The rotational evolution of cool dwarfs is poorly constrained after around 1-2 Gyr due to a lack of precise ages and rotation periods for old main-sequence stars. In this work we use velocity dispersion as an age proxy to reveal the temperature-dependent rotational evolution of low-mass Kepler dwarfs, and demonstrate that kinematic ages could be a useful tool for calibrating gyrochronology in the future. We find that a linear gyrochronology model, calibrated to fit the period-Teff relationship of the Praesepe cluster, does not apply to stars older than around 1 Gyr. Although late-K dwarfs spin more slowly than early-K dwarfs when they are young, at old ages we find that late-K dwarfs rotate at the same rate or faster than early-K dwarfs of the same age. This result agrees qualitatively with semi-empirical models that vary the rate of surface-to-core angular momentum transport as a function of time and mass. It also aligns with recent observations of stars in the NGC 6811 cluster, which indicate that the surface rotation rates of K dwarfs go through an epoch of inhibited evolution. We find that the oldest Kepler stars with measured rotation periods are late-K and early-M dwarfs, indicating that these stars maintain spotted surfaces and stay magnetically active longer than more massive stars. Finally, based on their kinematics, we confirm that many rapidly rotating GKM dwarfs are likely to be synchronized binaries.

中文翻译：

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使用银河运动学探索恒星自转的演化

由于缺乏老主序星的精确年龄和自转周期，冷矮星的自转演化在大约 1-2 Gyr 之后受到限制。在这项工作中，我们使用速度色散作为年龄代理来揭示低质量开普勒矮星与温度相关的旋转演化，并证明运动年龄可能是未来校准陀螺年代学的有用工具。我们发现一个线性陀螺年代学模型，经过校准以适应 Praesepe 星团的周期-Teff 关系，不适用于年龄超过 1 Gyr 的恒星。尽管晚 K 矮星在年轻时的自转速度比早 K 矮星慢，但在老年时，我们发现晚 K 矮星的自转速度与同龄的早 K 矮星相同或更快。该结果与半经验模型定性一致，该模型将表面到核心角动量传输的速率作为时间和质量的函数而变化。它还与最近对 NGC 6811 星团中恒星的观察结果一致，这表明 K 矮星的表面旋转率经历了一个演化受抑制的时期。我们发现具有测量自转周期的最古老的开普勒恒星是晚 K 和早 M 的矮星，这表明这些恒星保持斑点表面并且比更大质量的恒星保持更长时间的磁活动。最后，基于它们的运动学，我们确认许多快速旋转的 GKM 矮星很可能是同步双星。这表明 K 矮星的表面旋转速率经历了一个进化受抑制的时期。我们发现具有测量自转周期的最古老的开普勒恒星是晚 K 和早 M 的矮星，这表明这些恒星保持斑点表面并且比更大质量的恒星保持更长时间的磁活动。最后，基于它们的运动学，我们确认许多快速旋转的 GKM 矮星很可能是同步双星。这表明 K 矮星的表面旋转速率经历了一个进化受抑制的时期。我们发现具有测量自转周期的最古老的开普勒恒星是晚 K 和早 M 的矮星，这表明这些恒星保持斑点表面并且比更大质量的恒星保持更长时间的磁活动。最后，基于它们的运动学，我们确认许多快速旋转的 GKM 矮星很可能是同步双星。