Table 3.
Parameters of the activity–rotation relationship for different proxies.
| Reference | Spectra | Sample | Activity | Rotation | β | Rosat×102 | log Ract,sat | ||
|---|---|---|---|---|---|---|---|---|---|
| Type | Number | Proxy | Proxy | Local τc | Global τc | Local τc | Global τc | ||
| Soderblom et al. (1993) | F,G,K | ∼110 | Hα,Ca II IRT | v sin i | − | − | − | − | −(3.5–4) |
| Jackson & Jeffries (2010) | K,M | ∼240 | Ca II IRT | v sin i | ∼−1 | − | ∼10 | − | ∼−4.4 |
| Mohanty & Basri (2003) | M,L | ∼100 | Hα | v sin i | − | − | − | − | −(3.9–4.2) |
| Delfosse et al. (1998) | M | ∼120 | Hα | v sin i | − | − | − | − | −(3.5–4) |
| Newton et al. (2017) | M | ∼350 | Hα | Period | −1.7±0.1 | −2.0±0.2 | 21±2 | 6±1 | −3.8 |
| Douglas et al. (2014) | M | ∼100 | Hα | Period | −0.73±0.1 | −0.83±0.3 | 11±3 | 3.5±0.6 | −3.9 |
| McLean et al. (2012) | M,L | ∼160 | Radio | v sin i | −1.1 | − | − | − | −7.5 |
| Pizzolato et al. (2003) | F,G,K,M | ∼250 | X-ray | Period | −2 | − | ∼13 | − | −3.2±0.3 |
| Wright et al. (2011, 2018) | F,G,K,M | ∼820 | X-ray | Period | −2.3±0.5 | −2.2±0.1 | 14±6 | 5±0.2 | −3.1±0.2 |
| Mittag et al. (2018) | F,G,K,M | ∼170 |  |
Period | − | −0.93±0.1 | − | 3.3±0.7 | −3.6±0.2 |
| Yang & Liu (2019) | K,M | ∼1480 | Flare | Period | − | −3.9±0.2 | − | 6.6±0.5 | −4.1±0.1 |
| Lehtinen et al. (2020) | F,G,K | ∼150 |  |
Period | − | −1.0±0.1 | − | − | ∼−4.0 |
| This study | F,G,K,M | ∼6850 |  |
Period | − | −0.62±0.05 | − | 3.0±0.3 | −4.0±0.1 |
Notes. The studies on the rotation–activity relationship whose sample number Nstar>100. The column Ract,sat indicate the activity values in the saturation regime for different proxies. Parameters of this study are mean values of F-,G-,K-,M-type stars. Parameters derived by global τc for Rflare (Yang & Liu 2019) and 
(Mittag et al. 2018), RX (Wright et al. 2011) and RHα (Douglas et al. 2014; Newton et al. 2017) were fit by the emcee method used in this study, see Appendix C for details. The sample of Lehtinen et al. (2020) is lack of fast rotators, which may lead to a biased β. The sample of Soderblom et al. (1993) is from open cluster the Pleiades (tage∼125 Myr). The sample of Douglas et al. (2014) is from open cluster the Praesepe and the Hyades (tage∼750 Myr). The sample of Jackson & Jeffries (2010) is from open cluster NGC2516 (tage∼150 Myr). Parameters derived by local τc for X-ray are from Wright et al. (2018), which includes fully convective stars. About 45% stars of Wright et al. (2011) are from open clusters whose ages are from 40 Myr to 700 Myr.
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