A BCool survey of stellar magnetic cycles | Astronomy & Astrophysics (A&A)

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Table 2.

Results of the GP fit carried out on the B_l time series for all our stars.

Hyperparameter	Prior	HD 9986	HD 56124	HD 73350	HD 76151	HD 166435	HD 175726
B_l amplitude [G] (θ₁)	𝒰(0, 100)	$0 . 8_{- 0.3}^{+ 0.5}$ $0.8^{+0.5}_{-0.3}$	$1 . 8_{- 0.5}^{+ 0.7}$ $1.8^{+0.7}_{-0.5}$	$3 . 2_{- 0.9}^{+ 1.6}$ $3.2^{+1.6}_{-0.9}$	$2 . 8_{- 0.4}^{+ 0.4}$ $2.8^{+0.4}_{-0.4}$	$5 . 2_{- 1.2}^{+ 1.7}$ $5.2^{+1.7}_{-1.2}$	$4 . 7_{- 0.9}^{+ 1.0}$ $4.7^{+1.0}_{-0.9}$
Evolution time [d] (θ₂)	𝒰(1, 3000)	$852_{- 375}^{+ 497}$ $852^{+497}_{-375}$	$511_{- 275}^{+ 390}$ $511^{+390}_{-275}$	$1497_{- 931}^{+ 1002}$ $1497^{+1002}_{-931}$	$232_{- 41}^{+ 40}$ $232^{+40}_{-41}$	$652_{- 293}^{+ 541}$ $652^{+541}_{-293}$	$148_{- 140}^{+ 1954}$ $148^{+1954}_{-140}$
P_rot [d] (θ₃)	𝒰(1, 50)^( * )	$22 . 76_{- 2.36}^{+ 2.36}$ $22.76^{+2.36}_{-2.36}$	$21 . 32_{- 2.01}^{+ 1.96}$ $21.32^{+1.96}_{-2.01}$	$14 . 20_{- 1.79}^{+ 13.06}$ $14.20^{+13.06}_{-1.79}$	$16 . 70_{- 0.16}^{+ 0.18}$ $16.70^{+0.18}_{-0.16}$	$3 . 52_{- 0.03}^{+ 0.01}$ $3.52^{+0.01}_{-0.03}$	$4 . 04_{- 0.11}^{+ 0.11}$ $4.04^{+0.11}_{-0.11}$
Smoothness (θ₄)	𝒰(0.1, 1.2)	$0 . 4_{- 0.2}^{+ 0.3}$ $0.4^{+0.3}_{-0.2}$	$0 . 9_{- 0.3}^{+ 0.3}$ $0.9^{+0.3}_{-0.3}$	$0 . 2_{- 0.3}^{+ 0.4}$ $0.2^{+0.4}_{-0.3}$	$1 . 2_{- 0.1}^{+ 0.1}$ $1.2^{+0.1}_{-0.1}$	$1 . 0_{- 0.2}^{+ 0.2}$ $1.0^{+0.2}_{-0.2}$	$0 . 1_{- 0.1}^{+ 0.2}$ $0.1^{+0.2}_{-0.1}$
Uncorrelated noise [G] (S)	𝒰(0, 100)	$0 . 03_{- 0.11}^{+ 0.17}$ $0.03^{+0.17}_{-0.11}$	$0 . 93_{- 0.24}^{+ 0.26}$ $0.93^{+0.26}_{-0.24}$	$1 . 28_{- 0.61}^{+ 0.56}$ $1.28^{+0.56}_{-0.61}$	$0 . 71_{- 0.11}^{+ 0.11}$ $0.71^{+0.11}_{-0.11}$	$3 . 91_{- 0.39}^{+ 0.44}$ $3.91^{+0.44}_{-0.39}$	$1 . 45_{- 0.85}^{+ 0.73}$ $1.45^{+0.73}_{-0.85}$
$χ_{r}^{2}$ $\chi^2_r$		0.63	2.2	1.50	1.74	18.9	0.85
Residuals (RMS, [G])		0.83	1.7	2.13	1.06	4.26	1.27

Notes. The columns are: hyperparameter name, uniform prior distribution of the form 𝒰(min, max), and mode of the posterior distribution for each star. The error bars are the 16th and 84th percentiles of the posterior distribution. The rows list the five hyperparameters of the GP along with the χ² of the model and the RMS scatter of the residuals. ^( * ) the uniform prior was restricted to 1–10 d for HD 175726 and was changed to a Gaussian prior 𝒢(3.47 d, 0.10 d) for HD 166435 (see Sect. 6).

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