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Table 4

Inferred system parameters.

Parameter Units Prior Median and 68.3% CI Prior Median and 68.3% CI
Star
Stellar mass, m (M) N(0.885, 0.034) 0.892 ± 0.034
Stellar radius, R (RN)$\left( {R_ \odot ^{\rm{N}}} \right)$ N(0.845, 0.039) 0.824 ± 0.024
Stellar mean density, ρ (g cm−3) 1.59 ± 0.12
Surface gravity, log 𝑔 (cgs) 4.556 ± 0.024
K2 GP Prot (d) U(0.1, 100) 18.36 ± 0.51
Planets Planet b Planet b Planet c Planet c
Semi-major axis, a (au) 0.07487 ± 0.0009 0.0982 ± 0.0012
Eccentricity, e 0.04 ± 0.024 0.067 ± 0.017
Argument of pericenter, ω (°) 197 ± 26 252-+1181
Inclination, i (°) S (0, 180) 89. 7 ± 0.26 S (0, 90) 89.37 ± 0.15
Longitude of the ascending node, Ω (°) 180 (fixed at tref) U (90, 270) 180.84 ± 0.45
Mean anomaly, M0 (°) 257 ± 26 202+13−20
Mass ratio, mp/m U(0, 1) (10.357 ± 0.085)×10−5 U(0, 1) (3.746 ± 0.056)×10-5
Radius ratio, Rp/R U(0, 1) 0.07332 ± 0.00054 U(0, 1) 0.04321 ± 0.00044
Scaled semi-major axis, a/R 19.53 ± 0.51 25.61 ± 0.66
Impact parameter, b 0.217 ± 0.089 0.299 ± 0.065
T′0 - 2 450 000 (BJDTDB) U(5829, 7829) 6829.22231 ± 0.00016 U (5829, 7829) 6829.18490 ± 0.00054
P (d) U(5, 10) 7.922806 ± 0.000090 U(10, 15) 11.89770 ± 0.00046
K (m s−1) 10.66 ± 0.17 3.368 ± 0.063
Planet mass, mp (ME) 30.8 ± 1.3 11.12 ± 0.44
Planet radius, Rp (ReEN)$\left( {R_{e{\rm{E}}}^{\rm{N}}} \right)$ 6.59 ± 0.22 3.88 ± 0.14
Planet mean density, ρp (g cm−3) 0.590 ± 0.053 1 .046 ± 0.097
Planet surface gravity, log 𝑔p (cgs) 2.841 ± 0.028 2.859 ± 0.028
Equilibrium temperature, Teq (K) 857 ± 21 749 ± 19
Mutual inclination, Ib,c (°) 0.85 ± 0.44
eccosωcabacebcosωb${e_{\rm{c}}}\,\cos \,{\omega _{\rm{c}}} - {{{a_{\rm{b}}}} \over {{a_{\rm{c}}}}}{e_{\rm{b}}}\,\cos \,{\omega _{\rm{b}}}$ U(−1, 1) 0.00918 ± 0.00020
eccosωc+abacebcosωb${e_{\rm{c}}}\,\cos \,{\omega _{\rm{c}}} + {{{a_{\rm{b}}}} \over {{a_{\rm{c}}}}}{e_{\rm{b}}}\,\cos \,{\omega _{\rm{b}}}$ U(1, 1) −0.050 ± 0.040
ecsinωcabacebsinωb${e_{\rm{c}}}\,\sin \,{\omega _{\rm{c}}} - {{{a_{\rm{b}}}} \over {{a_{\rm{c}}}}}{e_{\rm{b}}}\,\sin \,{\omega _{\rm{b}}}$ U(1, 1) −0.05386 ± 0.00082
ecsinωc+abacebsinωb${e_{\rm{c}}}\,\sin \,{\omega _{\rm{c}}} + {{{a_{\rm{b}}}} \over {{a_{\rm{c}}}}}{e_{\rm{b}}}\,\sin \,{\omega _{\rm{b}}}$ U(1, 1) −0.071 ± 0.027
Planets Planet d Planet d Candidate planet e Candidate planet e
Semi-major axis, a (au) 0.03478 ± 0.00043 0.1387 ± 0.0017
Eccentricity, e <0.44 <0.15
Argument of pericenter, ω (°) 248110+72$248_{ - 110}^{ + 72}$ 245 ± 37
Inclination, i (°) S (0, 180) 89.7 ± 1.6 S (0, 180) 89.200.17+0.43$89.20_{ - 0.17}^{ + 0.43}$
Longitude of the ascending node, Ω (°) U(90, 270) 179.3 ± 7.3 U (90, 270) 179±10
Mean anomaly, M0 (°) 200 ± 100 152 ± 41
ecosω$\sqrt e \cos \,\omega $ U(1, 1) 0.02 ± 0.27 U(−1, 1) −0.08 ± 0.12
esinω$\sqrt e \sin \,\omega $ U(1, 1) 0.170.15+0.22$ - 0.17_{ - 0.15}^{ + 0.22}$ U(−1, 1) −0.174 ± 0.068
Mass ratio, mp/m U(0, 1) <2.1×10−5 † U(0, 1) <0.67×10−5 †
Radius ratio, Rp/R U(0, 1) 0.01165 ± 0.00066 U(0, 1) 0.0135 ± 0.0016
Scaled semi-major axis, a/R 9.07 ± 0.24 36.17 ± 0.94
Impact parameter, b 0.170.12+0.18$0.17_{ - 0.12}^{ + 0.18}$ 0.5440.15+0.099$0.544_{ - 0.15}^{ + 0.099}$
T'0 - 2 450 000 (BJDTDB) U(5829, 7829) 6828.9909 ± 0.0035 U (5829, 7829) 6832.2143 ± 0.0066
P (d) U(0, 5) 2.508270.00014+0.00027$2.50827_{ - 0.00014}^{ + 0.00027}$ U(15, 25) 19.9724 ± 0.0054
K (m s−1) <3.1 <0.51
Planet mass, mp (ME) <6.2 <2.0
Planet radius, Rp (ReEN)$\left( {R_{e{\rm{E}}}^{\rm{N}}} \right)$ 1.044 ± 0.064 1.22 ± 0.15
Planet mean density, ρp (g cm−3) <31 <8.4
Planet surface gravity, log 𝑔p (cgs) 2.95 ± 0.63 2.46 ± 0.40
Equilibrium temperature, Teq (K) 1258 ±31 630 ± 16

Notes. The table lists the prior, the posterior median, and the 68.3% CI for the photodynamical analysis (Sect. 4.2). The Jacobi orbital elements are given for the reference time tref = 2 456 829.222 BJDTDB. Upper limit at 99% confidence. The planetary equilibrium temperature is computed for zero albedo and full day-night heat redistribution. P′ and T0 should not be confused with the period or the time of conjunction, respectively, and they were only used to reduce the correlations between jump parameters, replacing the semimajor axis and the mean anomaly at tref. T0trefP2π(M0E+esinE)${T'_0} \equiv {t_{{\rm{ref}}}} - {{P'} \over {2\pi }}\left( {{M_0} - E + e\,\sin \,E} \right)$ with E=2arctan{ 1e1+etan[ 12(π2ω) ] },   P4π2a3Gm,    Kmpsinim2/31+e2(2πGP)1/3$E = 2\,\arctan \left\{ {\sqrt {{{1 - e} \over {1 + e}}\tan \left[ {{1 \over 2}\left( {{\pi \over 2} - \omega } \right)} \right]} } \right\},\,\,\,P' \equiv \sqrt {{{4{\pi ^2}{a^3}} \over {G{m_ \star }}}} ,\,\,\,\,K' \equiv {{{m_p}\sin \,i} \over {m_ \star ^{2/3}\sqrt {1 + {e^2}} }}{\left( {{{2\pi G} \over {P'}}} \right)^{1/3}}$. CODATA 2018: 𝒢 = 6.67430 ×10−11m3 kg−1 s−2. IAU 2012: au = 149 597 870 700 m. IAU 2015: RN=6.957×108 m, (GM)N=1.3271244×1020m3s2$R_ \odot ^{\rm{N}} = 6.957 \times {10^8}\,{\rm{m,}}\,\left( {GM} \right)_ \odot ^{\rm{N}} = 1.327\,1244 \times {10^{20}}\,{{\rm{m}}^3}\,{{\rm{s}}^{ - 2}}$, ReEN=6.378  1×106 m, (GM)EN=3.986004×1014m3s2,M=(GM)N/G,ME=(GM)EN/G,k2=(GM)N(86400 s)2/au3$R_{e{\rm{E}}}^{\rm{N}} = 6.378\,\,1 \times {10^6}\,{\rm{m,}}\,\left( {GM} \right)_{\rm{E}}^{\rm{N}} = 3.986\,004 \times {10^{14}}\,{{\rm{m}}^3}\,{{\rm{s}}^{ - 2}},\,{M_ \odot } = \left( {GM} \right)_ \odot ^{\rm{N}}/G,\,{{\rm{M}}_{\rm{E}}} = \left( {GM} \right)_{\rm{E}}^{\rm{N}}/G,\,{k^2} = \left( {GM} \right)_ \odot ^{\rm{N}}{\left( {86\,400\,{\rm{s}}} \right)^2}/{\rm{a}}{{\rm{u}}^3}$. N(µ, σ): Normal distribution with mean µ and standard deviation σ. U(a, b): A uniform distribution defined between a lower a and upper b limit. S (a, b): A sinusoidal distribution defined between a lower a and upper b limit. Transits occur when the sum of the true anomaly and the argument of pericenter equals −90°.

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