HADES RV Programme with HARPS-N at TNG - XVI. A super-Earth in the habitable zone of the GJ 3998 multi-planet system

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Table C.6

Parameter posteriors of our best model (d4), against the results published by A16.

Parameter name	Symbol	Unit	Prior	Posterior
				This work	A16
Long-term function parameters
Period	P_cyc	d	𝒰_log (200, 2000)	$316_{- 8}^{+ 14}$ ${316_{ - 8}^{ + 14}}$	-
RV phase	φ_{cyc, 0}	-	𝒰(0, 1)^w	${0.571}_{- 0.257}^{+ 0.255}$ ${0.571_{ - 0.257}^{ + 0.255}}$	-
RV amplitude	k_{cyc, 0}	m s⁻¹	𝒰 (0, 40)	${1.17}_{- 0.37}^{+ 0.36}$ ${1.17_{ - 0.37}^{ + 0.36}}$	-
FWHM phase	φ_{cyc, 1}	-	𝒰(0, 1)^w	${0.812}_{- 0.259}^{+ 0.247}$ ${0.812_{ - 0.259}^{ + 0.247}}$	-
FWHM amplitude	k_{cyc, 1}	m s⁻¹	𝒰 (0, 40)	${2.17}_{- 1.12}^{+ 1.04}$ ${2.17_{ - 1.12}^{ + 1.64}}$	-
RV second-order correction	α₀	m s⁻¹ d⁻²	𝒩(µ_lm, 200σ_lm)	$(- {3.25}_{- 4.56}^{+ 4.37}) \times 10^{- 7}$ ${\left( { - 3.25_{ - 4.56}^{ + 4.37}} \right) \times {{10}^{ - 7}}}$	-
RV first-order correction	β₀	m s⁻¹ d⁻¹	𝒩(µ_lm, 200σ_lm)	$(- {6.71}_{- 179.03}^{+ 173.14}) \times 10^{- 5}$ ${\left( { - 6.71_{ - 179.03}^{ + 173.14}} \right) \times {{10}^{ - 5}}}$	-
RV zero-order correction	γ₀	m s⁻¹	𝒩(µ_lm, 200σ_lm)	${2.48}_{- 1.70}^{+ 1.69}$ $2.48_{ - 1.70}^{ + 1.69}$	$- {0.27}_{- 0.43}^{+ 0.49}$ $- 0.27_{ - 0.43}^{ + 0.49}$
FWHM second-order correction	α₁	m s⁻¹ d⁻²	𝒩(µ_lm, 200σ_lm)	$({1.37}_{- 1.63}^{+ 1.59}) \times 10^{- 6}$ ${\left( {1.37_{ - 1.63}^{ + 1.59}} \right) \times {{10}^{ - 6}}}$	-
FWHM first-order correction	β₁	m s⁻1 d⁻¹	𝒩(µ_lm, 200σ_lm)	$({5.45}_{- 6.38}^{+ 6.15}) \times 10^{- 3}$ ${\left( {5.45_{ - 6.38}^{ + 6.13}} \right) \times {{10}^{ - 3}}}$	-
FWHM zero-order correction	γ₁	m s⁻¹	𝒩(µ_lm, 200σ_lm)	${3.27}_{- 5.61}^{+ 5.66}$ ${3.27_{ - 5.61}^{ + 5.66}}$	-
Dataset parameters
RV jitter	J_0,0	m s⁻¹	𝒰_log (10⁻³, 10³)	${1.29}_{- 0.14}^{+ 0.15}$ ${1.29_{ - 0.14}^{ + 0.15}}$	${1.19}_{- 0.14}^{+ 0.11}$ ${1.19_{ - 0.14}^{ + 0.11}}$
FWHM jitter	J_0,1	m s⁻¹	𝒰_log (10⁻³, 10³)	${0.03}_{- 0.03}^{+ 0.29}$ ${0.03_{ - 0.03}^{ + 0.29}}$	-
Stellar-activity parameters
Timescale	τ	d	𝒰_log (40, 10⁴)	$180_{- 55}^{+ 93}$ ${180_{ - 55}^{ + 93}}$	${34.4}_{- 2.0}^{+ 11.6}$ ${34.4_{ - 2.0}^{ + 11.6}}$
Period	P_rot	d	𝒰_log (2, 200)	30.2 ± 0.3	${0.83}_{- 0.19}^{+ 0.29}$ ${0.83_{ - 0.19}^{ + 0.29}}$
Sinescale (harmonic complexity)	^η	-	𝒰_log (10⁻², 10²)	${31.8}_{- 0.5}^{+ 0.6}$ ${31.8_{ - 0.5}^{ + 0.6}}$	${1.32}_{- 0.44}^{+ 0.70}$ ${1.32_{ - 0.44}^{ + 0.70}}$
RV amplitude	A₀	m s⁻¹	𝒰(−10³, 10³)	${0.41}_{- 0.04}^{+ 0.05}$ ${0.41_{ - 0.04}^{ + 0.05}}$	${18.1}_{- 4.4}^{+ 8.2}$ ${18.1_{ - 4.4}^{ + 8.2}}$ `
RV gradient amplitude	B₀	m s⁻¹ d⁻¹	𝒰(−10³, 10³)	${3.07}_{- 0.24}^{+ 0.29}$ ${3.07_{ - 0.24}^{ + 0.29}}$	-
FWHM amplitude	A₁	m s⁻¹	𝒰_log (10⁻³, 10³)	${6.03}_{- 1.41}^{+ 2.54}$ ${6.03_{ - 1.41}^{ + 2.54}}$	-
GJ 3998 b
Period	P_b	d	𝒰 (2, 3)	${2.65033}_{- (19)}^{+ (22)}$ ${2.65033_{ - (19)}^{ + (22)}}$	${2.64977}_{- (77)}^{+ (81)}$ ${2.64977_{ - (77)}^{ + (81)}}$
Phase	φ_b	-	𝒰(0, 1)^w	${0.148}_{- 0.094}^{+ 0.082}$ ${0.148_{ - 0.094}^{ + 0.082}}$	-
Inferior-conjunction ephemeris	ε_b	BJD-2 400 000	derived	${60202.964}_{- 0.216}^{+ 0.249}$ ${60202.964_{ - 0.216}^{ + 0.249}}$	${56905.895}_{- 0.040}^{+ 0.042}$ ${56905.895_{ - 0.040}^{ + 0.042}}$
RV semi-amplitude	k_{rv, b}	m s⁻¹	𝒰 (0, 5)	1.79 ± 0.18	${1.82}_{- 0.16}^{+ 0.14}$ ${1.82_{ - 0.16}^{ + 0.14}}$
Eccentricity	e_b	-	-	0	0
Semi-major axis	a_b	AU	derived	0.030 ± 0.001	0.029 ± 0.001
Minimum mass	m_b sin i_b	M_⊕	derived	${2.50}_{- 0.29}^{+ 0.30}$ ${2.50_{ - 0.29}^{ + 0.30}}$	2.47 ± 0.27
Incident flux	Φ_b	Φ_⊕	derived	$48_{- 9}^{+ 11}$ ${48_{ - 9}^{ + 11}}$	-
GJ 3998 c
Period	P_c	d	𝒰 (13, 14)	${13.727}_{- 0.004}^{+ 0.003}$ ${13.727_{ - 0.004}^{ + 0.003}}$	13.740 ± 0.016
Phase	φ_c	-	𝒰(0, 1)^w	${0.466}_{- 0.051}^{+ 0.055}$ ${0.466_{ - 0.051}^{ + 0.055}}$	-
Inferior-conjunction ephemeris	ε_c	BJD–2 400 000	derived	${60196.96}_{- 0.75}^{+ 0.70}$ $60196.96_{ - 0.75}^{ + 0.70}$	${56902.2}_{- 0.29}^{+ 0.24}$ $56902.2_{ - 0.29}^{ + 0.24}$
RV semi-amplitude	k_{rv, c}	m s⁻¹	𝒰 (0, 5)	2.86 ± 0.26	${2.67}_{- 0.23}^{+ 0.28}$ ${2.67_{ - 0.23}^{ + 0.28}}$
Eccentricity	e_c	-	-	0	${0.049}_{- 0.034}^{+ 0.052}$ ${0.049_{ - 0.034}^{ + 0.052}}$
Semi-major axis	a_c	AU	derived	0.090 ± 0.003	0.089 ± 0.003
Minimum mass	m_c sin i_c	M_⊕	derived	${6.82}_{- 0.75}^{+ 0.78}$ ${6.82_{ - 0.75}^{ + 0.78}}$	${6.26}_{- 0.76}^{+ 0.79}$ ${6.26_{ - 0.76}^{ + 0.79}}$
Incident flux	Φ_c	Φ_⊕	derived	${5.4}_{- 1.0}^{+ 1.3}$ ${5.4_{ - 1.0}^{ + 1.3}}$	-
GJ 3998 d
Period	P_d	d	𝒰 (30, 50)	41.78 ± 0.05	-
Phase	φ_d	-	𝒰(0, 1)^w	${0.785}_{- 0.080}^{+ 0.076}$ ${0.785_{ - 0.080}^{ + 0.076}}$	-
Inferior-conjunction ephemeris	ε_d	BJD–2 400 000	derived	${60170.55}_{- 3.15}^{+ 3.29}$ ${60170.55_{ - 3.15}^{ + 3.29}}$	-
RV semi-amplitude	k_{rv, d}	m s⁻¹	𝒰 (0, 5)	${1.74}_{- 0.25}^{+ 0.26}$ ${1.74_{ - 0.25}^{ + 0.26}}$	-
Eccentricity	e_d	-	-	0	-
Semi-major axis	a_d	AU	derived	0.189 ± 0.006	-
Minimum mass	m_d sin i_d	M_⊕	derived	${6.07}_{- 0.96}^{+ 1.00}$ ${6.07_{ - 0.96}^{ + 1.00}}$	-
Incident flux	Φ_d	Φ_⊕	derived	${1.2}_{- 0.2}^{+ 0.3}$ ${1.2_{ - 0.2}^{ + 0.3}}$	-

Notes. ^(w)Wrapped parameter. Reported uncertainties reflect the 16^th and the 84^th percentiles. P_b uncertainties are given in parentheses, to the order of the least significant figure. Some LTF parameters have priors informed by an initial Levenberg-Marquadt fitting procedure.

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