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Table 4.

Fitting parameters of the period–activity relationship in terms of the CgIW scenario along with the effective temperature.

Temperature range βg βi Psat Pg−to−I Rosat Rog−to−I log R HK , sat $ {\mathrm {log}} R^\prime_{\mathrm {HK,sat}} $ AgeC−to−g Ageg−to−I PI−to−W AgeI−to−W
(K) (day) (day) (Myr) (Myr) (day) (Gyr)
3500−4000 0 . 032 0.003 + 0.003 $ -0.032^{+0.003}_{-0.003} $ 0 . 000 0.01 + 0.01 $ -0.000^{+0.01}_{-0.01} $ 5 . 13 1.50 + 1.79 $ 5.13^{+1.79}_{-1.50} $ 22 . 92 2.55 + 1.86 $ 22.92^{+1.86}_{-2.55} $ 0 . 031 0.009 + 0.011 $ 0.031^{+0.011}_{-0.009} $ 0 . 138 0.015 + 0.011 $ 0.138^{+0.011}_{-0.015} $ 4 . 15 0.20 + 0.20 $ -4.15^{+0.20}_{-0.20} $ 429 107 + 106 $ 429^{+106}_{-107} $ 1494 181 + 141 $ 1494^{+141}_{-181} $ 116 19.5
3750−4250 0 . 041 0.003 + 0.003 $ -0.041^{+0.003}_{-0.003} $ 0 . 005 0.01 + 0.01 $ -0.005^{+0.01}_{-0.01} $ 4 . 57 0.86 + 0.56 $ 4.57^{+0.56}_{-0.86} $ 15 . 93 0.99 + 0.94 $ 15.93^{+0.94}_{-0.99} $ 0 . 039 0.007 + 0.005 $ 0.039^{+0.005}_{-0.007} $ 0 . 135 0.008 + 0.008 $ 0.135^{+0.008}_{-0.008} $ 4 . 15 0.15 + 0.15 $ -4.15^{+0.15}_{-0.15} $ 297 51 + 31 $ 297^{+31}_{-51} $ 972 70 + 70 $ 972^{+70}_{-70} $ 82 13.8
4000−4500 0 . 038 0.004 + 0.004 $ -0.038^{+0.004}_{-0.004} $ 0 . 008 0.01 + 0.01 $ -0.008^{+0.01}_{-0.01} $ 2 . 69 0.45 + 0.47 $ 2.69^{+0.47}_{-0.45} $ 13 . 57 0.97 + 0.86 $ 13.57^{+0.86}_{-0.97} $ 0 . 029 0.005 + 0.005 $ 0.029^{+0.005}_{-0.005} $ 0 . 146 0.010 + 0.009 $ 0.146^{+0.009}_{-0.010} $ 4 . 19 0.11 + 0.11 $ -4.19^{+0.11}_{-0.11} $ 144 32 + 30 $ 144^{+30}_{-32} $ 806 72 + 67 $ 806^{+67}_{-72} $ 65 10.9
4250−4750 0 . 052 0.005 + 0.005 $ -0.052^{+0.005}_{-0.005} $ 0 . 008 0.01 + 0.01 $ -0.008^{+0.01}_{-0.01} $ 2 . 00 0.51 + 0.45 $ 2.00^{+0.45}_{-0.51} $ 11 . 65 1.01 + 1.11 $ 11.65^{+1.11}_{-1.01} $ 0 . 026 0.006 + 0.006 $ 0.026^{+0.006}_{-0.006} $ 0 . 150 0.013 + 0.014 $ 0.150^{+0.014}_{-0.013} $ 4 . 15 0.14 + 0.14 $ -4.15^{+0.14}_{-0.14} $ 80 36 + 31 $ 80^{+31}_{-36} $ 675 76 + 89 $ 675^{+89}_{-76} $ 54 9.1
4500−5000 0 . 058 0.005 + 0.005 $ -0.058^{+0.005}_{-0.005} $ 0 . 012 0.01 + 0.01 $ -0.012^{+0.01}_{-0.01} $ 1 . 86 0.45 + 0.43 $ 1.86^{+0.43}_{-0.45} $ 10 . 41 0.63 + 0.68 $ 10.41^{+0.68}_{-0.63} $ 0 . 028 0.006 + 0.006 $ 0.028^{+0.006}_{-0.006} $ 0 . 157 0.009 + 0.010 $ 0.157^{+0.010}_{-0.009} $ 4 . 08 0.15 + 0.15 $ -4.08^{+0.15}_{-0.15} $ 62 31 + 27 $ 62^{+27}_{-31} $ 596 50 + 56 $ 596^{+56}_{-50} $ 47 7.7
4750−5250 0 . 065 0.005 + 0.005 $ -0.065^{+0.005}_{-0.005} $ 0 . 015 0.01 + 0.01 $ -0.015^{+0.01}_{-0.01} $ 1 . 51 0.31 + 0.35 $ 1.51^{+0.35}_{-0.31} $ 9 . 21 0.69 + 0.75 $ 9.21^{+0.75}_{-0.69} $ 0 . 026 0.006 + 0.006 $ 0.026^{+0.006}_{-0.006} $ 0 . 160 0.012 + 0.013 $ 0.160^{+0.013}_{-0.012} $ 4 . 03 0.15 + 0.15 $ -4.03^{+0.15}_{-0.15} $ 33 24 + 23 $ 33^{+23}_{-24} $ 517 55 + 63 $ 517^{+63}_{-55} $ 40 6.7
5000−5500 0 . 069 0.005 + 0.005 $ -0.069^{+0.005}_{-0.005} $ 0 . 018 0.01 + 0.01 $ -0.018^{+0.01}_{-0.01} $ 1 . 51 0.29 + 0.26 $ 1.51^{+0.26}_{-0.29} $ 8 . 16 0.44 + 0.49 $ 8.16^{+0.49}_{-0.44} $ 0 . 031 0.005 + 0.005 $ 0.031^{+0.005}_{-0.005} $ 0 . 165 0.009 + 0.010 $ 0.165^{+0.010}_{-0.009} $ 4 . 05 0.19 + 0.19 $ -4.05^{+0.19}_{-0.19} $ 29 20 + 16 $ 29^{+16}_{-20} $ 453 36 + 42 $ 453^{+42}_{-36} $ 35 5.7
5250−5750 0 . 085 0.007 + 0.007 $ -0.085^{+0.007}_{-0.007} $ 0 . 019 0.01 + 0.01 $ -0.019^{+0.01}_{-0.01} $ 1 . 66 0.28 + 0.25 $ 1.66^{+0.25}_{-0.28} $ 5 . 89 0.68 + 0.57 $ 5.89^{+0.57}_{-0.68} $ 0 . 040 0.007 + 0.006 $ 0.040^{+0.006}_{-0.007} $ 0 . 144 0.017 + 0.014 $ 0.144^{+0.014}_{-0.017} $ 4 . 07 0.22 + 0.22 $ -4.07^{+0.22}_{-0.22} $ 34 16 + 14 $ 34^{+14}_{-16} $ 291 49 + 45 $ 291^{+45}_{-49} $ 29 4.7
5500−6000 0 . 145 0.010 + 0.010 $ -0.145^{+0.010}_{-0.010} $ 0 . 023 0.01 + 0.01 $ -0.023^{+0.01}_{-0.01} $ 0 . 79 0.29 + 0.21 $ 0.79^{+0.21}_{-0.29} $ 4 . 24 0.71 + 0.58 $ 4.24^{+0.58}_{-0.71} $ 0 . 035 0.013 + 0.009 $ 0.035^{+0.009}_{-0.013} $ 0 . 131 0.021 + 0.018 $ 0.131^{+0.018}_{-0.021} $ 4 . 00 0.25 + 0.25 $ -4.00^{+0.25}_{-0.25} $ 0 0 + 11 $ 0^{+11}_{-0} $ 185 48 + 43 $ 185^{+43}_{-48} $ 22 3.7
5750−6250 0 . 192 0.010 + 0.010 $ -0.192^{+0.010}_{-0.010} $ 0 . 045 0.01 + 0.01 $ -0.045^{+0.01}_{-0.01} $ 0 2 . 02 0.35 + 0.62 $ 2.02^{+0.62}_{-0.35} $ 0 0 . 090 0.016 + 0.028 $ 0.090^{+0.028}_{-0.016} $ 4 . 00 0.27 + 0.27 $ -4.00^{+0.27}_{-0.27} $ 0 50 20 + 38 $ 50^{+38}_{-20} $ 16 2.6
6000−6500 0 . 089 0.02 + 0.02 $ -0.089^{+0.02}_{-0.02} $ 0 0 0 0 0 0 7 1.1

Notes. The period–activity relationship in terms of the CgIW scenario along with the effective temperature is shown in Fig. F.1, Fig. F.2, and Fig. F.3. This table present the fitting results. The parameters β represents the slope in each evolution phase. The parameters P and Ro represent the critical rotation periods and Rossby number that separate two neighboring phases, respectively. The parameter log R HK , sat $ {\mathrm {log}} R^\prime_{\mathrm {HK,sat}} $ represents the saturated activity. The parameter Age represents the corresponding age of the critical rotation period, which is derived from Eq. (5). The critical Rossby number of the transition from the I phase to the W phase is 0.7 (van Saders et al. 2016), which is used to calculate PI−to−W and AgeI−to−W. The median of the temperature range is used to calculate Rossby number and the critical ages. The uncertainty of log R HK , sat $ {\mathrm {log}} R^\prime_{\mathrm {HK,sat}} $ is calculated using the 1σ scatter of the fit.

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