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

Open Access

Table C.7

Comparison of posteriors from modelling of different RVs and activity indicators. These are: CCF RV & FWHM;, LBL RV & CCF FWHM (d4, our best model; boldface), LBL RV & S-index, LBL RV & Hα, LBL RV & Na I.

Parameter name	Symbol	Unit	Prior	Posterior
Parameter name	Symbol	Unit	Prior	RV_CCF & FWHM_CCF	RV_LBL & FWHM_CCF	RV_LBL & S-index	RV_LBL & Hα	RV_LBL & Na I
Long-term function parameters
Period	P_cyc	d	𝒰_log (200, 2000)	$1844_{- 162}^{+ 110}$ ${1844_{ - 162}^{ + 110}}$	$316_{- 8}^{+ 14}$ ${316_{ - 8}^{ + 14}}$	$332_{- 19}^{+ 47}$ ${332_{ - 19}^{ + 47}}$	$283_{- 13}^{+ 104}$ ${283_{ - 13}^{ + 104}}$	$1384_{- 945}^{+ 502}$ ${1384_{ - 95}^{ + 502}}$
RV phase	φ_cyc.0	-	𝒰(0, 1)^w	${0.507}_{- 0.156}^{+ 0.954}$ ${0.507_{ - 0.156}^{ + 0.954}}$	${0.643}_{- 0.230}^{+ 0.350}$ ${0.643_{ - 0.230}^{ + 0.350}}$	${0.690}_{- 0.302}^{+ 0.403}$ ${0.690_{ - 0.302}^{ + 0.403}}$	${0.736}_{- 0.233}^{+ 0.276}$ ${0.736_{ - 0.233}^{ + 0.276}}$	${0.723}_{- 0.236}^{+ 0.264}$ ${0.723_{ - 0.236}^{ + 0.264}}$
RV amplitude	k_{cyc, 0}	m s⁻¹	𝒰(0, 40)	${1.77}_{- 1.10}^{+ 1.19}$ $1.77_{ - 1.10}^{ + 1.19}$	${1.17}_{- 0.37}^{+ 0.36}$ $1.17_{ - 0.37}^{ + 0.36}$	${1.07}_{- 0.41}^{+ 0.36}$ $1.07_{ - 0.41}^{ + 0.36}$	${1.27}_{- 0.31}^{+ 0.30}$ $1.27_{ - 0.31}^{ + 0.30}$	${0.95}_{- 0.61}^{+ 0.55}$ $0.95_{ - 0.61}^{ + 0.55}$
Indicator phase	φ_cyc.1	-	𝒰(0, 1)^w	${0.932}_{- 0.197}^{+ 0.194}$ $0.932_{ - 0.197}^{ + 0.194}$	${0.882}_{- 0.226}^{+ 0.333}$ $0.882_{ - 0.226}^{ + 0.333}$	${0.00}_{- 0.35}^{+ 0.37}$ $0.00_{ - 0.35}^{ + 0.37}$	${0.984}_{- 0.257}^{+ 0.243}$ $0.984_{ - 0.2}^{ + 0.2}$	${0.994}_{- 0.224}^{+ 0.244}$ $0.994_{ - 0.224}^{ + 0.244}$
Indicator amplitude	k_{cyc, 1}	-	𝒰_log(10⁻³, 10³)	${3.42}_{- 2.28}^{+ 2.78}$ $3.42_{ - 2.28}^{ + 2.78}$	${2.17}_{- 1.12}^{+ 1.04}$ $2.17_{ - 1.12}^{ + 1.04}$	$({3.76}_{- 220}^{+ 2.26}) \times 10^{- 2}$ $\left( {3.76_{ - 220}^{ + 2.26}} \right) \times {10^{ - 2}}$	$({5.51}_{- 3.82}^{5.68}) \times 10^{- 3}$ $\left( {5.51_{ - 3.82}^{5.68}} \right) \times {10^{ - 3}}$	$({2.07}_{- 1.36}^{+ 1.30}) \times 10^{- 3}$ $\left( {2.07_{ - 136}^{ + 130}} \right) \times {10^{ - 3}}$
RV second-order correction	α₀	m s⁻¹ d⁻²	𝒩(μ_lm.200σ_lm)	$({1.48}_{- 9.75}^{+ 11.03}) \times 10^{- 7}$ ${\left( {1.48_{ - 975}^{ + 11.03}} \right) \times {{10}^{ - 7}}}$	$(- {3.25}_{- 4.56}^{+ 4.37}) \times 10^{- 7}$ ${\left( { - 3.25_{ - 4.56}^{ + 4.37}} \right) \times {{10}^{ - 7}}}$	$(- {6.74}_{- 7.25}^{+ 6.27}) \times 10^{- 7}$ ${\left( { - 6.74_{ - - 6527}^{ + 6.27}} \right) \times {{10}^{ - 7}}}$	$(- {6.63}_{- 3.76}^{+ 3.71}) \times 10^{- 7}$ ${\left( { - 6.63_{ - 3.76}^{ + 3.71}} \right) \times {{10}^{ - 7}}}$	$(- {5.34}_{- 3.96}^{+ 6.24}) \times 10^{- 7}$ ${\left( { - 5.34_{ - 3.96}^{ + 6.24}} \right) \times {{10}^{ - 7}}}$
RV first-order correction	β₀	m s⁻¹ d⁻¹	𝒩(μ_lm.200σ_lm)	$({1.35}_{- 3.75}^{+ 4.03}) \times 10^{- 3}$ ${\left( {1.35_{ - 3.75}^{ + 4.33}} \right) \times {{10}^{ - 3}}}$	$(- {6.71}_{- 179.03}^{+ 173.14}) \times 10^{- 5}$ ${\left( { - 6.71_{ - 179.03}^{1 + 14.4}} \right) \times {{10}^{ - 5}}}$	$(- {1.47}_{- 2.79}^{+ 2.42}) \times 10^{- 3}$ ${\left( { - 1.47_{ - 2.79}^{ + 2.42}} \right) \times {{10}^{ - 3}}}$	$(- {1.29}_{- 1.43}^{+ 1.42}) \times 10^{- 3}$ ${\left( { - 1.29_{ - 1.43}^{ + 1.42}} \right) \times {{10}^{ - 3}}}$	$(- {6.25}_{- 14.99}^{+ 20.67}) \times 10^{- 4}$ ${\left( { - 6.25_{ - 14.99}^{ + 20.67}} \right) \times {{10}^{ - 4}}}$
RV zero-order correction	γ₀	m s⁻¹	𝒩(μ_lm.200σ_lm)	${3.00}_{- 3.29}^{+ 3.30}$ ${3.00_{ - 3.29}^{ + 3.30}}$	${2.48}_{- 1.70}^{+ 1.69}$ ${2.48_{ - 1.70}^{ + 1.69}}$	${1.39}_{- 2.47}^{+ 2.21}$ ${1.39_{ - 2.47}^{ + 2.21}}$	${2.04}_{- 1.50}^{+ 1.34}$ ${2.04_{ - 1.50}^{ + 1.34}}$	${2.58}_{- 1.53}^{+ 1.40}$ ${2.58_{ - 1.53}^{ + 1.40}}$
Indicator second-order correction	α₁	-	𝒩(μ_lm.200σ_lm)	$({1.52}_{- 2.16}^{+ 2.53}) \times 10^{- 6}$ ${\left( {1.52_{ - 2.15}^{ + 2.53}} \right) \times {{10}^{ - 6}}}$	$({1.37}_{- 1.63}^{+ 1.59}) \times 10^{- 6}$ ${\left( {1.37_{ - 1.53}^{ + 1.59}} \right) \times {{10}^{ - 6}}}$	$({4.82}_{- 4.26}^{+ 3.92}) \times 10^{- 8}$ ${\left( {4.82_{ - 4.26}^{ + 3.47}} \right) \times {{10}^{ - 8}}}$	$({7.05}_{- 4.56}^{+ 4.67}) \times 10^{- 9}$ ${\left( {7.05_{ - 4.56}^{ + 4.57}} \right) \times {{10}^{ - 9}}}$	$({1.18}_{- 1.00}^{+ 0.95}) \times 10^{- 9}$ ${\left( {1.18_{ - 1.09}^{ + 0.95}} \right) \times {{10}^{ - 9}}}$ `
Indicator first-order correction	β₁	-	𝒩(μ_lm.200σ_lm)	$({5.98}_{- 8.60}^{+ 9.51}) \times 10^{- 3}$ ${\left( {5.98_{ - 8.60}^{ + 9.5}} \right) \times {{10}^{ - 3}}}$	$({5.45}_{- 6.38}^{+ 6.15}) \times 10^{- 3}$ ${\left( {5.45_{ - 6.38}^{ + 6.15}} \right) \times {{10}^{ - 3}}}$	$({2.92}_{- 1.66}^{+ 1.51}) \times 10^{- 4}$ ${\left( {2.92_{ - 1.56}^{ + 1.51}} \right) \times {{10}^{ - 4}}}$	$({4.84}_{- 1.80}^{+ 1.81}) \times 10^{- 5}$ ${\left( {4.84_{ - 1.80}^{ + 1.8}} \right) \times {{10}^{ - 5}}}$	$({7.94}_{- 3.89}^{+ 3.64}) \times 10^{- 6}$ ${\left( {7.94_{ - 3.69}^{ + 3.64}} \right) \times {{10}^{ - 6}}}$
Indicator zero-order correction	γ₁	-	𝒩(μ_lm.200σ_lm)	${2.87}_{- 7.29}^{+ 7.77}$ ${2.87_{ - 7.29}^{ + 7.77}}$	${3.27}_{- 5.61}^{+ 5.66}$ ${3.27_{ - 5.61}^{ + 5.66}}$	$({3.98}_{- 1.42}^{+ 1.34}) \times 10^{- 1}$ ${\left( {3.98_{ - 1.42}^{ + 1.34}} \right) \times {{10}^{ - 1}}}$	$({7.54}_{- 1.69}^{+ 1.63}) \times 10^{- 2}$ ${\left( {7.54_{ - 1.69}^{ + .63}} \right) \times {{10}^{ - 2}}}$	$({1.17}_{- 0.34}^{+ 0.33}) \times 10^{- 2}$ ${\left( {1.17_{ - 0.34}^{ + 033}} \right) \times {{10}^{ - 2}}}$
Dataset parameters
RV jitter	J_{0, 0}	m s⁻¹	𝒰_log(10⁻³,10³)	1.46 ±0.24	${1.29}_{- 0.14}^{+ 0.15}$ ${1.29_{ - 0.14}^{ + 0.15}}$	${1.28}_{- 0.14}^{+ 0.15}$ ${1.28_{ - 0.14}^{ + 0.15}}$	${1.31}_{- 0.15}^{+ 0.16}$ ${1.31_{ - 0.15}^{ + 0.16}}$	${1.30}_{- 0.14}^{+ 0.15}$ ${1.30_{ - 0.14}^{ + 0.15}}$
Indicator jitter	J_{0, 1}	-	𝒰_log(10⁻³,10³)	$({4.46}_{- 4.12}^{+ 34.56}) \times 10^{- 2}$ ${\left( {4.46_{ - 4.12}^{ + 34.56}} \right) \times {{10}^{ - 2}}}$	$({2.90}_{- 2.62}^{+ 28.85}) \times 10^{- 2}$ ${\left( {2.90_{ - 2.62}^{ + 28.85}} \right) \times {{10}^{ - 2}}}$	$({3.05}_{- 1.65}^{+ 4.46}) \times 10^{- 3}$ ${\left( {3.05_{ - 1.65}^{ + 4.46}} \right) \times {{10}^{ - 3}}}$	$({9.59}_{- 0.66}^{+ 0.70}) \times 10^{- 3}$ ${\left( {9.59_{ - 0.66}^{ + 0.70}} \right) \times {{10}^{ - 3}}}$	$({1.51}_{- 0.21}^{+ 0.21}) \times 10^{- 3}$ ${\left( {1.51_{ - 0.21}^{ + 0.21}} \right) \times {{10}^{ - 3}}}$
Stellar-activity parameters
Timescale	τ	d	𝒰_log (40,10⁴)	$180_{- 60}^{+ 119}$ ${180_{ - 60}^{ + 119}}$	$180_{- 55}^{+ 93}$ ${180_{ - 55}^{ + 93}}$	$321_{- 121}^{+ 278}$ ${321_{ - 121}^{ + 278}}$	$130_{- 34}^{+ 52}$ ${130_{ - 34}^{ + 52}}$	$153_{- 41}^{+ 65}$ ${153_{ - 41}^{ + 65}}$
Period	P	d	𝒰_log (2, 200)	${30.2}_{- 0.3}^{+ 0.4}$ ${30.2_{ - 0.3}^{ + 0.4}}$	30.2 ± 0.3	30.2 ± 0.2	30.1 ±0.3	29.9 ±0.3
Sinescale (harmonic complexity)	η	-	𝒰_log(10⁻²,10²)	${1.00}_{- 0.28}^{+ 0.53}$ ${1.00_{ - 0.28}^{ + 0.53}}$	${0.82}_{- 0.19}^{+ 0.29}$ ${0.82_{ - 0.19}^{ + 0.29}}$	${0.93}_{- 0.25}^{+ 0.45}$ ${0.93_{ - 0.25}^{ + 0.45}}$	${0.65}_{- 0.13}^{+ 0.18}$ ${0.65_{ - 0.13}^{ + 0.18}}$	${0.59}_{- 0.14}^{+ 0.19}$ ${0.59_{ - 0.14}^{ + 0.19}}$
RV amplitude	A₀	ms ¹	𝒰(−10³,10³)	${2.77}_{- 0.88}^{+ 2.02}$ ${2.77_{ - 0.88}^{ + 2.02}}$	${1.32}_{- 0.44}^{+ 0.70}$ ${1.32_{ - 0.44}^{ + 0.19}}$	${2.00}_{- 0.77}^{+ 1.87}$ ${2.00_{ - 0.77}^{ + 1.15}}$	${0.76}_{- 0.47}^{+ 0.46}$ ${0.76_{ - 0.47}^{ + 0.46}}$	${1.17}_{- 0.68}^{+ 0.63}$ ${1.17_{ - 0.68}^{ + 0.63}}$
RV gradient amplitude	B₀	ms¹ d ¹	𝒰(−10³,10³)	$({2.56}_{- 0.86}^{+ 1.90}) \times 10^{1}$ ${\left( {2.56_{ - 0.88}^{ + 0.65}} \right) \times {{10}^1}}$	$({1.81}_{- 0.44}^{+ 0.82}) \times 10^{1}$ ${\left( {1.81_{ - 0.44}^{ + 0.82}} \right) \times {{10}^1}}$	$({2.30}_{- 0.75}^{+ 1.89}) \times 10^{1}$ ${\left( {2.30_{ - 0.05}^{ + 1.89}} \right) \times {{10}^1}}$	$({1.53}_{- 0.29}^{+ 0.46}) \times 10^{1}$ ${\left( {1.53_{ - 0.29}^{ + 0.46}} \right) \times {{10}^1}}$	$({1.45}_{- 0.30}^{+ 0.49}) \times 10^{1}$ ${\left( {1.45_{ - 0.40}^{ + 0.49}} \right) \times {{10}^1}}$
Indicator amplitude	A₁	-	𝒰_log(10⁻³,10³)	${7.09}_{- 2.02}^{+ 4.88}$ ${7.09_{ - 2.02}^{ + 4.88}}$	${6.03}_{- 1.40612}^{+ 2.54140}$ ${6.03_{ - 1.40612}^{ + 2.5140}}$	$({1.38}_{- 0.44}^{+ 1.08}) \times 10^{- 1}$ ${\left( {1.38_{ - 0.44}^{ + 1.08}} \right) \times {{10}^{ - 1}}}$	$({1.98}_{- 0.35}^{+ 0.53}) \times 10^{- 2}$ ${\left( {1.98_{ - 0.35}^{ + 0.53}} \right) \times {{10}^{ - 2}}}$	$({3.65}_{- 0.67}^{+ 1.02}) \times 10^{- 3}$ ${\left( {3.65_{ - 0.67}^{ + 1.02}} \right) \times {{10}^{ - 3}}}$
GJ 3998 b
Period	P_b	d	𝒰 (2,3)	${2.65060}_{- (53)}^{+ (120)}$ $2.65060_{ - (53)}^{ + (120)}$	${2.65033}_{- (19)}^{+ (22)}$ $2.65033_{ - (19)}^{ + (22)}$	${2.65030}_{- (19)}^{+ (22)}$ $2.65030_{ - (19)}^{ + (22)}$	${2.65029}_{- (16)}^{+ (18)}$ $2.65029_{ - (16)}^{ + (18)}$	${2.65027}_{- (16)}^{+ (17)}$ $2.65027_{ - (16)}^{ + (17)}$
Phase	φ_b	-	𝒰(0, 1)^w	${0.263}_{- 0.236}^{+ 0.253}$ $0.263_{ - 0.236}^{ + 0.253}$	${0.148}_{- 0.095}^{+ 0.082}$ $0.148_{ - 0.095}^{ + 0.082}$	${0.159}_{- 0.098}^{+ 0.080}$ $0.159_{ - 0.098}^{ + 0.008}$	${0.166}_{- 0.076}^{+ 0.068}$ $0.166_{ - 0.076}^{ + 0.068}$	${0.172}_{- 0.075}^{+ 0.068}$ $0.172_{ - 0.075}^{ + 0.068}$
RV semi-amnlitude	k_{rv, b}	ms ¹	𝒰 (0,5)	1.62 + 0.24	1.79 + 0.18	1.82 + 0.18	1.84 + 0.18	1.84 + 0.18
GJ 3998 c
Period	P_c	d	𝒰(13, 14)	${13.724}_{- 0.005}^{+ 0.004}$ $13.724_{ - 0.005}^{ + 0.004}$	${13.727}_{- 0.004}^{+ 0.003}$ $13.727_{ - 0.004}^{ + 0.003}$	13.726 ± 0.004	13.727 ±0.004	13.727 ±0.004
Phase	φ_c	-	𝒰(0, 1)^w	${0.511}_{- 0.069}^{+ 0.073}$ $0.511_{ - 0.069}^{ + 0.073}$	${0.466}_{- 0.051}^{+ 0.055}$ $0.466_{ - 0.051}^{ + 0.055}$	${0.483}_{- 0.056}^{+ 0.058}$ $0.483_{ - 0.056}^{ + 0.058}$	${0.492}_{- 0.057}^{+ 0.058}$ $0.492_{ - 0.057}^{ + 0.058}$	${0.495}_{- 0.060}^{+ 0.062}$ $0.495_{ - 0.060}^{ + 0.062}$
RV semi-amplitude	k_rv,c	ms ¹	𝒰(0, 5)	${2.92}_{- 0.33}^{+ 0.34}$ $2.92_{ - 0.33}^{ + 0.34}$	2.82 ± 0.26	2.68 ± 0.25	${3.01}_{- 0.30}^{+ 0.31}$ $3.01_{ - 0.30}^{ + 0.31}$	2.73 ± 0.29
GJ 3998 d
Period	P_d	d	𝒰(30, 50)	${41.77}_{- 10.53}^{+ 0.11}$ $41.77_{ - 10.53}^{ + 0.11}$	41.78 ±0.05	41.78 ±0.05	${41.78}_{- 0.05}^{+ 0.06}$ $41.78_{ - 0.05}^{ + 0.06}$	${41.79}_{- 0.05}^{+ 0.06}$ $41.79_{ - 0.05}^{ + 0.06}$
Phase	φ_d	-	𝒰(0, 1)^w	${0.753}_{- 0.181}^{+ 0.221}$ $0.753_{ - 0.181}^{ + 0.221}$	${0.785}_{- 0.080}^{+ 0.077}$ $0.785_{ - 0.080}^{ + 0.077}$	${0.781}_{- 0.088}^{+ 0.086}$ $0.781_{ - 0.088}^{ + 0.086}$	${0.785}_{- 0.083}^{+ 0.078}$ $0.785_{ - 0.083}^{ + 0.078}$	${0.770}_{- 0.087}^{+ 0.084}$ $0.770_{ - 0.087}^{ + 0.084}$
RV semi-amplitude	k_{rv, d}	m s⁻¹	𝒰(0,5)	${1.52}_{- 0.45}^{+ 0.41}$ ${1.52_{ - 0.45}^{ + 0.41}}$	${1.74}_{- 0.25}^{+ 0.26}$ ${1.74_{ - 0.25}^{ + 0.26}}$	${1.69}_{- 0.27}^{+ 0.26}$ ${1.69_{ - 0.27}^{ + 0.26}}$	1.90 ±0.27	${1.67}_{- 0.28}^{+ 0.27}$ ${1.67_{ - 0.28}^{ + 0.27}}$

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. Models with Hα and Na I used the prior 𝒰_log (10⁻⁴,1) for their LTF amplitudes.

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.