TRADES: A new software to derive orbital parameters from observed transit times and radial velocities - Revisiting Kepler-11 and Kepler-9

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Table 2

Parameters of the Kepler-11 system. Epoch of reference: 2 455 190.0 (BJD_UTC).

Parameter	Lis2011^a	K11-I^b	K11-II^c	Lis2013^d	K11-III^e


M_b [ M_⊕ ]	5.06 ± 0.95
R_b [ R_⊕ ]	1.97 ± 0.19
P_b [ days ]	10.3045 ± 0.0003
e _b	0
ω_b [° ]	90
M_b [° ]	73.467 ± 0.003			–
i_b [° ]


M_c [ M_⊕ ]	15.82 ± 2.21
R_c [ R_⊕ ]	3.15 ± 0.30
P_c [ days ]	13.0247 ± 0.0003
e _c	0
ω_c [° ]	90
M_c [° ]	288.267 ± 0.005			–
i_c [° ]


M_d [ M_⊕ ]	5.69 ± 1.27
R_d [ R_⊕ ]	3.43 ± 0.32
P_d [ days ]	22.6849 ± 0.0007
e _d	0
ω_d [° ]	90
M_d [° ]	69.245 ± 0.002			–
i_d [° ]


M_e [ M_⊕ ]	8.22 ± 1.58
R_e [ R_⊕ ]	4.52 ± 0.43
P_e [ days ]	32.0001 ± 0.0008
e _e	0
ω_e [° ]	90
M_e [° ]	122.211 ± 0.003			–
i_e [° ]


M_f [ M_⊕ ]	1.90 ± 0.95
R_f [ R_⊕ ]	2.61 ± 0.25
P_f [ days ]	46.6908 ± 0.0010
e _f	0
ω_f [° ]	90
M_f [° ]	297.667 ± 0.006			–
i_f [° ]


M_g [ M_⊕ ]	< 300			< 25
R_g [ R_⊕ ]	3.66 ± 0.35
P_g [ days ]	118.3808 ± 0.0025
e _g	0			< 0.15
ω_g [° ]	90
M_g [° ]	211.997 ± 0.005			–
i_g [° ]


χ²/ dof	110.34 / 89	110.15 / 88	110.74 / 76		341.75 / 190
	1.24	1.25	1.46		1.80

Notes. Masses (M), periods (P), eccentricities (e), argument of pericenters (ω), and mean anomaly (M) of the best-fit simulation with 2σ confidence intervals from bootstrap analysis and ± 1σ from LM. Inclinations (i) fixed to the Lis2011 model.

^(a)

Dynamical model as reported in Lissauer et al. (2011a, SI) with circular orbit for each planet, e fixed to 0, and ω fixed to 90° (ecosω and esinω set to zero in the discovery paper).

^(b)

Orbital solution from the analysis of T₀s from Lissauer et al. (2011a) for the first three quarters of Kepler data. Parameters fitted: M, P, and M. e fixed to 0 and ω fixed to 90°.

^(c)

Orbital solution from the analysis of T₀s from Lissauer et al. (2011a) for the first three quarters of Kepler data. Parameters fitted: M, P, e, ω, and M.

^(d)

Dynamical model from (Lissauer et al. 2013). Parameters determined from the analysis of 14 quarters of Kepler data. The values of the mean anomaly were not reported in the paper (neither the time of passage at the pericenter).

^(e)

Best orbital solution (simulation number 9) of Fig. 6 from the analysis of T₀s from Mazeh et al. (2013) for the first 12 quarters of Kepler data. Parameters fitted: M, P, e, ω, and M.

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