Absolute densities, masses, and radii of the WASP-47 system determined dynamically

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Volume 595 (November 2016)

A&A, 595 (2016) L5

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Table A.1

Inferred system parameters.

Parameter		MAP	95% HDI	Median	Stellar models
				and 68.3% CI	median and 68.3% CI

Star
Stellar mass, M_⋆	[M_⊙]	1.0174	[0.242, 3.126]	1.11	1.029 ± 0.031
Stellar radius, R_⋆^•	[]	1.1299	[0.804, 1.698]	1.16 ± 0.26	1.132 ± 0.012
Stellar mean density, ρ_⋆^•	[gcm^-3]	0.9943	[0.9713, 1.0259]	0.999 ± 0.015
Surface gravity, log g	[cgs]	4.33946	[4.2069, 4.5192]	4.354 ± 0.084	4.3428 ± 0.0058
q₁^†,• K2		0.3864	[0.3585, 0.4179]	0.387 ± 0.015
q₂^†,• K2		0.4279	[0.3984, 0.4642]	0.430 ± 0.016
Linear limb darkening, u_a K2		0.5319	[0.51646, 0.55534]	0.535 ± 0.010
Quadratic darkening, u_b K2		0.0897	[0.0455, 0.1333]	0.087 ± 0.021
q₁^†,• EulerCam		0.2929	[0.1912, 0.3903]	0.282 ± 0.052
q₂^†,• EulerCam		0.643	[0.427, 0.885]	0.64 ± 0.13
u_a EulerCam		0.6957	[0.5398, 0.8123]	0.682 ± 0.067
u_b EulerCam		–0.154	[–0.383, 0.067]	–0.15 ± 0.11
Planet b
Semi-major axis, a	[au]	0.050918	[0.03631, 0.07665]	0.052 ± 0.011	0.05111 ± 0.00051
Eccentricity, e		0.00380	[0.00000, 0.01052]	0.0028
Inclination, i^•	[°]	88.927	[88.734, 89.403]	89.02 ± 0.17
Argument of pericentre, ω	[°]	3.747	[–131.20, 171.20]	30 ± 79
Longitude of the ascending node, Ω	[°]	180^∗
Mean anomaly, M₀	[°]	144.870	[–16.80, 285.60]	118 ± 78
^•		0.0615	[–0.0439, 0.0946]	0.028 ± 0.037
^•		0.0040	[–0.0543, 0.0916]	0.018 ± 0.042
Radius ratio, R_p/R_⋆^•		0.102036	[0.101564, 0.102303]	0.10193 ± 0.00018
Mass ratio, M_p/M_⋆^•		0.0010609	[0.000667, 0.001416]	0.00104 ± 0.00024	0.001061 ± 1.7 × 10^-5
Scaled semi-major axis, a/R_⋆		9.6901	[9.6125, 9.7899]	9.705 ± 0.047
^•–2450000	[BJD_TDB]	6982.978187	[6982.977745, 6982.978868]	6982.97823 ± 0.00032	6982.97826 ± 0.00016
P ′ ^•	[d]	4.160666	[4.160061, 4.161365]	4.16071 ± 0.00038	4.16075 ± 0.00016
K ′	[m s^-1]	141.22	[138.43, 145.19]	142.0 ± 1.7
Planet mass, M_p	[M_E]	359.37	[174.61, 769.82]	383	363.8 ± 8.6
	[M_J]	1.1307	[0.549, 2.422]	1.21	1.145 ± 0.027
Planet radius, R_p	[]	12.576	[8.95, 18.91]	12.9 ± 2.8	12.59 ± 0.14
	[]	1.1219	[0.798, 1.687]	1.15 ± 0.25	1.123 ± 0.013
Planet mean density, ρ_p	[gcm^-3]	0.9929	[0.627, 1.376]	0.98 ± 0.21	1.001 ± 0.023
Planet surface gravity, log g_p	[cgs]	3.34763	[3.33826, 3.36825]	3.3522 ± 0.0071
Planet c
Semi-major axis, a	[au]	1.3694	[0.973, 2.060]	1.41 ± 0.30	1.375 ± 0.019
Eccentricity, e		0.366	[0.115, 0.575]	0.36 ± 0.12
Inclination, i^•	[°]	72.829	[21.93, 151.28]	87 ± 45
Argument of pericentre, ω	[°]	141.946	[72.04, 172.82]	136 ± 20
Longitude of the ascending node, Ω^•	[°]	167.77	[0, 360]	[0, 360]
Mean anomaly, M₀	[°]	222.333	[201.60, 288.00]	229 ± 15
^•		–0.4767	[–0.669, 0.052]	–0.41
^•		0.373	[0.063, 0.645]	0.40 ± 0.14
Mass ratio, M_p/M_⋆^•		0.001375	[0.000565, 0.002547]	0.00133
Scaled semi-major axis, a/R_⋆		260.60	[258.94, 263.72]	261.4 ± 1.3
^•–2450000	[BJD_TDB]	7162.464	[7118.25, 7182.95]	7156 ± 18
P ′ ^•	[d]	580.289	[561.83, 594.05]	580.7 ± 9.6
K ′	[m s^-1]	36.241	[18.84, 43.52]	29.4 ± 6.1
Planet mass, M_p	[M_E]	465.688	[101.22, 1116.23]	500	470
	[M_J]	1.465	[0.318, 3.512]	1.57	1.47
M_psini	[M_E]	444.932	[150.95, 845.06]	380	361
	[M_J]	1.3999	[0.475, 2.659]	1.21	1.13
Planet d
Semi-major axis, a	[au]	0.085769	[0.0613, 0.1289]	0.088 ± 0.019	0.08609 ± 0.00087
Eccentricity, e		0.00752	[0.00000, 0.02388]	0.0060
Inclination, i^•	[°]	90.839	[88.965, 89.515]^†	89.22 ± 0.13^†
Argument of pericentre, ω	[°]	4.655	[–116.80, 185.60]	27 ± 89
Longitude of the ascending node, Ω^•	[°]	178.736	[174.12, 188.44]	181.4 ± 4.1
Mean anomaly, M₀	[°]	93.201	[–81.20, 221.19]	68 ± 87
^•		0.0865	[–0.0683, 0.1511]	0.033 ± 0.065
^•		0.0070	[–0.0987, 0.1331]	0.020 ± 0.066
Radius ratio, R_p/R_⋆^•		0.029264	[0.029004, 0.029622]	0.02931 ± 0.00015
Mass ratio, M_p/M_⋆^•		4.564 × 10^-5	[3.792, 5.280] × 10^-5	(4.54 ± 0.38) × 10^-5
Scaled semi-major axis, a/R_⋆		16.3223	[16.1715, 16.4699]	16.327 ± 0.079
^•–2450000	[BJD_TDB]	6988.37565	[6988.3527, 6988.3993]	6988.375 ± 0.014	6988.3770 ± 0.0015
P ′ ^•	[d]	9.09585	[9.0740, 9.1215]	9.095 ± 0.014	9.0961 ± 0.0012
K ′	[m s^-1]	4.681	[3.434, 6.300]	4.77 ± 0.81	4.71 ± 0.31
Planet mass, M_p	[M_E]	15.46	[3.99, 44.34]	16.8	15.7 ± 1.1
Planet radius, R_p	[]	3.6067	[2.565, 5.470]	3.71 ± 0.82	3.619 ± 0.044
Planet mean density, ρ_p	[gcm^-3]	1.811	[1.490, 2.097]	1.80 ± 0.16
Planet surface gravity, log g_p	[cgs]	3.0661	[2.9480, 3.1967]	3.074 ± 0.067	3.068 ± 0.030
Planet e
Semi-major axis, a	[au]	0.016816	[0.01199, 0.02532]	0.0173 ± 0.0038	0.01688 ± 0.00017
Eccentricity, e		0.0160	[0.0000, 0.1176]	0.030
Inclination, i^•	[°]	91.82	[83.15, 97.56]	86.2 ± 2.1^†
Argument of pericentre, ω	[°]	84.92	[0, 360]	160 ± 140
Longitude of the ascending node, Ω^•	[°]	193.34	[120.60, 233.53]	187 ± 33
Mean anomaly, M₀	[°]	244.10	[0, 360]	190 ± 120
^•		0.011	[–0.282, 0.306]	–0.02 ± 0.18
^•		0.1260	[–0.2911, 0.1952]	0.034
Radius ratio, R_p/R_⋆^•		0.014328	[0.014066, 0.014774]	0.01439 ± 0.00016
Mass ratio, M_p/M_⋆^•		3.026 × 10^-5	[0.975, 4.591] × 10^-5	(2.54 ± 0.93) × 10^-5
Scaled semi-major axis, a/R_⋆		3.2001	[3.1748, 3.2334]	3.205 ± 0.015
^•–2450000	[BJD_TDB]	6979.765020	[6979.763101, 6979.765758]	6979.76455 ± 0.00094
P ′ ^•	[d]	0.7896264	[0.7895968, 0.7896653]	0.789636 ± 1.7 × 10^-5
K ′	[m s^-1]	7.01	[2.21, 9.32]	6.1 ± 1.9
Planet mass, M_p	[M_E]	10.25	[1.77, 22.70]	9.1	9.1
Planet radius, R_p	[]	1.7659	[1.256, 2.692]	1.82 ± 0.40	1.778 ± 0.031
Planet mean density, ρ_p	[gcm^-3]	10.23	[3.39, 15.98]	8.5 ± 3.2	8.8 ± 2.7
Planet surface gravity, log g_p	[cgs]	3.508	[3.026, 3.695]	3.45
Data
K2 jitter^•		0.89868	[0.89319, 0.90644]	0.8997 ± 0.0034
EulerCam jitter^•		0.8931	[0.8449, 1.0135]	0.934 ± 0.040
CORALIE 2012 jitter^•		1.093	[0.736, 1.597]	1.09 ± 0.25
CORALIE 2016a jitter^•		0.828	[0.711, 1.405]	1.03 ± 0.19
CORALIE 2016b jitter^•		0.372	[0.216, 1.438]	0.57
PFS jitter^•		2.242	[1.605, 3.153]	2.31 ± 0.39
CORALIE 2012 offset^•	[km s^-1]	27.07055	[27.05995, 27.08424]	27.0711 ± 0.0068
CORALIE 2016a offset^•	[km s^-1]	27.08882	[27.07833, 27.09232]	27.0852 ± 0.0037
CORALIE 2016b offset^•	[km s^-1]	27.05459	[27.04380, 27.07814]	27.0612 ± 0.0078
PFS offset^•	[km s^-1]	–0.02253	[–0.02696, 0.00107]	–0.0112 ± 0.0076

Notes. The table includes: MAP, 95% HDI, posterior median, and 68.3% CI for the model-free photodynamical analysis, and the latter for the precision-improved parameters using theoretical stellar models. The astrocentric orbital elements are given for the reference time t_ref = 2456979.5 BJD_TDB. with , , . CODATA 2014: = 6.674 08 × 10^-11m³kg^-1s^-2. IAU 2012: au = 149 597 870 700 m. IAU 2015: = 6.957 × 10⁸ m, = 1.327 124 4 × 10²⁰m³s^-2, = 6.378 1 × 10⁶ m, = 3.986 004 × 10¹⁴m³s^-2, = 7.149 2 × 10⁷ m, = 1.266 865 3 × 10¹⁷m³s^-2. M_⊙ = /, M_E = /, M_J = /, k² = (86400 s)²/au³.

^(•)

emcee jump parameter.

^(†)

Kipping (2013) parametrisation for the limb-darkening coefficients to consider only physical values.

^(∗)

Fixed at t_ref.

^(†)

Reflected with respect to i = 90°, the supplementary angle is equally probable.

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