界或围绕岩石核心的气态外壳的密度一致（$\sim 0.4{{\ \rm per\ cent}}$）。基于 RV 建模和对 Kepler-37 TTV 的重新分析，