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 1

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

Parameter	Prior	Posterior
Offsets
γ_rv	U(−10¹⁰, 10¹⁰)	$- {19.39}_{- 2.73}^{+ 2.88}$ $- 19.39_{ - 2.73}^{ + 2.88}$
γ_phot.	U(−10¹⁰, 10¹⁰)	${1360.895}_{- 0.808}^{+ 0.865}$ $1360.895_{ - 0.808}^{ + 0.865}$

Jitter
σ_jit.,rv	trunc N (0, 200)	${0.6822}_{- 0.0266}^{+ 0.0274}$ ${0.6822_{ - 0.0266}^{ + 0.0274}}$
σ_{jit., phot.}	trunc N (0, 200)	${0.000878}_{- 0.0006608}^{+ 0.000784}$ ${0.000878_{ - 0.0006608}^{ + 0.000784}}$

Active regions (spots + faculae)
P_rot.	log U(5, 200)	${26.8212}_{- 0.0758}^{+ 0.0773}$ $26.8212_{ - 0.0758}^{ + 0.0773}$
$\bar{i}$ ${\bar i}$	cos(x) (x ∈ [0, 90])	${2.52}_{- 1.78}^{+ 2.87}$ ${2.52_{ - 1.78}^{ + 2.87}}$
µ_{δ, spots}	cos(x) (x ∈ [0, 90])	${14.8}_{- 10.9}^{+ 15.5}$ ${14.8_{ - 10.9}^{ + 15.5}}$
σ_{δ, spots}	log U(5, 90)	${13.5}_{- 6.7}^{+ 22.9}$ ${13.5_{ - 6.7}^{ + 22.9}}$
ρ_spots	log U(5, 10⁵)	${40.14}_{- 3.16}^{+ 3.58}$ ${40.14_{ - 3.16}^{ + 3.58}}$
σ_{spots, rv-phot.}	N (0, 200)	$- {0.266}_{- 0.110}^{+ 0.118}$ ${ - 0.266_{ - 0.110}^{ + 0.118}}$
σ_{spots, rv-cb}	N (0, 200)	${0.998}_{- 0.109}^{+ 0.111}$ ${0.998_{ - 0.109}^{ + 0.111}}$
σ_{spots, phot.}	N (0, 200)	$- {0.2230}_{- 0.0118}^{+ 0.0117}$ ${ - 0.2230_{ - 0.0118}^{ + 0.0117}}$
α_{spots, 180}	U(0, 1)	${0.1323}_{- 0.0504}^{+ 0.0541}$ ${0.1323_{ - 0.0504}^{ + 0.0541}}$
µ_{δ, faculae}	cos(x) (x ∈ [0, 90])	${5.96}_{- 4.08}^{+ 5.15}$ ${5.96_{ - 4.08}^{ + 5.15}}$
σ_{δ, faculae}	log U(5, 90)	${7.19}_{- 1.59}^{+ 2.85}$ ${7.19_{ - 1.59}^{ + 2.85}}$
ρ_faculae	log U(5, 10⁵)	${73.34}_{- 7.47}^{+ 8.59}$ ${73.34_{ - 7.47}^{ + 8.59}}$
σ_{faculae, rv-phot.}	N (0, 200)	$- {0.179}_{- 0.157}^{+ 0.166}$ ${ - 0.179_{ - 0.157}^{ + 0.166}}$
σ_{faculae, rv-cb}	N (0, 200)	${3.61}_{- 1.50}^{+ 1.59}$ $3.61_{ - 1.50}^{ + 1.59}$
σ_{faculae, phot.}	N (0, 200)	${1.073}_{- 0.461}^{+ 0.476}$ $1.073_{ - 0.461}^{ + 0.476}$
α_{faculae, 180}	U(0, 1)	${0.00309}_{- 0.00230}^{+ 0.00466}$ $0.00309_{ - 0.00230}^{ + 0.00466}$

Magnetic cycle
ρ_{spots, mag.}	log U(50, 10⁵)	$1816_{- 1655}^{+ 16588}$ ${1816_{ - 1655}^{ + 16588}}$
η_{spots, mag.}	log U(10⁻⁵, 10⁵)	${0.0009}_{- 0.0008}^{+ 0.0158}$ ${0.0009_{ - 0.0008}^{ + 0.0158}}$
ρ_{faculae, mag.}	log U(50, 10⁵)	$35707_{- 25554}^{+ 36258}$ ${35707_{ - 25554}^{ + 36258}}$
η_{faculae, mag.}	log U(10⁻⁵, 10⁵)	${6.17}_{- 2.86}^{+ 2.93}$ ${6.17_{ - 2.86}^{ + 2.93}}$

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