TESS and ESPRESSO discover a super-Earth and a mini-Neptune orbiting the K-dwarf TOI-238

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Volume 685 (May 2024)

A&A, 685 (2024) A56

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Table E.1

Priors and measured parameters of the models described in sections 4.2, 4.3 and 4.4.

Parameter	Priors	0-Planets	1-Planet (Kep)	2-Planets (Kep)
Zero points
V0 HARPS_FWHM [m s⁻¹]	𝒩 (0, 17)	${4.2}_{- 9.3}^{+ 8.9}$ $\[4.2_{-9.3}^{+8.9}\]$	${5.8}_{- 7.8}^{+ 7.6}$ $\[5.8_{-7.8}^{+7.6}\]$	${4.6}_{- 9.0}^{+ 8.3}$ $\[4.6_{-9.0}^{+8.3}\]$
V0 ESP_FWHM [m s⁻¹]	𝒩 (0, 17)	$- {0.9}_{- 5.8}^{+ 6.5}$ $\[-0.9_{-5.8}^{+6.5}\]$	$- {0.6}_{- 5.4}^{+ 5.2}$ $\[-0.6_{-5.4}^{+5.2}\]$	$- {0.3}_{- 5.8}^{+ 6.3}$ $\[-0.3_{-5.8}^{+6.3}\]$
V0 HARPS_BIS [m s⁻¹]	𝒩 (0, 6.2)	${0.1}_{- 2.0}^{+ 2.0}$ $\[0.1_{-2.0}^{+2.0}\]$	${0.8}_{- 2.0}^{+ 2.3}$ $\[0.8_{-2.0}^{+2.3}\]$	${0.4}_{- 1.9}^{+ 2.0}$ $\[0.4_{-1.9}^{+2.0}\]$
V0 ESP_BIS [m s⁻¹]	𝒩 (0, 6.2)	$- {0.1}_{- 1.3}^{+ 1.3}$ $\[-0.1_{-1.3}^{+1.3}\]$	$- {0.3}_{- 1.3}^{+ 1.2}$ $\[-0.3_{-1.3}^{+1.2}\]$	${0.2}_{- 1.3}^{+ 1.4}$ $\[0.2_{-1.3}^{+1.4}\]$
V0 HARPS_RV [m s⁻¹]	𝒩 (0, 5.9)	$- {0.6}_{- 2.4}^{+ 2.3}$ $\[-0.6_{-2.4}^{+2.3}\]$	$- {1.9}_{- 3.2}^{+ 2.9}$ $\[-1.9_{-3.2}^{+2.9}\]$	$- {1.0}_{- 2.3}^{+ 2.0}$ $\[-1.0_{-2.3}^{+2.0}\]$
V0 ESP_RV [m s⁻¹]	𝒩 (0, 5.9)	${0.1}_{- 1.7}^{+ 1.6}$ $\[0.1_{-1.7}^{+1.6}\]$	${0.7}_{- 2.1}^{+ 2.0}$ $\[0.7_{-2.1}^{+2.0}\]$	$- {0.2}_{- 1.5}^{+ 1.5}$ $\[-0.2_{-1.5}^{+1.5}\]$
V0 TESS [ppm]	𝒩 (0, 3070)	$700_{- 2700}^{+ 2600}$ $\[700_{-2700}^{+2600}\]$	$500_{- 2500}^{+ 2600}$ $\[500_{-2500}^{+2600}\]$	$400_{- 2600}^{+ 2700}$ $\[400_{-2600}^{+2700}\]$
GP Parameters
A_FWHM [m s-1]	𝒰 (0, 85)	${23.7}_{- 5.1}^{+ 9.5}$ $\[23.7_{-5.1}^{+9.5}\]$	${21.2}_{- 4.0}^{+ 7.2}$ $\[21.2_{-4.0}^{+7.2}\]$	${22.7}_{- 4.5}^{+ 6.9}$ $\[22.7_{-4.5}^{+6.9}\]$
A11_RV [m s⁻¹]	𝒰 (-29.3, 26.3)	${4.7}_{- 1.5}^{+ 2.1}$ $\[4.7_{-1.5}^{+2.1}\]$	${6.5}_{- 1.6}^{+ 2.0}$ $\[6.5_{-1.6}^{+2.0}\]$	${4.1}_{- 1.3}^{+ 1.7}$ $\[4.1_{-1.3}^{+1.7}\]$
A12_rv [m s⁻¹]	𝒰 (-58.6, 58.6)	$- {1.6}_{- 5.2}^{+ 4.5}$ $\[-1.6_{-5.2}^{+4.5}\]$	$- {3.9}_{- 6.3}^{+ 5.0}$ $\[-3.9_{-6.3}^{+5.0}\]$	$- {1.4}_{- 4.7}^{+ 4.2}$ $\[-1.4_{-4.7}^{+4.2}\]$
P_{rot FWHM} (days)	𝒩 (25.0, 2.5)	${24.50}_{- 0.84}^{+ 0.86}$ $\[24.50_{-0.84}^{+0.86}\]$	${24.28}_{- 0.62}^{+ 0.67}$ $\[24.28_{-0.62}^{+0.67}\]$	${24.42}_{- 0.82}^{+ 0.85}$ $\[24.42_{-0.82}^{+0.85}\]$
ln L_FWHM (days)	𝒩 (4.0, 0.4)	${3.57}_{- 0.17}^{+ 0.17}$ $\[3.57_{-0.17}^{+0.17}\]$	${3.62}_{- 0.18}^{+ 0.18}$ $\[3.62_{-0.18}^{+0.18}\]$	${3.56}_{- 0.18}^{+ 0.18}$ $\[3.56_{-0.18}^{+0.18}\]$
ln ω_FWHM	𝒰 (-5, 5)	$- {0.27}_{- 0.41}^{+ 0.39}$ $\[-0.27_{-0.41}^{+0.39}\]$	$- {0.50}_{- 0.37}^{+ 0.36}$ $\[-0.50_{-0.37}^{+0.36}\]$	$- {0.34}_{- 0.37}^{+ 0.34}$ $\[-0.34_{-0.37}^{+0.34}\]$
A_bis [m s⁻¹]	𝒰 (0, 31)	${5.8}_{- 1.1}^{+ 1.2}$ $\[5.8_{-1.1}^{+1.2}\]$	${6.1}_{- 1.1}^{+ 1.3}$ $\[6.1_{-1.1}^{+1.3}\]$	${5.5}_{- 1.2}^{+ 1.3}$ $\[5.5_{-1.2}^{+1.3}\]$
A21_rv [m s⁻¹]	𝒰 (-29.3, 29.3)	$- {5.1}_{- 1.3}^{+ 1.1}$ $\[-5.1_{-1.1}^{+1.3}\]$	$- {7.4}_{- 1.5}^{+ 1.4}$ $\[-7.4_{-1.5}^{+1.4}\]$	$- {5.0}_{- 1.4}^{+ 1.2}$ $\[-5.0_{-1.4}^{+1.2}\]$
A22_rv [m s⁻¹]	𝒰 (-58.6, 58.6)	${8.7}_{- 3.7}^{+ 3.6}$ $\[8.7_{-3.7}^{+3.6}\]$	$- {2.0}_{- 7.8}^{+ 8.7}$ $\[-2.0_{-7.8}^{+8.7}\]$	${10.6}_{- 3.5}^{+ 4.0}$ $\[10.6_{-3.5}^{+4.0}\]$
P_rot _bis (days)	𝒩 (25.0, 2.5)	${26.53}_{- 0.46}^{+ 4.45}$ $\[26.53_{-0.46}^{+4.45}\]$	${26.06}_{- 0.73}^{+ 0.79}$ $\[26.06_{-0.73}^{+0.79}\]$	${26.64}_{- 0.43}^{+ 0.41}$ $\[26.64_{-0.43}^{+0.41}\]$
ln L_BIS	𝒩 (4.0, 0.4)	${3.87}_{- 0.22}^{+ 0.19}$ $\[3.87_{-0.22}^{+0.19}\]$	${3.36}_{- 0.20}^{+ 0.27}$ $\[3.36_{-0.20}^{+0.27}\]$	${3.89}_{- 0.23}^{+ 0.20}$ $\[3.89_{-0.23}^{+0.20}\]$
ln ω_bis	𝒰 (-5, 5)	$- {2.4}_{- 1.7}^{+ 1.3}$ $\[-2.4_{-1.7}^{+1.3}\]$	$- {1.56}_{- 2.08}^{+ 0.74}$ $\[-1.56_{-2.08}^{+0.74}\]$	$- {2.1}_{- 1.8}^{+ 1.0}$ $\[-2.1_{-1.8}^{+1.0}\]$
ln A_TESS [ppm]	𝒰 (0, 20)	${10.60}_{- 0.21}^{+ 0.20}$ $\[10.60_{-0.21}^{+0.20}\]$	${10.55}_{- 0.19}^{+ 0.20}$ $\[10.55_{-0.19}^{+0.20}\]$	${10.62}_{- 0.20}^{+ 0.20}$ $\[10.62_{-0.20}^{+0.20}\]$
P_{rot TESS} (days)	𝒩 (25, 2.5)	${23.8}_{- 2.5}^{+ 2.5}$ $\[23.8_{-2.5}^{+2.5}\]$	${24.2}_{- 2.6}^{+ 2.5}$ $\[24.2_{-2.6}^{+2.5}\]$	${26.7}_{- 2.8}^{+ 2.8}$ $\[26.7_{-2.8}^{+2.8}\]$
ln L_TESS (days)	𝒩 (4.0, 0.4)	${3.58}_{- 0.30}^{+ 0.30}$ $\[3.58_{-0.30}^{+0.30}\]$	${3.60}_{- 0.32}^{+ 0.31}$ $\[3.60_{-0.32}^{+0.31}\]$	${3.57}_{- 0.30}^{+ 0.29}$ $\[3.57_{-0.30}^{+0.29}\]$
Planet b
Phase	𝒰 (0, 1)		${0.1212}_{- 0.0026}^{+ 0.0025}$ $\[0.1212_{-0.0026}^{+0.0025}\]$	${0.1213}_{- 0.0027}^{+ 0.0025}$ $\[0.1213_{-0.0027}^{+0.0025}\]$
P_orb (days)	𝒩 (1.2731, 0.1)		${1.2730988}_{- 0.0000028}^{+ 0.0000027}$ $\[1.2730988_{-0.0000028}^{+0.0000027}\]$	${1.2730989}_{- 0.0000028}^{+ 0.0000027}$ $\[1.2730989_{-0.0000028}^{+0.0000027}\]$
ln R_p [R_⊕]	𝒰 (-5, 5)		${0.327}_{- 0.065}^{+ 0.057}$ $\[0.327_{-0.065}^{+0.057}\]$	${0.337}_{- 0.061}^{+ 0.059}$ $\[0.337_{-0.061}^{+0.059}\]$
ln M_p [M_⊕]	𝒰 (-5, 5)		${1.37}_{- 0.14}^{+ 0.12}$ $\[1.37_{-0.14}^{+0.12}\]$	${1.23}_{- 0.15}^{+ 0.13}$ $\[1.23_{-0.15}^{+0.13}\]$
b	𝒰 (0, 1)		< 0.61	< 0.57
$\sqrt{e} \cos (ω)$ $\\,{\sqrt{e}}\operatorname{cos}(\omega)\]$	𝒩 (0, 0.3)		$- {0.06}_{- 0.14}^{+ 0.16}$ $\[-0.06_{-0.14}^{+0.16}\]$	${0.02}_{- 0.16}^{+ 0.17}$ $\[0.02_{-0.16}^{+0.17}\]$
$\sqrt{e} \sin (ω)$ $\\,{\sqrt{e}}\operatorname{sin}(\omega)\]$	𝒩 (0, 0.3)		$- {0.02}_{- 0.16}^{+ 0.16}$ $\[-0.02_{-0.16}^{+0.16}\]$	$- {0.02}_{- 0.15}^{+ 0.15}$ $\[-0.02_{-0.15}^{+0.15}\]$
Planet c
Phase	𝒰 (0, 1)			${0.624938}_{- 0.00050}^{+ 0.00063}$ $\[0.624938_{-0.00050}^{+0.00063}\]$
P_orb (days)	𝒩 (8.5, 0.5)			${8.465651}_{- 0.000029}^{+ 0.000035}$ $\[8.465651_{-0.000029}^{+0.000035}\]$
ln R_p [R_⊕]	𝒰 (-5, 5)			${0.776}_{- 0.092}^{+ 0.084}$ $\[0.776_{-0.092}^{+0.084}\]$
ln M_p [M_⊕]	𝒰 (-5, 5)			${1.89}_{- 0.19}^{+ 0.16}$ $\[1.89_{-0.19}^{+0.16}\]$
b	𝒰 (0, 1)			${0.774}_{- 0.057}^{+ 0.052}$ $\[0.774_{-0.057}^{+0.052}\]$
$\sqrt{e} \cos (ω)$ $\\,{\sqrt{e}}\operatorname{cos}(\omega)\]$	𝒩 (0, 0.3)			${0.22}_{- 0.17}^{+ 0.13}$ $\[0.22_{-0.17}^{+0.13}\]$
$\sqrt{e} \sin (ω)$ $\\,{\sqrt{e}}\operatorname{sin}(\omega)\]$	𝒩 (0, 0.3)			${0.00}_{- 0.19}^{+ 0.19}$ $\[0.00_{-0.19}^{+0.19}\]$
Limb darkening
q₁	𝒩 (0.4676, 0.0067)		${0.4677}_{- 0.0021}^{+ 0.0021}$ $\[0.4677_{-0.0021}^{+0.0021}\]$	${0.4679}_{- 0.0021}^{+ 0.0021}$ $\[0.4679_{-0.0021}^{+0.0021}\]$
q₂	𝒩 (0.1442, 0.011)		${0.1443}_{- 0.0033}^{+ 0.0034}$ $\[0.1443_{-0.0033}^{+0.0034}\]$	${0.1441}_{- 0.0034}^{+ 0.0033}$ $\[0.1441_{-0.0034}^{+0.0033}\]$
Stellar parameters
M_* [M_⊙]	𝒩 (0.790, 0.043)		${0.783}_{- 0.042}^{+ 0.041}$ $\[0.783_{-0.042}^{+0.041}\]$	${0.788}_{- 0.041}^{+ 0.040}$ $\[0.788_{-0.041}^{+0.040}\]$
R_* [R_⊙]	𝒩 (0.733, 0.034)		${0.746}_{- 0.028}^{+ 0.029}$ $\[0.746_{-0.028}^{+0.029}\]$	${0.746}_{- 0.028}^{+ 0.027}$ $\[0.746_{-0.028}^{+0.027}\]$
Jitter
ln Jit HARPS_fwhm [m s⁻¹]	𝒰 (-5, 5)	${1.36}_{- 0.21}^{+ 0.19}$ $\[1.36_{-0.21}^{+0.19}\]$	${1.44}_{- 0.22}^{+ 0.22}$ $\[1.44_{-0.22}^{+0.22}\]$	${1.36}_{- 0.22}^{+ 0.21}$ $\[1.36_{-0.22}^{+0.21}\]$
ln Jit ESP_FWHM [m s⁻¹]	𝒩 (-5, 5)	${2.27}_{- 0.13}^{+ 0.13}$ $\[2.27_{-0.13}^{+0.13}\]$	${2.27}_{- 0.12}^{+ 0.12}$ $\[2.27_{-0.12}^{+0.12}\]$	${2.28}_{- 0.14}^{+ 0.13}$ $\[2.28_{-0.14}^{+0.13}\]$
ln Jit HARPS_bis [m s⁻¹]	𝒩 (-5, 5)	${1.11}_{- 0.21}^{+ 0.19}$ $\[1.11_{-0.21}^{+0.19}\]$	${1.23}_{- 0.19}^{+ 0.17}$ $\[1.23_{-0.19}^{+0.17}\]$	${1.19}_{- 0.18}^{+ 0.17}$ $\[1.19_{-0.18}^{+0.17}\]$
ln Jit ESP_bis [m s⁻¹]	𝒩 (-5, 5)	${1.45}_{- 0.15}^{+ 0.15}$ $\[1.45_{-0.15}^{+0.15}\]$	${1.40}_{- 0.14}^{+ 0.14}$ $\[1.40_{-0.14}^{+0.14}\]$	${1.58}_{- 0.15}^{+ 0.14}$ $\[1.58_{-0.15}^{+0.14}\]$
ln Jit HARPS_rv [m s⁻¹]	𝒩 (-5, 5)	${1.12}_{- 0.15}^{+ 0.16}$ $\[1.12_{-0.15}^{+0.16}\]$	${0.74}_{- 0.21}^{+ 0.22}$ $\[0.74_{-0.21}^{+0.22}\]$	${0.45}_{- 0.22}^{+ 0.20}$ $\[0.45_{-0.22}^{+0.20}\]$
ln Jit ESP_RV [m s⁻¹]	𝒩 (-5, 5)	${1.25}_{- 0.13}^{+ 0.13}$ $\[1.25_{-0.13}^{+0.13}\]$	${0.37}_{- 0.29}^{+ 0.32}$ $\[0.37_{-0.29}^{+0.32}\]$	${0.69}_{- 0.17}^{+ 0.17}$ $\[0.69_{-0.17}^{+0.17}\]$
Model statistics
lnZ		-82110.6	-81614.9	-81582.5
Δ lnZ vs 0p			497.7	528.1
RMS O - C RV [m s⁻¹]		2.96	1.53	1.26
RMSO-CRV_esp [m s⁻¹]		2.91	0.95	1.05
RMS O - C RV_harps [m s⁻¹]		3.02	2.11	1.51

Notes. All Upper limits are 99.7% limits

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