Photo-dynamical characterisation of the TOI-178 resonant chain - Exploring the robustness of transit-timing variations and radial velocity mass characterisations

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Volume 688 (August 2024)

A&A, 688 (2024) A211

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Table C.2

Fitted properties of the star and noise parameters

Parameter	Prior	photo–dynamical	photo–dynamical + RV
offset RV	𝒰(−1.0e+300,1.0e+300)	–	${57159.10}_{- 0.16}^{+ 4.14}$ ${57159.10_{ - 0.16}^{ + 4.14}}$
offset Hα	𝒰(−1.0e+300,1.0e+300)	–	${0.3242}_{- 0.0081}^{+ 0.0084}$ ${0.3242_{ - 0.0081}^{ + 0.0084}}$
offset FWHM	𝒰(−1.0e+300,1.0e+300)	–	${6729.20}_{- 0.22}^{+ 0.79}$ ${6729.20_{ - 0.22}^{ + 0.79}}$
σ RV	𝒰(0.0e+00,3.0e+01)	–	${0.94}_{- 0.11}^{+ 0.30}$ ${0.94_{ - 0.11}^{ + 0.30}}$
σ Hα	𝒰(0.0e+00,3.0e+01)	–	${0.00107}_{- 6.5 e - 04}^{+ 4.6 e - 04}$ ${0.00107_{ - 6.5e - 04}^{ + 4.6e - 04}}$
σ FWHM	𝒰(0.0e+00,3.0e+01)	–	${3.84}_{- 0.16}^{+ 0.81}$ ${3.84_{ - 0.16}^{ + 0.81}}$
GPα₀₀₀	𝒩(0.0e+00,2.0e+02)	–	${10.83}_{- 5.49}^{+ 0.06}$ ${10.83_{ - 5.49}^{ + 0.06}}$
GPα₀₁₀	𝒩(0.0e+00,2.0e+02)	–	${0.003}_{- 0.021}^{+ 0.021}$ ${0.003_{ - 0.021}^{ + 0.021}}$
GPα₀₁₁	𝒩(0.0e+00,2.0e+02)	–	$- {0.003}_{- 0.022}^{+ 0.020}$ ${ - 0.003_{ - 0.022}^{ + 0.020}}$
GPα₀₂₀	𝒩(0.0e+00,2.0e+02)	–	$- {12.06}_{- 4.27}^{+ 0.15}$ ${ - 12.06_{ - 4.27}^{ + 0.15}}$
GPα₀₂₁	𝒩(0.0e+00,2.0e+02)	–	${21.57}_{- 0.49}^{+ 0.25}$ ${21.57_{ - 0.49}^{ + 0.25}}$
GPα₁₀₀	𝒩(0.0e+00,2.0e+02)	–	${16.35}_{- 1.25}^{+ 0.28}$ ${16.35_{ - 1.25}^{ + 0.28}}$
GPα₁₁₀	𝒩(0.0e+00,2.0e+02)	–	${0.016}_{- 0.014}^{+ 0.013}$ ${0.016_{ - 0.014}^{ + 0.013}}$
GPβ₁₁₀	𝒩(0.0e+00,2.0e+02)	–	$- {0.014}_{- 0.013}^{+ 0.012}$ ${ - 0.014_{ - 0.013}^{ + 0.012}}$
GPα₁₁₁	𝒩(0.0e+00,2.0e+02)	–	$- 9.1 e - 04_{- 0.009}^{+ 0.010}$ ${ - 9.1e - 04_{ - 0.009}^{ + 0.010}}$
GPα₁₂₀	𝒩(0.0e+00,2.0e+02)	–	${28.73}_{- 0.05}^{+ 2.06}$ ${28.73_{ - 0.05}^{ + 2.06}}$
GPβ₁₂₀	𝒩(0.0e+00,2.0e+02)	–	$- {56.46}_{- 0.19}^{+ 0.57}$ ${ - 56.46_{ - 0.19}^{ + 0.57}}$
GPα₁₂₁	𝒩(0.0e+00,2.0e+02)	–	$- {12.46}_{- 0.13}^{+ 1.92}$ ${ - 12.46_{ - 0.13}^{ + 1.92}}$
GPβ₁₂₁	𝒩(0.0e+00,2.0e+02)	–	$- {9.09}_{- 1.64}^{+ 0.42}$ ${ - 9.09_{ - 1.64}^{ + 0.42}}$
GPα₂₀₀	𝒩(0.0e+00,2.0e+02)	–	$- {2.33}_{- 0.97}^{+ 0.35}$ ${ - 2.33_{ - 0.97}^{ + 0.35}}$
GPα₂₁₀	𝒩(0.0e+00,2.0e+02)	–	$- {0.008}_{- 0.014}^{+ 0.009}$ ${ - 0.008_{ - 0.014}^{ + 0.009}}$
GPβ₂₁₀	𝒩(0.0e+00,2.0e+02)	–	${0.006}_{- 0.011}^{+ 0.012}$ ${0.006_{ - 0.011}^{ + 0.012}}$
GPα₂₁₁	𝒩(0.0e+00,2.0e+02)	–	$- {0.005}_{- 0.016}^{+ 0.013}$ ${ - 0.005_{ - 0.016}^{ + 0.013}}$
GPα₂₂₀	𝒩(0.0e+00,2.0e+02)	–	$- {14.33}_{- 0.08}^{+ 4.16}$ ${ - 14.33_{ - 0.08}^{ + 4.16}}$
GPβ₂₂₀	𝒩(0.0e+00,2.0e+02)	–	${29.22}_{- 4.11}^{+ 0.12}$ ${29.22_{ - 4.11}^{ + 0.12}}$
GPα₂₂₁	𝒩(0.0e+00,2.0e+02)	–	$- {38.19}_{- 0.79}^{+ 1.16}$ ${ - 38.19_{ - 0.79}^{ + 1.16}}$
GPβ₂₂₁	𝒩(0.0e+00,2.0e+02)	–	$- {11.72}_{- 0.23}^{+ 3.19}$ ${ - 11.72_{ - 0.23}^{ + 3.19}}$
GPα₃₀₀	𝒩(0.0e+00,2.0e+02)	–	${12.43}_{- 2.97}^{+ 0.14}$ ${12.43_{ - 2.97}^{ + 0.14}}$
GPα₃₁₀	𝒩(0.0e+00,2.0e+02)	–	${0.009}_{- 0.010}^{+ 0.010}$ ${0.009_{ - 0.010}^{ + 0.010}}$
GPβ₃₁₀	𝒩(0.0e+00,2.0e+02)	–	$- {0.008}_{- 0.012}^{+ 0.011}$ ${ - 0.008_{ - 0.012}^{ + 0.011}}$
GPα₃₁₁	𝒩(0.0e+00,2.0e+02)	–	$1.3 e - 04_{- 0.0031}^{+ 0.0033}$ ${1.3e - 04_{ - 0.0031}^{ + 0.0033}}$
GPα₃₂₀	𝒩(0.0e+00,2.0e+02)	–	${53.01}_{- 3.67}^{+ 0.31}$ ${53.01_{ - 3.67}^{ + 0.31}}$
GPβ₃₂₀	𝒩(0.0e+00,2.0e+02)	–	$- {24.08}_{- 0.64}^{+ 0.89}$ ${ - 24.08_{ - 0.64}^{ + 0.89}}$
GPα₃₂₁	𝒩(0.0e+00,2.0e+02)	–	${0.68}_{- 0.15}^{+ 4.75}$ ${0.68_{ - 0.15}^{ + 4.75}}$
GPβ₃₂₁	𝒩(0.0e+00,2.0e+02)	–	$- {5.31}_{- 3.48}^{+ 0.12}$ ${ - 5.31_{ - 3.48}^{ + 0.12}}$
GPα₄₀₀	𝒩(0.0e+00,2.0e+02)	–	$- {6.51}_{- 0.85}^{+ 0.51}$ ${ - 6.51_{ - 0.85}^{ + 0.51}}$
GPα₄₁₀	𝒩(0.0e+00,2.0e+02)	–	$- {0.0084}_{- 0.0084}^{+ 0.0081}$ ${ - 0.0084_{ - 0.0084}^{ + 0.0081}}$
GPβ₄₁₀	𝒩(0.0e+00,2.0e+02)	–	$- {0.0043}_{- 0.0060}^{+ 0.0071}$ ${ - 0.0043_{ - 0.0060}^{ + 0.0071}}$
GPα₄₁₁	𝒩(0.0e+00,2.0e+02)	–	${0.0025}_{- 0.0051}^{+ 0.0051}$ ${0.0025_{ - 0.0051}^{ + 0.0051}}$
GPα₄₂₀	𝒩(0.0e+00,2.0e+02)	–	$- {9.96}_{- 0.28}^{+ 0.27}$ ${ - 9.96_{ - 0.28}^{ + 0.27}}$
GPβ₄₂₀	𝒩(0.0e+00,2.0e+02)	–	${7.21}_{- 0.99}^{+ 0.55}$ ${7.21_{ - 0.99}^{ + 0.55}}$
GPα₄₂₁	𝒩(0.0e+00,2.0e+02)	–	${9.25}_{- 1.16}^{+ 0.32}$ ${9.25_{ - 1.16}^{ + 0.32}}$
GPβ₄₂₁	𝒩(0.0e+00,2.0e+02)	–	${1.26}_{- 0.10}^{+ 2.55}$ ${1.26_{ - 0.10}^{ + 2.55}}$
GP P	𝓛𝒰(20.00,60.00)	–	${59.75}_{- 0.55}^{+ 0.10}$ ${59.75_{ - 0.55}^{ + 0.10}}$
GP ρ	𝓛𝒰(10.00,100000.00)	–	${1051.07}_{- 4.97}^{+ 0.16}$ ${1051.07_{ - 4.97}^{ + 0.16}}$

Notes. Noise parameters for the RV fit. σ are the jitter term for the velocity and indicators. P is the period of the GP. ρ is the decay timescale. α_klm and β_klm are amplitudes of the cosine and sine terms in the spleaf.term.MultiFourierKernel (https://obswww.unige.ch/%7Edelisle/spleaf/doc/_autosummary/spleaf.term.MultiFourierKernel.html#spleaf.term.MultiFourierKernel), respectively, with k the harmonic (f = k/P), l the timeseries, and m the mode.

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