EMPEROR - I. Exoplanet MCMC parallel tempering for RV orbit retrieval

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Volume 704 (December 2025)

A&A, 704 (2025) A323

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Table D.5

GJ 699 RV parameter comparison table.

Parameter	Prior	𝒢𝒫 _3SHO	𝒢𝒫 _rotS (K₁)	𝒢𝒫 _grotS	𝒢𝒫 _2rot	𝒢𝒫 _grot+Mag

Offsets and Jitter
γ_E18	~ 𝒩 (0,3)	$- {0.03}_{- 0.45}^{+ 0.32}$ $- 0.03_{ - 0.45}^{ + 0.32}$	$- {0.39}_{- 0.28}^{+ 0.28}$ $- 0.39_{ - 0.28}^{ + 0.28}$	$- {0.52}_{- 0.72}^{+ 0.72}$ $- 0.52_{ - 0.72}^{ + 0.72}$	$- {0.20}_{- 0.55}^{+ 0.55}$ $- 0.20_{ - 0.55}^{ + 0.55}$	$- {0.40}_{- 0.05}^{+ 0.61}$ $- 0.40_{ - 0.05}^{ + 0.61}$
γ_E19	~ 𝒩 (0,3)	$- {1.12}_{- 0.19}^{+ 0.58}$ ${ - 1.12_{ - 0.19}^{ + 0.58}}$	$- {1.3}_{- 0.29}^{+ 0.22}$ ${ - 1.3_{ - 0.29}^{ + 0.22}}$	$- {1.53}_{- 0.59}^{+ 0.55}$ ${ - 1.53_{ - 0.59}^{ + 0.55}}$	$- {0.08}_{- 0.40}^{+ 0.2}$ ${ - 0.08_{ - 0.40}^{ + 0.2}}$	$- {1.50}_{- 0.20}^{+ 0.27}$ ${ - 1.50_{ - 0.20}^{ + 0.27}}$
σ_E18	~ℒ 𝒩 (0.5,1)	${0.39}_{- 0.06}^{+ 0.10}$ $0.39_{ - 0.06}^{ + 0.10}$	${0.55}_{- 0.18}^{+ 0.2}$ $0.55_{ - 0.18}^{ + 0.2}$	${0.45}_{- 0.11}^{+ 0.05}$ $0.45_{ - 0.11}^{ + 0.05}$	${0.45}_{- 0.05}^{+ 0.10}$ $0.45_{ - 0.05}^{ + 0.10}$	${0.56}_{- 0.20}^{+ 0.20}$ $0.56_{ - 0.20}^{ + 0.20}$
σ_E19	~ℒ 𝒩 (0.5,1)	${0.53}_{- 0.05}^{+ 0.05}$ $0.53_{ - 0.05}^{ + 0.05}$	${0.55}_{- 0.01}^{+ 0.04}$ $0.55_{ - 0.01}^{ + 0.04}$	${0.54}_{- 0.01}^{+ 0.03}$ $0.54_{ - 0.01}^{ + 0.03}$	${0.55}_{- 0.01}^{+ 0.04}$ $0.55_{ - 0.01}^{ + 0.04}$	${0.56}_{- 0.01}^{+ 0.04}$ $0.56_{ - 0.01}^{ + 0.04}$

Rotation

𝒢𝒫 _SHO^ρ₁	~ 𝒰 (50,300)	${0.37}_{- 0.35}^{+ 0.02}$ $0.37_{ - 0.35}^{ + 0.02}$	-	-	-	-
𝒢𝒫 _SHOσ₁	~ℒ 𝒩 (0.5,2)	${145.63}_{+ 59.93}^{+ 29.93}$ $145.63_{ + 59.93}^{ + 29.93}$	-	-	-	-
𝒢𝒫 _SHOτ₁	~ℒ 𝒩 (3,2)	${19.3}_{- 2.46}^{+ 4.15}$ $19.3_{ - 2.46}^{ + 4.15}$	-	-	-	-

𝒢𝒫 _SHO^ρ₂	~ 𝒰 (25, 150)	${1.50}_{- 0.18}^{+ 0.01}$ $1.50_{ - 0.18}^{ + 0.01}$	-	-	-	-
𝒢𝒫 _SHO^σ₂	~ℒ 𝒩 (0.5,2)	${64.74}_{- 1.43}^{+ 5.03}$ $64.74_{ - 1.43}^{ + 5.03}$	-	-	-	-
𝒢𝒫 _SHOτ₂	~ℒ 𝒩 (3,2)	${27.93}_{- 5.81}^{+ 5.33}$ $27.93_{ - 5.81}^{ + 5.33}$	-	-	-	-

𝒢𝒫 _rotρ	~ 𝒰 (50, 300)	-	${124.68}_{- 14.67}^{+ 12.14}$ ${124.68_{ - 14.67}^{ + 12.14}}$	-	${148.27}_{- 6.15}^{+ 2.69}$ ${148.27_{ - 6.15}^{ + 2.69}}$	-
𝒢𝒫 _rotσ	~ 𝒰 (0,7.1)	-	${1.51}_{- 0.22}^{+ 0.24}$ ${1.51_{ - 0.22}^{ + 0.24}}$	-	${2.04}_{- 0.21}^{+ 0.06}$ ${2.04_{ - 0.21}^{ + 0.06}}$	-
𝒢𝒫 _rotQ0	~ 𝒰 (0, 50)	-	${1.74}_{- 0.89}^{+ 1.05}$ ${1.74_{ - 0.89}^{ + 1.05}}$	-	${1.35}_{- 0.55}^{+ 0.17}$ ${1.35_{ - 0.55}^{ + 0.17}}$	-
𝒢𝒫 _rotδQ	~ 𝒰 (0, 50)	-	${0.28}_{- 0.28}^{+ 0.05}$ ${0.28_{ - 0.28}^{ + 0.05}}$	-	${28.31}_{- 14.69}^{+ 21.69}$ ${28.31_{ - 14.69}^{ + 21.69}}$	-
𝒢𝒫_rot f	~ 𝒰 (0,1)	-	${0.88}_{- 0.01}^{+ 0.12}$ ${0.88_{ - 0.01}^{ + 0.12}}$	-	${0.82}_{- 0.18}^{+ 0.18}$ ${0.82_{ - 0.18}^{ + 0.18}}$	-

𝒢𝒫 _grot^ρ	~ 𝒰 (50, 300)	-	-	${124.7}_{- 18.01}^{+ 14.04}$ ${124.7_{ - 18.01}^{ + 14.04}}$	-	${128.18}_{- 4.19}^{+ 2.49}$ ${128.18_{ - 4.19}^{ + 2.49}}$
𝒢𝒫 _grotτ	~ℒ 𝒩 (3,2)	-	-	${27.82}_{- 5.64}^{+ 5.15}$ ${27.82_{ - 5.64}^{ + 5.15}}$	-	${50.62}_{- 0.62}^{+ 0.11}$ ${50.62_{ - 0.62}^{ + 0.11}}$
𝒢𝒫 _grot^A₁	~ℒ 𝒩 (0.5,0.5)	-	-	${1.30}_{- 0.64}^{+ 0.72}$ ${1.30_{ - 0.64}^{ + 0.72}}$	-	${2.8}_{- 0.74}^{+ 0.99}$ ${2.8_{ - 0.74}^{ + 0.99}}$
𝒢𝒫 _grotA₂	~ℒ 𝒩 (0.5,0.5)	-	-	${3.46}_{- 1.24}^{+ 1.17}$ ${3.46_{ - 1.24}^{ + 1.17}}$	-	${6.9}_{- 0.41}^{+ 0.17}$ ${6.9_{ - 0.41}^{ + 0.17}}$

Magnetic Cycle

𝒢𝒫 _SHO^ρ₃	~ 𝒩 (3250, 300)	${1.41}_{- 0.02}^{+ 0.81}$ $1.41_{ - 0.02}^{ + 0.81}$	-	-	-	-
𝒢𝒫 _SHO^σ₃	~ℒ 𝒩 (0.5,0.5)	${3033.9}_{- 27.5}^{+ 316.9}$ $3033.9_{ - 27.5}^{ + 316.9}$	-	-	-	-
𝒢𝒫 _SHOτ₃	~ 𝒰 (0, 3e4)	$17369_{- 8566}^{+ 12420}$ $17369_{ - 8566}^{ + 12420}$	-	-	-	-

P_m	~ 𝒩 (3250, 300)	-	${2984.0}_{- 250.7}^{+ 291.1}$ $2984.0_{ - 250.7}^{ + 291.1}$	${3225.31}_{- 176.8}^{+ 68.66}$ $3225.31_{ - 176.8}^{ + 68.66}$		${3227.5}_{- 196.7}^{+ 35.4}$ $3227.5_{ - 196.7}^{ + 35.4}$
K_m	~ℒ 𝒩 (0.5,2)	-	${2.7}_{- 0.29}^{+ 0.33}$ ${2.7_{ - 0.29}^{ + 0.33}}$	${3.04}_{- 0.83}^{+ 0.75}$ ${3.04_{ - 0.83}^{ + 0.75}}$	-	${2.97}_{- 0.38}^{+ 0.17}$ ${2.97_{ - 0.38}^{ + 0.17}}$
ϕ_m	~ 𝒰 (0, 2π)	-	${4.73}_{- 0.18}^{+ 0.18}$ ${4.73_{ - 0.18}^{ + 0.18}}$	${4.88}_{- 0.11}^{+ 0.06}$ ${4.88_{ - 0.11}^{ + 0.06}}$	-	${4.87}_{- 0.11}^{+ 0.02}$ ${4.87_{ - 0.11}^{ + 0.02}}$
K₂	~ℒ 𝒩 (0.5,2)	-	-	_-	-	-
ϕ₂	~ 𝒰 (0, 2π)	-	-	-	-	-

𝒢𝒫 _rotρ	~ 𝒰 (800, 5000)	-	-	-	${3186.0}_{- 87.4}^{+ 159.9}$ $3186.0_{ - 87.4}^{ + 159.9}$	-
𝒢𝒫 _rotσ	~ 𝒰 (0,7.1)	-	--	-	${1.28}_{- 0.23}^{+ 0.34}$ $1.28_{ - 0.23}^{ + 0.34}$	-
𝒢𝒫 _rotQ0	~ 𝒰 (0, 50)	--	-	-	${28.24}_{- 14.78}^{+ 19.78}$ $28.24_{ - 14.78}^{ + 19.78}$	-
𝒢𝒫 _rotδQ	~ 𝒰 (0, 50)	-	-	--	${8.16}_{- 8.1}^{+ 9.13}$ $8.16_{ - 8.1}^{ + 9.13}$	-
𝒢𝒫_rot f	~ 𝒰 (0,1)	-	-	-	${0.65}_{- 0.28}^{+ 0.33}$ $0.65_{ - 0.28}^{ + 0.33}$	-

Kepleria 𝒩 Orbit

P₁	~ 𝒰 (0.5, 50)	${3.1536}_{- 5 e - 4}^{+ 5 e - 5}$ ${3.1536_{ - 5e - 4}^{ + 5e - 5}}$	${3.1529}_{- 5 e - 4}^{+ 7 e - 4}$ ${3.1529_{ - 5e - 4}^{ + 7e - 4}}$	${3.15}_{- 5 e - 4}^{+ 6 e - 5}$ ${3.15_{ - 5e - 4}^{ + 6e - 5}}$	${3.1534}_{- 2 e - 4}^{+ 2 e - 4}$ ${3.1534_{ - 2e - 4}^{ + 2e - 4}}$	${3.1535}_{- 4 e - 4}^{+ 3 e - 4}$ ${3.1535_{ - 4e - 4}^{ + 3e - 4}}$
K₁	~ 𝒰 (0, 6.5)	${0.59}_{- 0.09}^{+ 0.08}$ ${0.59_{ - 0.09}^{ + 0.08}}$	${0.56}_{- 0.08}^{+ 0.01}$ ${0.56_{ - 0.08}^{ + 0.01}}$	${0.56}_{- 0.04}^{+ 0.03}$ ${0.56_{ - 0.04}^{ + 0.03}}$	${0.55}_{- 0.03}^{+ 0.04}$ ${0.55_{ - 0.03}^{ + 0.04}}$	${0.57}_{- 0.08}^{+ 0.08}$ ${0.57_{ - 0.08}^{ + 0.08}}$
ϕ₁	~ 𝒰 (0, 2π)	${3.95}_{- 2.3}^{+ 1.68}$ ${3.95_{ - 2.3}^{ + 1.68}}$	${4.21}_{- 2.56}^{+ 1.68}$ ${4.21_{ - 2.56}^{ + 1.68}}$	${1.53}_{- 0.15}^{+ 1.54}$ ${1.53_{ - 0.15}^{ + 1.54}}$	${2.44}_{- 0.63}^{+ 1.07}$ ${2.44_{ - 0.63}^{ + 1.07}}$	${1.27}_{- 0.05}^{+ 1.88}$ ${1.27_{ - 0.05}^{ + 1.88}}$
e₁	~ 𝒩 (0, 0.1)	${0.03}_{- 0.03}^{+ 0.01}$ ${0.03_{ - 0.03}^{ + 0.01}}$	${0.04}_{- 0.04}^{+ 0.05}$ ${0.04_{ - 0.04}^{ + 0.05}}$	${0.03}_{- 0.03}^{+ 0.01}$ ${0.03_{ - 0.03}^{ + 0.01}}$	${0.01}_{- 0.01}^{+ 0.02}$ ${0.01_{ - 0.01}^{ + 0.02}}$	${0.06}_{- 0.06}^{+ 0.05}$ ${0.06_{ - 0.06}^{ + 0.05}}$
ω₁	~ 𝒰 (0, 2π)	${4.22}_{- 0.03}^{+ 2.06}$ ${4.22_{ - 0.03}^{ + 2.06}}$	${3.7}_{- 2.26}^{+ 1.76}$ ${3.7_{ - 2.26}^{ + 1.76}}$	${0.48}_{- 0.48}^{+ 2.63}$ ${0.48_{ - 0.48}^{ + 2.63}}$	${5.58}_{- 0.94}^{+ 0.7}$ ${5.58_{ - 0.94}^{ + 0.7}}$	${0.67}_{- 0.67}^{+ 1.82}$ ${0.67_{ - 0.67}^{ + 1.82}}$

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