By controlling instrumental errors to below 10 cm/s, the EXtreme PREcision Spectrograph (EXPRES) allows for a more insightful study of photospheric velocities that can mask weak Keplerian signals. Gaussian Processes (GP) have become a standard tool for modeling correlated noise in radial velocity datasets. While GPs are constrained and motivated by physical properties of the star, in some cases they are still flexible enough to absorb unresolved Keplerian signals. We apply GP regression to EXPRES radial velocity measurements of the 3.5 Gyr old chromospherically active Sun-like star, HD 101501. We obtain tight constraints on the stellar rotation period and the evolution of spot distributions using 28 seasons of ground-based photometry, as well as recent $TESS$ data. Light curve inversion was carried out on both photometry datasets to reveal the spot distribution and spot evolution timescales on the star. We find that the $> 5$ m/s rms radial velocity variations in HD 101501 are well-modeled with a GP stellar activity model without planets, yielding a residual rms scatter of 45 cm/s. We carry out simulations, injecting and recovering signals with the GP framework, to demonstrate that high-cadence observations are required to use GPs most efficiently to detect low-mass planets around active stars like HD 101501. Sparse sampling prevents GPs from learning the correlated noise structure and can allow it to absorb prospective Keplerian signals. We quantify the moderate to high-cadence monitoring that provides the necessary information to disentangle photospheric features using GPs and to detect planets around active stars.

中文翻译：

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快递。二、寻找活跃恒星周围的行星：以HD 101501为例

通过将仪器误差控制在 10 cm/s 以下，极精密光谱仪 (EXPRES) 可以更深入地研究可以掩盖微弱开普勒信号的光球速度。高斯过程 (GP) 已成为对径向速度数据集中的相关噪声进行建模的标准工具。虽然 GP 受到恒星物理特性的限制和激励，但在某些情况下，它们仍然足够灵活，可以吸收未解析的开普勒信号。我们将 GP 回归应用于 3.5 Gyr 旧色球活动类太阳恒星 HD 101501 的 EXPRES 径向速度测量值。我们使用 28 个季节的地面测光获得对恒星旋转周期和光斑分布演化的严格约束，以及作为最近的 $TESS$ 数据。在两个测光数据集上都进行了光变曲线反演，以揭示恒星上的光斑分布和光斑演化时间尺度。我们发现 HD 101501 中 $> 5 $ m/s rms 径向速度变化是用没有行星的 GP 恒星活动模型很好地建模的，产生了 45 cm/s 的残余 rms 散射。我们使用 GP 框架进行模拟、注入和恢复信号，以证明需要高节奏的观测才能最有效地使用 GP 来检测 HD 101501 等活动恒星周围的低质量行星。稀疏采样可防止 GP 学习相关噪声结构，并可以让它吸收预期的开普勒信号。