Estimating stellar ages is important for advancing our understanding of stellar and exoplanet evolution and investigating the history of the Milky Way. However, ages for low-mass stars are hard to infer as they evolve slowly on the main sequence. In addition, empirical dating methods are difficult to calibrate for low-mass stars as they are faint. In this work, we calculate ages for Kepler F, G, and crucially K and M dwarfs, using their rotation and kinematic properties. We apply the simple assumption that the velocity dispersion of stars increases over time and adopt an age–velocity-dispersion relation (AVR) to estimate average stellar ages for groupings of coeval stars. We calculate the vertical velocity dispersion of stars in bins of absolute magnitude, temperature, rotation period, and Rossby number and then convert velocity dispersion to kinematic age via an AVR. Using this method, we estimate gyro-kinematic ages for 29,949 Kepler stars with measured rotation periods. We are able to estimate ages for clusters and asteroseismic stars with an rms of 1.22 Gyr and 0.26 Gyr respectively. With our Astraea machine-learning algorithm, which predicts rotation periods, we suggest a new selection criterion (a weight of 0.15) to increase the size of the McQuillan et al. catalog of Kepler rotation periods by up to 25%. Using predicted rotation periods, we estimated gyro-kinematic ages for stars without measured rotation periods and found promising results by comparing 12 detailed age–element abundance trends with literature values.

估计恒星年龄对于增进我们对恒星和系外行星演化的理解以及研究银河系的历史非常重要。然而，低质量恒星的年龄很难推断，因为它们在主序带上演化缓慢。此外，经验定年方法很难校准低质量恒星，因为它们很暗。在这项工作中，我们使用它们的旋转和运动学特性计算开普勒 F、G 以及关键的 K 和 M 矮人的年龄。我们应用恒星的速度色散随时间增加的简单假设，并采用年龄-速度-色散关系（AVR）来估计同时期恒星分组的平均恒星年龄。我们计算绝对星等、温度、自转周期、和罗斯比数，然后通过 AVR 将速度色散转换为运动年龄。使用这种方法，我们估计测量自转周期的 29,949 颗开普勒星的陀螺运动年龄。我们能够分别以 1.22 Gyr 和 0.26 Gyr 的 rms 估计星团和星震星的年龄。使用我们的Astraea机器学习算法来预测旋转周期，我们建议了一个新的选择标准（权重为 0.15）来增加 McQuillan 等人的规模。开普勒旋转周期目录最多增加 25%。使用预测的自转周期，我们估计了没有测量自转周期的恒星的陀螺运动年龄，并通过将 12 种详细的年龄-元素丰度趋势与文献值进行比较，发现了有希望的结果。