Characterisation of TOI-406 as a showcase of the THIRSTEE program - A two-planet system straddling the M-dwarf density gap

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Volume 692 (December 2024)

A&A, 692 (2024) A238

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Table 5

Best-fit parameters of the TOI-406 system.

Planetary parameters
	TOI-406 b	TOI-406 c

P(d)	${13.175682}_{- 0.000016}^{+ 0.000017}$ ${13.175682_{ - 0.000016}^{ + 0.000017}}$	${3.307441}_{- 0.000008}^{+ 0.000010}$ ${3.307441_{ - 0.000008}^{ + 0.000010}}$
T₀ (TBJD)^(a)	1388.570 ± 0.001	1385.388 ± 0.002
a/R_★	${44.6}_{- 3.1}^{+ 2.6}$ ${44.6_{ - 3.1}^{ + 2.6}}$	${17.6}_{- 1.3}^{+ 1.1}$ ${17.6_{ - 1.3}^{ + 1.1}}$
α(AU)	0.0809 ± 0.0031	0.0322 ± 0.0013
R_p/R_★	0.0466 ± 0.0011	${0.0297}_{- 0.0017}^{+ 0.0016}$ ${0.0297_{ - 0.0017}^{ + 0.0016}}$
R_p (R_⊕)	${2.08}_{- 0.15}^{+ 0.16}$ $2.08_{ - 0.15}^{ + 0.16}$	1.32 ± 0.12
b	${0.43}_{- 0.20}^{+ 0.14}$ $0.43_{ - 0.20}^{ + 0.14}$	0.73 ± 0.06
i (deg)	${89.4}_{- 0.2}^{+ 0.3}$ $89.4_{ - 0.2}^{ + 0.3}$	${87.6}_{- 0.4}^{+ 0.3}$ $87.6_{ - 0.4}^{ + 0.3}$
T₁₄ (h)	${2.17}_{- 0.06}^{+ 0.07}$ $2.17_{ - 0.06}^{ + 0.07}$	1.05 ± 0.05
e	${0.056}_{- 0.034}^{+ 0.035}$ ${0.056_{ - 0.034}^{ + 0.035}}$	${0.032}_{- 0.023}^{+ 0.037}$ ${0.032_{ - 0.023}^{ + 0.037}}$
ω (deg)	$169_{- 45}^{+ 41}$ ${169_{ - 45}^{ + 41}}$	$- 6_{- 118}^{+ 88}$ ${ - 6_{ - 118}^{ + 88}}$
K (m s⁻¹)	${3.25}_{- 0.38}^{+ 0.41}$ $3.25_{ - 0.38}^{ + 0.41}$	1.63 ± 0.12
M_p (M_⊕)	${6.57}_{- 0.90}^{+ 1.00}$ ${6.57_{ - 0.90}^{ + 1.00}}$	${2.08}_{- 0.22}^{+ 0.23}$ ${2.08_{ - 0.22}^{ + 0.23}}$
ρ_p (g cm⁻³)	4.1 ± 1.1	4.9 ± 1.4
$ρ / ρ_{\oplus, s}^{(b)}$ $\rho /\rho _{ \oplus ,s}^{(b)}$	0.42 ± 0.11	0.78 ± 0.22
S_p(S_⊕)	3.0 ± 0.5	19 ± 3
$T_{eq}^{(c)} (K)$ $T_{{\rm{eq}}}^{(c)}({\rm{K}})$	368 ± 14	584 ± 22
$ɡ_{p}^{(d)} (m s^{- 2})$ $_{\rm{p}}^{(d)}\left( {{\rm{m}}\,{{\rm{s}}^{ - 2}}} \right)$	15.0 ± 3.3	11.6 ± 1.4

Common parameters

ρ_★ (ρ_⊙)	${6.7}_{- 1.4}^{+ 1.3}$ $6.7_{ - 1.4}^{ + 1.3}$
u_1,TESS	0.15 ± 0.05
u_2,TESS	0.45 ± 0.05
u_1,i	0.20 ± 0.08
u_2,i	0.37 ± 0.09
u_1,g	0.24 ± 0.10
u_2,g	0.31 ± 0.10
$σ_{j, ESPRESSO}^{e} (m s^{- 1})$ ${\sigma _{{\rm{j}},{\rm{ESPRESSO}}}^{\rm{e}}\left( {{\rm{m}}\,{{\rm{s}}^{ - 1}}} \right)}$	${0.18}_{- 0.12}^{+ 0.16}$ ${0.18_{ - 0.12}^{ + 0.16}}$
$σ_{j, HARPS}^{e} (m s^{- 1})$ ${\sigma _{{\rm{j}},{\rm{HARPS}}}^{\rm{e}}\left( {{\rm{m}}\,{{\rm{s}}^{ - 1}}} \right)}$	${5.1}_{- 1.0}^{+ 1.1}$ ${5.1_{ - 1.0}^{ + 1.1}}$
$σ_{j, NIRPS}^{e} (m s^{- 1})$ $\sigma _{{\rm{j}},{\rm{NIRPS}}}^{\rm{e}}\left( {{\rm{m}}\,{{\rm{s}}^{ - 1}}} \right)$	3.4 ± 0.7
$γ_{ESPRESSO}^{f} (m s^{- 1})$ $\gamma _{{\rm{ESPRESSO }}}^{\rm{f}}\left( {{\rm{m}}\,{{\rm{s}}^{ - 1}}} \right)\quad$	$- {1.8}_{- 5.0}^{+ 5.8}$ $- 1.8_{ - 5.0}^{ + 5.8}$
$γ_{HARPS}^{f} (m s^{- 1})$ $\gamma _{{\rm{HARPS }}}^{\rm{f}}\left( {{\rm{m}}{{\rm{s}}^{ - 1}}} \right)$	14737 ± 3
$γ_{NIRPS}^{f} (m s^{- 1})$ $\gamma _{{\rm{NIRPS }}}^{\rm{f}}\left( {{\rm{m}}{{\rm{s}}^{ - 1}}} \right)$	14977 ± 1
c₀ (m s⁻¹)	3275.50 (fixed)
c₁ (m s⁻¹ d⁻¹)	−0.041 ± 0.14
c₂ (m s⁻¹ d⁻¹)	0.0003 ± 0.0002

GP hyper-parameters

P_rot (d)	29.2 ± 0.5
P_dec (m s⁻¹)	$62_{- 3}^{+ 6}$ $62_{ - 3}^{ + 6}$
w (m s⁻¹)	${0.73}_{- 0.14}^{+ 0.16}$ $0.73_{ - 0.14}^{ + 0.16}$
$A_{ESPRESSO}^{g} (m s^{- 1})$ ${A_{{\rm{ESPRESSO }}}^{\rm{g}}\left( {{\rm{m}}\,{{\rm{s}}^{ - 1}}} \right)}$	${6.0}_{- 1.4}^{+ 2.0}$ ${6.0_{ - 1.4}^{ + 2.0}}$
$A_{FWHM}^{g} (m s^{- 1})$ ${A_{{\rm{FWHM}}}^{\rm{g}}\left( {{\rm{m}}\,{{\rm{s}}^{ - 1}}} \right)}$	${5.8}_{- 1.8}^{+ 2.6}$ ${5.8_{ - 1.8}^{ + 2.6}}$
$A_{HARPS}^{g} (m s^{- 1})$ ${A_{{\rm{HARPS }}}^{\rm{g}}\left( {{\rm{m}}\,{{\rm{s}}^{ - 1}}} \right)}$	${4.5}_{- 2.3}^{+ 2.9}$ ${4.5_{ - 2.3}^{ + 2.9}}$
$A_{NIRPS}^{g} (m s^{- 1})$ ${A_{{\rm{NIRPS }}}^{\rm{g}}\left( {{\rm{m}}\,{{\rm{s}}^{ - 1}}} \right)}$	${1.4}_{- 1.0}^{+ 2.0}$ ${1.4_{ - 1.0}^{ + 2.0}}$

Notes. Parameters were determined from the joint fit (Sect. 6.3) including all the available RV datasets. ^(a)TESS Barycentric Julian date (BJD−2457 000). ^(b)Scaled Earth’s bulk density (see Fig. 15). ^(c) $T_{eq} = T_{⋆} {(\frac{R_{⋆}}{2 a})}^{1 / 2} {[f (1 - A_{B})]}^{1 / 4}$ ${T_{{\rm{eq}}}} = {T_ \star }{\left( {{{{R_ \star }} \over {2a}}} \right)^{1/2}}{\left[ {f\left( {1 - {A_B}} \right)} \right]^{1/4}}$ , assuming f = 1 and a null Bond albedo (A_B = 0). ^(d)Planetary surface gravity. ^(e)RV jitter term. ^(f)RV offset term. ^(g)GP amplitude.

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