FENRIR: A statistical model of stellar variability - I. A physics-based, fast Gaussian process model to represent stellar activity and perform statistical Doppler imaging

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Volume 696 (April 2025)

A&A, 696 (2025) A141

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Table 2

Set of parameters explored in the MCMC of the opp. lat. run, with their priors and posteriors (median and 68.27% interval).

Parameter	Prior	Posterior
Offsets
γ_rv	U(−10¹⁰, 10¹⁰)	$- {19.45}_{- 2.80}^{+ 2.89}$ ${ - 19.45_{ - 2.80}^{ + 2.89}}$
γ_phot.	U(−10¹⁰, 10¹⁰)	${1360.866}_{- 0.838}^{+ 0.880}$ ${1360.866_{ - 0.838}^{ + 0.880}}$

Jitter
σ_{jit, rv}	trunc N (0, 200)	${0.6820}_{- 0.0268}^{+ 0.0280}$ ${0.6820_{ - 0.0268}^{ + 0.0280}}$
σ_{jit., phot.}	trunc N (0, 200)	${0.000852}_{- 0.000596}^{+ 0.00913}$ ${0.000852_{ - 0.000596}^{ + 0.00913}}$

Active regions (spots + faculae)
P_rot.	log U(5, 200)	${26.8175}_{- 0.0744}^{+ 0.0750}$ $26.8175_{ - 0.0744}^{ + 0.0750}$
$\bar{i}$ ${\bar i}$	cos(x) (x ∈ [0, 90])	${3.40}_{- 2.47}^{+ 5.09}$ $3.40_{ - 2.47}^{ + 5.09}$
δ_spots	cos(x) (x ∈ [0, 90])	${10.5}_{- 7.5}^{+ 12.5}$ $10.5_{ - 7.5}^{ + 12.5}$
ρ_spots	log U(5, 10⁵)	${40.33}_{- 3.35}^{+ 3.70}$ ${40.33_{ - 3.35}^{ + 3.70}}$
σ_{spots, rv-phot.}	N (0, 200)	$- {0.277}_{- 0.111}^{+ 0.115}$ ${ - 0.277_{ - 0.111}^{ + 0.115}}$
σ_{spots, rv-cb}	N (0, 200)	${1.007}_{- 0.111}^{+ 0.111}$ ${1.007_{ - 0.111}^{ + 0.111}}$
σ_{spots, phot.}	N (0, 200)	$- {0.2229}_{- 0.0120}^{+ 0.0119}$ ${ - 0.2229_{ - 0.0120}^{ + 0.0119}}$
α_{spots, 180}	U(0, 1)	${0.1323}_{- 0.051}^{+ 0.0566}$ ${0.1323_{ - 0.051}^{ + 0.0566}}$
δ_faculae	cos(x) (x ∈ [0,90])	${7.93}_{- 5.53}^{+ 6.18}$ ${7.93_{ - 5.53}^{ + 6.18}}$
ρ_faculae	log U(5, 10⁵)	${73.23}_{- 7.46}^{+ 8.60}$ ${73.23_{ - 7.46}^{ + 8.60}}$
σ_{faculae, rv-phot.}	N (0, 200)	$- {0.182}_{- 0.153}^{+ 0.159}$ ${ - 0.182_{ - 0.153}^{ + 0.159}}$
σ_{faculae, rv-cb}	N (0, 200)	${3.67}_{- 1.56}^{+ 1.60}$ ${3.67_{ - 1.56}^{ + 1.60}}$
σ_{faculae, phot.}	N (0, 200)	${1.101}_{- 0.479}^{+ 0.477}$ ${1.101_{ - 0.479}^{ + 0.477}}$
α_{faculae, 180}	U(0, 1)	${0.00334}_{- 0.00249}^{+ 0.00488}$ ${0.00334_{ - 0.00249}^{ + 0.00488}}$

Magnetic cycle
ρ_{spots, mag.}	log U(50, 10⁵)	$2175_{- 2003}^{+ 23489}$ ${2175_{ - 2003}^{ + 23489}}$
η_{spots, mag.}	log U(10⁻⁵, 10⁵)	${0.0010}_{- 0.0010}^{+ 0.0225}$ ${0.0010_{ - 0.0010}^{ + 0.0225}}$
ρ_{faculae, mag.}	log U(50, 10⁵)	$38349_{- 27830}^{+ 37932}$ ${38349_{ - 27830}^{ + 37932}}$
η_{faculae, mag.}	log U(10⁻⁵, 10⁵)	${4.49}_{- 2.12}^{+ 2.05}$ ${4.49_{ - 2.12}^{ + 2.05}}$

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