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Table 2

Derived parameters of TOI-2431 b from a joint analysis of available transit and RV data.

Parameter Description Prior distribution Posterior distribution (FCO fit, adopted) Posterior distribution (GP fit)
MCMC input parameters:
P (days) Orbital period 𝒩(0.224195, 4 × 10−7) 0.22419578−5×10−8+5×10−8Mathematical equation: $\[0.22419578_{-5 \times 10^{-8}}^{+5 \times 10^{-8}}\]$ 0.22419578−5×10−8+5×10−8Mathematical equation: $\[0.22419578_{-5 \times 10^{-8}}^{+5 \times 10^{-8}}\]$
T0 (BJD) Time of transit (BJD - 2460000) 𝒩(258.8689, 4.6 × 10−4) 258.86855−0.00015+0.00016Mathematical equation: $\[258.86855_{-0.00015}^{+0.00016}\]$ 258.86855−0.00015+0.00016Mathematical equation: $\[258.86855_{-0.00015}^{+0.00016}\]$
e Eccentricity 0 (Adopted) 0 (Adopted) 0 (Adopted)
ω (deg) Argument of periapsis 90 (Adopted) 90 (Adopted) 90 (Adopted)
b Impact parameter 𝒰(0, 1) 0.573−0.033+0.031Mathematical equation: $\[0.573_{-0.033}^{+0.031}\]$ 0.572−0.035+0.033Mathematical equation: $\[0.572_{-0.035}^{+0.033}\]$
K (m s−1) RV semi-amplitude 𝒰(0, 1000) 8.2−2.1+2.1Mathematical equation: $\[8.2_{-2.1}^{+2.1}\]$ 6.8−2.0+2.1Mathematical equation: $\[6.8_{-2.0}^{+2.1}\]$
Rp/R* Radius ratio 𝒰(0, 1) 0.02131−0.00032+0.00033Mathematical equation: $\[0.02131_{-0.00032}^{+0.00033}\]$ 0.02128−0.00032+0.00036Mathematical equation: $\[0.02128_{-0.00032}^{+0.00036}\]$
ρ* (g cm−3) Density of star 𝒩(3.23, 0.18) 3.25−0.18+0.18Mathematical equation: $\[3.25_{-0.18}^{+0.18}\]$ 3.24−0.18+0.18Mathematical equation: $\[3.24_{-0.18}^{+0.18}\]$
q1 TESS limb darkening coefficient 𝒰(0, 1) 0.56−0.18+0.22Mathematical equation: $\[0.56_{-0.18}^{+0.22}\]$ 0.59−0.19+0.23Mathematical equation: $\[0.59_{-0.19}^{+0.23}\]$
q2 TESS limb darkening coefficient 𝒰(0, 1) 0.24−0.16+0.27Mathematical equation: $\[0.24_{-0.16}^{+0.27}\]$ 0.23−0.16+0.26Mathematical equation: $\[0.23_{-0.16}^{+0.26}\]$
mdilution, TESS Dilution factor of TESS 1 (Adopted) 1 (Adopted) 1 (Adopted)
mflux, TESS Offset relative flux 𝒩(0.0, 0.1) −0.000057−0.000031+0.000032Mathematical equation: $\[-0.000057_{-0.000031}^{+0.000032}\]$ −0.00006−0.00003+0.00003Mathematical equation: $\[-0.00006_{-0.00003}^{+0.00003}\]$
GPσ, TESS (ppm) Amplitude of the TESS GP ℒ(10−6, 106) 0.00027−0.000017+0.000020Mathematical equation: $\[0.00027_{-0.000017}^{+0.000020}\]$ 0.00027−0.000017+0.000019Mathematical equation: $\[0.00027_{-0.000017}^{+0.000019}\]$
GPρ, TESS (days) Length-scale of the Matern kernel ℒ(10−6, 106) 0.68−0.073+0.087Mathematical equation: $\[0.68_{-0.073}^{+0.087}\]$ 0.68−0.078+0.084Mathematical equation: $\[0.68_{-0.078}^{+0.084}\]$
σTESS (ppm) Light curve jitter ℒ(10−6, 106) 177−10+9.8Mathematical equation: $\[177_{-10}^{+9.8}\]$ 176−10+9.8Mathematical equation: $\[176_{-10}^{+9.8}\]$
B (m s−1)2 Amplitude of the RV GP ℒ(10−6, 106) − 137−65+179Mathematical equation: $\[137_{-65}^{+179}\]$
C Constant scaling term of the RV GP ℒ(10−6, 106) − 0.40−0.40+7620Mathematical equation: $\[0.40_{-0.40}^{+7620}\]$
L (days) Char. timescale of the RV GP ℒ(10−3, 103) − 1.6−1.3+6.8Mathematical equation: $\[1.6_{-1.3}^{+6.8}\]$
PGP (days) Period of the quasi-periodic RV GP 𝒰(1, 100) − 47−31+35Mathematical equation: $\[47_{-31}^{+35}\]$
vγ, obs. log (m s−1) Systematic velocity (NEID, GP) 𝒰(−50, 50) − −2.7−5.5+5.4Mathematical equation: $\[-2.7_{-5.5}^{+5.4}\]$
vγ, HPF (m s−1) Systematic velocity (HPF, GP) 𝒰(−50, 50) − 1.3−9.5+8.9Mathematical equation: $\[1.3_{-9.5}^{+8.9}\]$
vγ, 1 (m s−1) Systematic velocity (NEID 1) 𝒰(−50, 50) −17−3.4+3.3Mathematical equation: $\[-17_{-3.4}^{+3.3}\]$ −
vγ, 2 (m s−1) Systematic velocity (NEID 2) 𝒰(−50, 50) −2.6−4.0+3.8Mathematical equation: $\[-2.6_{-4.0}^{+3.8}\]$ −
vγ, 3 (m s−1) Systematic velocity (NEID 3) 𝒰(−50, 50) −8.6−2.5+2.6Mathematical equation: $\[-8.6_{-2.5}^{+2.6}\]$ −
σRV, NEID (m s−1) RV jitter (NEID, GP) ℒ(10−6, 106) − 0.0047−0.0046+0.63Mathematical equation: $\[0.0047_{-0.0046}^{+0.63}\]$
σRV, HPF (m s−1) RV jitter (HPF, GP) ℒ(10−6, 106) − 0.0069−0.0069+2.2Mathematical equation: $\[0.0069_{-0.0069}^{+2.2}\]$
σRV, 1 (m s−1) RV jitter (NEID 1) 𝒰(0.001, 10) 3.7−2.6+3.6Mathematical equation: $\[3.7_{-2.6}^{+3.6}\]$ 0 (Adopted)
σRV, 2 (m s−1) RV jitter (NEID 2) 𝒰(0.001, 10) 4.2−2.9+3.6Mathematical equation: $\[4.2_{-2.9}^{+3.6}\]$ 0 (Adopted)
σRV, 3 (m s−1) RV jitter (NEID 3) 𝒰(0.001, 10) 2.9−2.0+3.2Mathematical equation: $\[2.9_{-2.0}^{+3.2}\]$ 0 (Adopted)
Derived parameters:
Mp (M⊕) Planet mass − 6.2−1.6+1.6Mathematical equation: $\[6.2_{-1.6}^{+1.6}\]$ 5.1−1.5+1.6Mathematical equation: $\[5.1_{-1.5}^{+1.6}\]$
Rp (R⊕) Planet radius − 1.534−0.033+0.034Mathematical equation: $\[1.534_{-0.033}^{+0.034}\]$ 1.533−0.033+0.034Mathematical equation: $\[1.533_{-0.033}^{+0.034}\]$
ρp (g cm−3) Planet density − 9.4−2.5+2.5Mathematical equation: $\[9.4_{-2.5}^{+2.5}\]$ 7.8−2.4+2.5Mathematical equation: $\[7.8_{-2.4}^{+2.5}\]$
i (deg) Inclination − 74−0.96+1.01Mathematical equation: $\[74_{-0.96}^{+1.01}\]$ 74−1.0+1.1Mathematical equation: $\[74_{-1.0}^{+1.1}\]$
a (AU) Semimajor axis − 0.0063−0.0001+0.0001Mathematical equation: $\[0.0063_{-0.0001}^{+0.0001}\]$ 0.0063−0.0001+0.0001Mathematical equation: $\[0.0063_{-0.0001}^{+0.0001}\]$
ESM ESM − 27 27
Teq, a = 0 (K) Equilibrium temp. (AB = 0) − 2063−30+30Mathematical equation: $\[2063_{-30}^{+30}\]$ 2063−30+30Mathematical equation: $\[2063_{-30}^{+30}\]$
Teq, a = 0.3 (K) Equilibrium temp. (AB = 0.3) − 1887−28+28Mathematical equation: $\[1887_{-28}^{+28}\]$ 1887−28+28Mathematical equation: $\[1887_{-28}^{+28}\]$

Notes. 𝒩(μ, σ) denotes a normal prior with mean (μ) and standard deviation (σ), 𝒰(a, b) denotes a uniform prior with a start value (a) and an end value (b), and ℒ(a, b) denotes a log-uniform prior with a start value (a) and an end value (b). The posteriors from the FCO fit and the GP fit are consistent.

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