A fast method for deriving relative small-scale magnetic field variations from high-resolution spectroscopy

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Volume 708 (April 2026)

A&A, 708 (2026) A207

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Table B.1

GP hyper-parameters obtained for EV Lac, DS Leo, and Barnard’s star from SPIRou spectra.

	Value	Prior
GP fit for EV Lac
μ (kG)	$- {0.10}_{- 0.20}^{+ 0.19}$ $Mathematical equation: $-0.10^{+0.19}_{-0.20}$$	U(−10, 10)
σ (kG)	${0.03}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $0.03^{+0.01}_{-0.01}$$	U(0, 1000)
α (kG)	${0.33}_{- 0.09}^{+ 0.14}$ $Mathematical equation: $0.33^{+0.14}_{-0.09}$$	U(0, 100)
l (d)	$420_{- 64}^{+ 73}$ $Mathematical equation: $420^{+73}_{-64}$$	U(100, 800)
β	${0.60}_{- 0.11}^{+ 0.13}$ $Mathematical equation: $0.60^{+0.13}_{-0.11}$$	U(0, 10)
P_rot (d)	${4.361}_{- 0.001}^{+ 0.001}$ $Mathematical equation: $4.361^{+0.001}_{-0.001}$$	U(0, 10)
$χ_{r}^{2}$ $Mathematical equation: $\chi^2_r$$	1.05
RMS	0.06 (kG)

GP fit for DS Leo
μ (kG)	${0.01}_{- 0.02}^{+ 0.02}$ $Mathematical equation: $0.01^{+0.02}_{-0.02}$$	U(−5, 5)
σ (kG)	${0.01}_{- 0.01}^{+ 0.00}$ $Mathematical equation: $0.01^{+0.00}_{-0.01}$$	U(0, 1000)
α (kG)	${0.08}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $0.08^{+0.01}_{-0.01}$$	U(0, 10)
l (d)	$58_{- 7}^{+ 7}$ $Mathematical equation: $58^{+7}_{-7}$$	U(30, 500)
β	${0.61}_{- 0.09}^{+ 0.10}$ $Mathematical equation: $0.61^{+0.10}_{-0.09}$$	U(0, 20)
P_rot (d)	${14.063}_{- 0.081}^{+ 0.080}$ $Mathematical equation: $14.063^{+0.080}_{-0.081}$$	U(5, 20)
$χ_{r}^{2}$ $Mathematical equation: $\chi^2_r$$	0.74
RMS	0.02 (kG)

GP fit for Barnard's star
μ (kG)	${0.02}_{- 0.03}^{+ 0.03}$ $Mathematical equation: $0.02^{+0.03}_{-0.03}$$	U(−10, 10)
σ (kG)	${0.00}_{- 0.00}^{+ 0.00}$ $Mathematical equation: $0.00^{+0.00}_{-0.00}$$	U(0, 1000)
α (kG)	${0.11}_{- 0.02}^{+ 0.02}$ $Mathematical equation: $0.11^{+0.02}_{-0.02}$$	U(0, 10)
l (d)	$137_{- 29}^{+ 26}$ $Mathematical equation: $137^{+26}_{-29}$$	U(50, 500)
β	${0.60}_{- 0.10}^{+ 0.12}$ $Mathematical equation: $0.60^{+0.12}_{-0.10}$$	U(0, 20)
P_rot (d)	${146.338}_{- 5.333}^{+ 7.961}$ $Mathematical equation: $146.338^{+7.961}_{-5.333}$$	U(50, 200)
$χ_{r}^{2}$ $Mathematical equation: $\chi^2_r$$	0.82
RMS	0.05 (kG)

Notes. The hyper-parameters of the kernel are the mean value (μ), the standard deviation of the added uncorrelated noise (σ), the amplidute (α), the decay time (l), the smoothing factor β and the recurrence period (P_rot).

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