GI 725A b: A potential super-Earth detected with SOPHIE and SPIRou in an M dwarf binary system at 3.5 pc

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Volume 693 (January 2025)

A&A, 693 (2025) A164

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Table 3

Results of the models applied in the SOPHIE and SPIRou data, independently and jointly.

			Planet_b,SOPHIE	Planet_b,SPIRou	Planet_{b,SOPHIE+SPIRou}		GP_SOPHIE + GP_SPIRou + Planet_{b,SOPHIE+SPIRou}
Parameter	Units	Prior	e free	e free	e free	e = 0	e = 0, η_3,SOPHIE=η_3,SPIRou	e = 0 η_2,3,SOPHIE=η_2,3,SPIRou
Orbital parameters

P_b	days	𝒰(11, 11.5)	11.210 ± 0.012	${11.238}_{- 0.018}^{+ 0.025}$ $11.238_{ - 0.018}^{ + 0.025}$	${11.2155}_{- 0.0052}^{+ 0.0065}$ $11.2155_{ - 0.0052}^{ + 0.0065}$	11.2183 ± 0.0060	11.2202 ± 0.0049	11.2201 ± 0.0051
T conj_b	BJD-2450 000	𝒰(8591,8602)	${8598.4}_{- 1.7}^{+ 1.5}$ $8598.4_{ - 1.7}^{ + 1.5}$	${8596.3}_{- 1.9}^{+ 1.5}$ $8596.3_{ - 1.9}^{ + 1.5}$	8597 8±1 0	8597.0 ± 0.6	8596.7 ± 0.5	8597.7 ± 0.5
e_b			${0.24}_{- 0.17}^{+ 0.27}$ $0.24_{ - 0.17}^{ + 0.27}$	${0.23}_{- 0.16}^{+ 0.23}$ $0.23_{ - 0.16}^{ + 0.23}$	${0.20}_{- 0.14}^{+ 0.19}$ $0.20_{ - 0.14}^{ + 0.19}$	≡ 0.0	≡ 0.0	≡ 0.0
ω_b	rad		${2.6}_{- 1.1}^{+ 1.5}$ $2.6_{ - 1.1}^{ + 1.5}$	$- {2.6}_{- 2.4}^{+ 1.6}$ $- 2.6_{ - 2.4}^{ + 1.6}$	${2.9}_{- 0.72}^{+ 1.20}$ $2.9_{ - 0.72}^{ + 1.20}$	≡ 0.0	≡ 0.0	≡ 0.0
K_b	m/s	ℐ (0.01,10)	${1.63}_{- 0.35}^{+ 0.38}$ $1.63_{ - 0.35}^{ + 0.38}$	1.69 ± 0.44	1.69 ± 0.26	1.61 ± 0.24	1.67 ± 0.20	1.67 ± 0.20

Derived planet parameters

M_b sin i	M_⊕		2.56 ± 0.55	${2.68}_{- 0.70}^{+ 0.67}$ $2.68_{ - 0.70}^{ + 0.67}$	2.71 ± 0.42	2.69 ± 0.41	2.79 ± 0.35	2.78 ± 0.35
a_b	AU		0.068 ± 0.001	0.068 ± 0.001	0.068 ± 0.001	0.068 ± 0.001	0.068 ± 0.001	0.068 ± 0.001

Instrumental parameter posteriors

γ_SOPHIE	m/s		${0.39}_{- 0.23}^{+ 0.22}$ $0.39_{ - 0.23}^{ + 0.22}$		0.38 ± 0.22	0.35 ± 0.22	${0.62}_{- 0.73}^{+ 0.83}$ $0.62_{ - 0.73}^{ + 0.83}$	${0.61}_{- 0.75}^{+ 0.90}$ $0.61_{ - 0.75}^{ + 0.90}$
σ_SOPHIE	m/s	ℐ(0.01,5)	2 23 ± 0 20		2.2 ± 0.20	2.22 ± 0.20	${1.08}_{- 0.55}^{+ 0.31}$ $1.08_{ - 0.55}^{ + 0.31}$	${1.09}_{- 0.52}^{+ 0.31}$ $1.09_{ - 0.52}^{ + 0.31}$
γ_SPIRou	m/s			$- {0.02}_{- 0.26}^{+ 0.25}$ $- 0.02_{ - 0.26}^{ + 0.25}$	$- {0.04}_{- 0.25}^{+ 0.26}$ $- 0.04_{ - 0.25}^{ + 0.26}$	−0.04 ± 0.26	−0.35 ± 0.61	−0.26 ± 0.47
σ_SPIRou	m/s	ℐ(0.01,5)		3.36 ± 0.20	3.35 ± 0.20	3.36 ± 0.21	3.01 ± 0.21	3.01 ± 0.22

GP Hyper-parameters posteriors

η_1,SOPHIE		ℐ(0.01,5)					${2.46}_{- 0.43}^{+ 0.59}$ $2.46_{ - 0.43}^{ + 0.59}$	${2.52}_{- 0.47}^{+ 0.67}$ $2.52_{ - 0.47}^{ + 0.67}$
η_2,SOPHIE	days	𝒰(100,500)					$125_{- 18}^{+ 29}$ $125_{ - 18}^{ + 29}$	η_{2,SOPHIE,SPIRou}
η_4,SOPHIE		𝒰(0.1,1.0)					${0.44}_{- 0.19}^{+ 0.30}$ $0.44_{ - 0.19}^{ + 0.30}$	${0.45}_{- 0.20}^{+ 0.31}$ $0.45_{ - 0.20}^{ + 0.31}$
η_1,SPIRou		ℐ(0.01,5)					${1.53}_{- 0.40}^{+ 0.51}$ $1.53_{ - 0.40}^{ + 0.51}$	1.43 ± 0.40
η_2,SPIRou	days	𝒰(100,500)					$351_{- 130}^{+ 99}$ $351_{ - 130}^{ + 99}$	η_{2,SOPHIE,SPIRou}
η_4,SPIRou		𝒰(0.1,1.0)					${0.32}_{- 0.14}^{+ 0.22}$ $0.32_{ - 0.14}^{ + 0.22}$	${0.30}_{- 0.14}^{+ 0.21}$ $0.30_{ - 0.14}^{ + 0.21}$
η_{2,SOPHIE,SPIRou}	days	𝒰(100,500)						$134_{- 23}^{+ 35}$ $134_{ - 23}^{ + 35}$
η_{3,SOPHIE,SPIRou}	days	𝒰(103.1,6.1)					105.0 ± 2.6	104.8 ± 3.2

Model diagnostics

RMS	m/s		2.8	3.6	3.3	3.3	2.7	2.7
ln ℒ			−413.3	−546.5	−957.6	−959.1	−945.9	−941.9
BIC					1942.3	1933.5	1920.6	1918.9
ΔBIC					−8.8	0	13.1	14.6

Notes. Below each model’s name is indicated if the eccentricity is fixed to e = 0 or free, and which GP hyper-parameters are shared between the instruments. The symbol 𝒰(a, b) describes a uniform prior, with a and b being the minimum and maximum limits, respectively. The symbol ℐ (a, b) describes a Jeffrey’s prior, with a and b being the minimum and maximum limits, respectively. The symbol N(a, b) describes a normal distribution centred in a and standard deviation b.

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