Giant Outer Transiting Exoplanet Mass (GOT’EM) survey - VII. TOI-6041: A multi-planet system including a warm Neptune exhibiting strong transit-timing variations

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Table 4

Median values and 68% confidence intervals for TOI-6041 and its two planets.

Parameter	Description	Model Priors	Value
Stellar parameters
M_*…. ….	Mass (M_⨀)……………..	—	${0.885}_{- 0.036}^{+ 0.042}$ $Mathematical equation: $0.885_{ - 0.036}^{ + 0.042}$$
R_*……..	Radius (R_⨀)…………..	—	0.879 ± 0.026
L_*………….	Luminosity (L_⨀)………….	—	0.613 ± 0.033
F_Bol	Bolometric flux (cgs)…………..		3.73 ± 0.20 × 10⁻⁹
ρ_*……..	Density (cgs)………	—	${1.84}_{- 0.17}^{+ 0.19}$ $Mathematical equation: $1.84_{ - 0.17}^{ + 0.19}$$
log g……….	Surface gravity (cgs)……….	—	${4.498}_{- 0.030}^{+ 0.031}$ $Mathematical equation: $4.498_{ - 0.030}^{ + 0.031}$$
T_eff……….	Effective temperature (K)………	—	$5445_{- 96}^{+ 97}$ $Mathematical equation: $5445_{ - 96}^{ + 97}$$
[Fe/H]……….	Metallicity (dex)………….	𝒩[0.02, 0.08]	${0.104}_{- 0.068}^{+ 0.069}$ $Mathematical equation: $0.104_{ - 0.068}^{ + 0.069}$$
[Fe/H]₀……..	Initial metallicity¹ …………..	—	${0.111}_{- 0.067}^{+ 0.069}$ $Mathematical equation: $0.111_{ - 0.067}^{ + 0.069}$$
Age………	Age (Gyr)…………	—	${7.9}_{- 3.9}^{+ 3.7}$ $Mathematical equation: $7.9_{ - 3.9}^{ + 3.7}$$
EEP……….	Equal evolutionary phase³ …………	—	$359_{- 21}^{+ 27}$ $Mathematical equation: $359_{ - 21}^{ + 27}$$
A_V…………	V-band extinction (mag)…………..	𝒰[0.01, 0.74]	${0.260}_{- 0.070}^{+ 0.062}$ $Mathematical equation: $0.260_{ - 0.070}^{ + 0.062}$$
σ_SED…………	SED photometry error scaling……	—	${0.36}_{- 0.10}^{+ 0.17}$ $Mathematical equation: $0.36_{ - 0.10}^{ + 0.17}$$
ϖ……….	Parallax (mas)……….	𝒩[13.79, 0.02]	13.794 ± 0.020
d……….	Distance (pc)…………..	—	72.49 ± 0.10
Planetary Parameters:			TOI-6041 b	TOI-6041 c
P…………	Period (d)………….	—	${26.04945}_{- 0.00034}^{+ 0.00033}$ $Mathematical equation: $26.04945_{ - 0.00034}^{ + 0.00033}$$	${88.0}_{- 1.3}^{+ 1.6}$ $Mathematical equation: $88.0_{ - 1.3}^{ + 1.6}$$
R_P……………	Radius (R_⨁)………..	—	${4.55}_{- 0.17}^{+ 0.18}$ $Mathematical equation: $4.55_{ - 0.17}^{ + 0.18}$$	—
M_p………….	Mass (M_⨁)………..	—	10.81 ± 6.36 (<28.9²)	—
T_C…………	Observed time of conjunction⁴ ((BJD_TDB)	—	${2459890.1062}_{- 0.0085}^{+ 0.0086}$ $Mathematical equation: $2459890.1062_{ - 0.0085}^{ + 0.0086}$$	—
a……….	Semi-major axis (AU)………..	—	${0.1651}_{- 0.0022}^{+ 0.0026}$ $Mathematical equation: $0.1651_{ - 0.0022}^{ + 0.0026}$$	${0.3721}_{- 0.0063}^{+ 0.0067}$ $Mathematical equation: $0.3721_{ - 0.0063}^{ + 0.0067}$$
i………….	Inclination (degrees)…………	—	${88.955}_{- 0.062}^{+ 0.063}$ $Mathematical equation: $88.955_{ - 0.062}^{ + 0.063}$$	90.00 (fixed)
${\dot{ω}}_{GR}$ $Mathematical equation: ${{\dot \omega }_{{\rm{GR}}}}$$ ……….	Computed GR precession (°/century). .	—	${0.0801}_{- 0.0022}^{+ 0.0025}$ $Mathematical equation: $0.0801_{ - 0.0022}^{ + 0.0025}$$	${0.01054}_{- 0.00039}^{+ 0.00041}$ $Mathematical equation: $0.01054_{ - 0.00039}^{ + 0.00041}$$
T_eq………..	Equilibrium temp⁵ (K)……….	—	${605.6}_{- 8.3}^{+ 8.4}$ $Mathematical equation: $605.6_{ - 8.3}^{ + 8.4}$$	403.5 ± 5.9
τ_circ…….	Tidal circ timescale (Gyr)……….	—	$11500_{- 6800}^{+ 7800}$ $Mathematical equation: $11500_{ - 6800}^{ + 7800}$$	${2.7}_{- 1.4}^{+ 3.5} \times 10^{5}$ $Mathematical equation: $2.7_{ - 1.4}^{ + 3.5} \times {10^5}$$
K………	RV semi-amplitude (m/s)……….	—	2.5 ± 1.5 (<6.7²)	12.1 ± 1.4
R_P / R_*……….	Radius of planet in stellar radii………	—	${0.04753}_{- 0.00057}^{+ 0.00058}$ $Mathematical equation: $0.04753_{ - 0.00057}^{ + 0.00058}$$	—
a / R_*………	Semi-major axis in stellar radii………	—	40.4 ± 1.3	—
δ	(R_P/R_*)²…………….	—	${0.002259}_{- 0.000054}^{+ 0.000056}$ $Mathematical equation: $0.002259_{ - 0.000054}^{ + 0.000056}$$	—
δ_CHEOPS ……….	Transit depth in CHEOPS (frac)………	—	${0.002360}_{- 0.000039}^{+ 0.000040}$ $Mathematical equation: $0.002360_{ - 0.000039}^{ + 0.000040}$$	—
δ_TESS ………	Transit depth in TESS (frac)…………	—	0.002321 ± 0.000038	—
τ…………	In/egress transit duration (d)…………	—	0.0145 ± 0.0011	—
T₁₄………	Total transit duration (d)…………	—	0.1526 ± 0.0013	—
T_FWHM………	FWHM transit duration (d)…………	—	0.1381 ± 0.0011	—
b……….	Transit impact parameter …………..		${0.738}_{- 0.022}^{+ 0.020}$ $Mathematical equation: $0.738_{ - 0.022}^{ + 0.020}$$	—
δ_{S,2.5 μm}……..	BB eclipse depth at 2.5 μm (ppm)….	—	${0.317}_{- 0.039}^{+ 0.043}$ $Mathematical equation: $0.317_{ - 0.039}^{ + 0.043}$$	—
δ_{S,5.0 μm}……	BB eclipse depth at 5.0 μm (ppm)….	—	${13.71}_{- 0.96}^{+ 1.0}$ $Mathematical equation: $13.71_{ - 0.96}^{ + 1.0}$$	—
δ_{S,7.5 μm}……	BB eclipse depth at 7.5 μm (ppm) ….	—	${41.9}_{- 2.3}^{+ 2.4}$ $Mathematical equation: $41.9_{ - 2.3}^{ + 2.4}$$	—
ρ_P………	Density (cgs)…………	—	${0.62}_{- 0.36}^{+ 0.39} (< {1.79}^{2})$ $Mathematical equation: $0.62_{ - 0.36}^{ + 0.39}( < {1.79^2})$$	—
logg_P………….	Surface gravity (cgs)………..	—	${2.72}_{- 0.32}^{+ 0.20}$ $Mathematical equation: $2.72_{ - 0.32}^{ + 0.20}$$	${2.85}_{- 0.12}^{+ 0.14}$ $Mathematical equation: $2.85_{ - 0.12}^{ + 0.14}$$
Θ………	Safronov Number…………	—	0.031 ± 0.018	${0.221}_{- 0.030}^{+ 0.040}$ $Mathematical equation: $0.221_{ - 0.030}^{ + 0.040}$$
〈F〉………	Incident Flux (10⁹ erg s−¹ cm ²)………	—	${0.0305}_{- 0.0016}^{+ 0.0017}$ $Mathematical equation: $0.0305_{ - 0.0016}^{ + 0.0017}$$	${0.00601}_{- 0.00034}^{+ 0.00036}$ $Mathematical equation: $0.00601_{ - 0.00034}^{ + 0.00036}$$
T_S……….	Observed Time of eclipse⁴ (BJD_TDB) . .	—	${2459903.1291}_{- 0.0085}^{+ 0.0086}$ $Mathematical equation: $2459903.1291_{ - 0.0085}^{ + 0.0086}$$	—
T_P………	Time of periastron (TJD_TDB)…..	—	${2459890.1053}_{- 0.0085}^{+ 0.0086}$ $Mathematical equation: $2459890.1053_{ - 0.0085}^{ + 0.0086}$$	$2 ._{458774}^{- 0.000013} \times 10^{6}$ $Mathematical equation: ${\rm{2}}{\rm{.458774}}_{ - {\rm{0}}{\rm{.000013}}}^{ + {\rm{0}}{\rm{.000010}}} \times {10^6}$$
T_A………..	Time of asc node (TJD_TDB)………	—	${2459909.6424}_{- 0.0085}^{+ 0.0086}$ $Mathematical equation: $2459909.6424_{ - 0.0085}^{ + 0.0086}$$	${2458839.6}_{- 12}^{+ 9.1}$ $Mathematical equation: $2458839.6_{ - 12}^{ + 9.1}$$
T_D………	Time of desc node (TJD_TDB)……….	—	${2459896.6176}_{- 0.0085}^{+ 0.0086}$ $Mathematical equation: $2459896.6176_{ - 0.0085}^{ + 0.0086}$$	${2458795.6}_{- 12}^{+ 9.8}$ $Mathematical equation: $2458795.6_{ - 12}^{ + 9.8}$$
M_P sin i……….	Minimum mass (M_⨁)………	—	10.81 ± 6.36 (<28.9²)	${77.9}_{- 8.9}^{+ 9.2}$ $Mathematical equation: $77.9_{ - 8.9}^{ + 9.2}$$
d / R_*……..	Separation at mid transit………	—	40.4 ± 1.3	—
P_T………	A priori non-grazing transit prob ….	—	${0.02356}_{- 0.00073}^{+ 0.00074}$ $Mathematical equation: $0.02356_{ - 0.00073}^{ + 0.00074}$$	—

Notes.¹ The metallicity of the star at birth;² the 3σ upper limits³ corresponding to static points in a star’s evolutionary history (see Sect. 2 in Dotter 2016);⁴ reference epoch = 2456438.359500,⁵ assuming no albedo and perfect redistribution.

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