标题： 旋转恒星的四个年龄在自转-活动关系和陀螺时标中的作用 显示英文标题

标题： Four ages of rotating stars in the rotation--activity relationship and gyrochronology

摘要： 恒星自转年代学和自转-活动关系是确定恒星演化阶段的标准方法。然而，到目前为止，演化阶段定义上的差异已经在物理和数学上引发了许多问题，并阻碍了我们理解内部发电机过程如何影响可观测性质。为了解决这个问题，我们寻求一种统一的方案，以显示恒星自转年代学与自转-活动关系之间的一一映射。我们获得了6846颗恒星的色球活动水平 $R'_{\rm HK}$ 和它们的自转周期，以研究自转-活动关系。我们应用三段模型来拟合这种关系，并发现它在 \( Ro\$<0.7$\) 范围内由三个区间最佳拟合。我们将这些区间关联到恒星自转年代学的对流、间隙和界面阶段。此外，我们在I阶段晚期建议了一个额外的时期。我们进一步使用三段模型，在温度分组中拟合周期-活动关系，并根据有效温度确定过渡阶段的持续时间。通过比较g到I转变的关键温度和周期与年龄从1百万年到25亿年的10个年轻疏散星团的缓慢旋转序列，我们得出结论，我们的新模型找到了纯I序列，没有快速旋转的异常值，这定义了零年龄I序列（ZAIS）。我们提出，关于I序列何时开始工作的共识存在模糊性。这种模糊性来自疏散星团中颜色-周期图的视觉收敛序列。这个视觉收敛序列比ZAIS更年轻，并且实际上是与自旋减速停滞相关的预I序列。我们的结果统一了低质量恒星演化的自转-活动关系和恒星自转年代学，为此我们提出了“CgIW”情景。 显示英文摘要

摘要： Gyrochronology and the rotation--activity relationship are standard techniques used to determine the evolution phase.The mismatch in the definition of the evolutionary phases has so far raised many issues in physics and mathematics and hampered the understanding of how the internal dynamo processes affect the observable properties.To address this problem, we seek a unified scheme that shows a one-to-one mapping from gyrochronology to the rotation--activity relationship.We obtained the chromospheric activity $R'_{\rm HK}$ of 6846 stars and their rotation periods to investigate the rotation--activity relationship.We apply a three-interval model to fit the relationship and find that it is best fitted by three intervals in the range of Ro$<0.7$.We associate those intervals to the convective, gap and interface phases of gyrochronology.Furthermore,we suggest an additional epoch at late times of the I phase.We further use the three-interval models to fit the period--activity relationship in temperature bins and determine the duration of the transition phase as a function of effective temperature.By comparing the critical temperature and period of the g-to-I transition with the slowly rotating sequence of 10 young open clusters whose ages range from 1 Myr to 2.5 Gyr, we conclude that our new model finds the pure I sequence without fast rotating outliers, which defines the zero-age I sequence (ZAIS).We propose that there is an ambiguous consensus on when the I sequence starts to work.This ambiguity is from the visually convergent sequence of the color--period diagrams in open clusters.This visually convergent sequence is younger than the ZAIS and is actually the pre-I sequence that can be associated with the stall of the spin-down. Our results unify the rotation--activity relationship and gyrochonology for the stellar evolution of low-mass stars, for which we coined the ``CgIW" scenario.