It is well established that late-type main-sequence (MS) stars display a relationship between X-ray activity and the Rossby number, Ro, the ratio of rotation period to the convective turnover time. This manifests itself as a saturated regime (where X-ray activity is constant) and an unsaturated regime (where X-ray activity anti-correlates with Rossby number). However, this relationship breaks down for the fastest rotators. We cross-correlated SuperWASP visually classified photometric light curves and All-Sky Automated Survey for Supernovae automatically classified photometric light curves with XMM-Newton X-ray observations to identify 3 178 stars displaying a photometrically defined rotational modulation in their light curve and corresponding X-ray observations. We fitted a power-law to characterise the rotation–activity relation of 900 MS stars. We identified that automatically classified rotationally modulated light curves are not as reliable as visually classified light curves for this work. We found a power-law index in the unsaturated regime of G- to M-type stars of $\beta=-1.84\,\pm\,0.18$ for the SuperWASP catalogue, in line with the canonical value of $\beta=-2$ . We find evidence of supersaturation in the fastest rotating K-type stars, with a power-law index of $\beta_{s}=1.42\pm0.26$ .

中文翻译：

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SuperWASP 和 ASAS-SN 场星样本的恒星自转-活动关系

众所周知，晚型主序（MS）星显示出 X 射线活动和罗斯比数之间的关系，罗，旋转周期与对流周转时间的比率。这表现为饱和状态（其中 X 射线活动是恒定的）和不饱和状态（其中 X 射线活动与罗斯比数反相关）。但是，对于最快的旋转器，这种关系会失效。我们将 SuperWASP 视觉分类光度曲线和超新星全天自动巡天自动分类光度曲线与 XMM-牛顿 X 射线观测结果进行交叉关联，以识别 3 178 颗在其光度曲线中显示出光度定义旋转调制的恒星和相应的 X-射线观测。我们拟合了一个幂律来描述 900 颗 MS 恒星的自转-活动关系。我们发现自动分类的旋转调制光曲线不如视觉分类的光曲线可靠。我们在 G 型到 M 型恒星的不饱和状态中发现了幂律指数 $\beta=-1.84\,\pm\,0.18$ 对于 SuperWASP 目录，符合规范值 $\beta=-2$ . 我们在旋转速度最快的 K 型恒星中发现了过饱和的证据，其幂律指数为 $\beta_{s}=1.42\pm0.26$ .