Characterizing planetary systems with SPIRou: Detection of a sub-Neptune in a 6-day period orbit around the M dwarf Gl 410

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Volume 700 (August 2025)

A&A, 700 (2025) A222

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Table C.1

Prior and posterior distributions of the quasi-periodic GP models fit to the SOPHIE RV time series and the SPIRou B_ℓ measurements.

Parameter		Prior distribution	Posterior distribution
GP + Keplerian `RadVel` model of the SOPHIE RVs (circular orbit)
GP
Offset [m s^–1]	V₀			$4_{- 11}^{+ 16}$ $4_{ - 11}^{ + 16}$
Amplitude [m s^–1]	A	𝒰 (0, 75)		$21_{- 8}^{+ 19}$ $21_{ - 8}^{ + 19}$
Decay time [days]	l	𝒰 (0, 2000)		$602_{- 230}^{+ 370}$ $602_{ - 230}^{ + 370}$
Cycle length (period) [days]	P	Gaussian (13.9 ± 0.1)		13.84 ± 0.02
Smoothing parameter	Γ	𝒰 (0, 2.0)		${0.5}_{- 0.2}^{+ 0.3}$ $0.5_{ - 0.2}^{ + 0.3}$
Uncorr. Noise [m s^–1 ]	σ	𝒰 (0.0, 15)		6±1
Keplerian
Period [days]	P_b	𝒰 (0.0, 20)		${6.020}_{- 0.0056}^{+ 0.0051}$ $6.020_{ - 0.0056}^{ + 0.0051}$
Semi-amplitude [m s^–1 ]	K_b	𝒰 (0.0, 20)		${7.6}_{- 1.4}^{+ 1.3}$ $7.6_{ - 1.4}^{ + 1.3}$
Time of inferior conjunction [days]	Τ coqj_b	𝒰 (2459648.0 ± 10)
Time of periastron [days]	Τ peri_b			2459646.53 ± 0.19
Semimajor axis [au]	a_b			0.0531 ± 0.0007
M_b sin(i) [M_⊕]				14.4 ± 2.6
GP of SPIRou’s B_ℓ measurements
			ln units	linear units
Amplitude [G]	ln A	𝒰 (2, 6)	${2.78}_{- 0.12}^{+ 0.14}$ $2.78_{ - 0.12}^{ + 0.14}$	${16.1}_{- 1.9}^{+ 2.4}$ $16.1_{ - 1.9}^{ + 2.4}$
Decay time [days]	ln l	𝒰 (3, 5)	${4.03}_{- 0.13}^{+ 0.13}$ $4.03_{ - 0.13}^{ + 0.13}$	$56_{- 7}^{+ 8}$ $56_{ - 7}^{ + 8}$
Smoothing parameter	ln Γ	𝒰 (0, 2.0)	${0.84}_{- 0.26}^{+ 0.26}$ $0.84_{ - 0.26}^{ + 0.26}$	${2.31}_{- 0.54}^{+ 0.68}$ $2.31_{ - 0.54}^{ + 0.68}$
Cycle length (period) [days]	ln P	𝒰 (ln (12.91), ln (14.91))	${2.6342}_{- 0.0063}^{+ 0.0067}$ $2.6342_{ - 0.0063}^{ + 0.0067}$	${13.93}_{- 0.09}^{+ 0.09}$ $13.93_{ - 0.09}^{ + 0.09}$
Uncorr. Noise [G]	ln σ	𝒰 (–10, 10)	$- {3.8}_{- 4.2}^{+ 4.0}$ $- 3.8_{ - 4.2}^{ + 4.0}$	${0.02}_{- 0.02}^{+ 1.16}$ $0.02_{ - 0.02}^{ + 1.16}$
GP of the SOPHIE optical RVs using SPIRou’s B_ℓ as an activity proxy
Offset [m s^–1]	V₀	median(RV) + 𝒰 (–10, 10)		$- {13833.6}_{- 3.5}^{+ 3.8}$ $- 13833.6_{ - 3.5}^{ + 3.8}$
Amplitude [m s^–1]	ln A	𝒰 (–0.7, 2.8)	${2.50}_{- 0.32}^{+ 0.24}$ $2.50_{ - 0.32}^{ + 0.24}$	${12.2}_{- 3.4}^{+ 3.2}$ $12.2_{ - 3.4}^{ + 3.2}$
Decay time [days]	ln l	B_ℓ Posterior	${4.08}_{- 0.13}^{+ 0.13}$ $4.08_{ - 0.13}^{ + 0.13}$	${59.4}_{- 7.1}^{+ 8.5}$ $59.4_{ - 7.1}^{ + 8.5}$
Smoothing parameter	ln Γ	B_ℓ Posterior	${1.03}_{- 0.25}^{+ 0.23}$ $1.03_{ - 0.25}^{ + 0.23}$	${2.8}_{- 0.6}^{+ 0.7}$ $2.8_{ - 0.6}^{ + 0.7}$
Cycle length (period) [days]	ln P	B_ℓ Posterior	${2.6333}_{- 0.0051}^{+ 0.0055}$ $2.6333_{ - 0.0051}^{ + 0.0055}$	${13.92}_{- 0.07}^{+ 0.08}$ $13.92_{ - 0.07}^{ + 0.08}$
Uncorr. Noise [m s^–1]	ln σ	𝒰 (0, 5)	${2.03}_{- 0.23}^{+ 0.24}$ $2.03_{ - 0.23}^{ + 0.24}$	${7.6}_{- 1.6}^{+ 2.1}$ $7.6_{ - 1.6}^{ + 2.1}$

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