Observations of scattered light from exoplanet atmospheres

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Volume 685 (May 2024)

A&A, 685 (2024) A104

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Table 2

Reflected light and thermal emission phase curve parameters inferred from Kepler observations.

Parameter	TrES-2 b	Kepler-7 b	Kepler-41 b	HAT-P-7 b	KOI-13 b
Model comparison results
Homogeneity	Hom.	Inhom.	Inhom.	Hom.	Inhom.
Phase Func.	C-S.	C-S.	Iso.	Iso.	C-S.
Weight Inh.	0.00	0.90	1.00	0.28	0.72
Weight C-S	1.00	1.00	0.00	0.00	0.77

Posterior distributions
ω	${0.06}_{- 0.03}^{+ 0.02}$ $0.06_{ - 0.03}^{ + 0.02}$	${0.99}_{- 0.01}^{+ 0.00}$ $0.99_{ - 0.01}^{ + 0.00}$	${0.92}_{- 0.06}^{+ 0.04}$ $0.92_{ - 0.06}^{ + 0.04}$	${0.40}_{- 0.07}^{+ 0.07}$ $0.40_{ - 0.07}^{ + 0.07}$	${0.98}_{- 0.02}^{+ 0.01}$ $0.98_{ - 0.02}^{ + 0.01}$
A_g	${0.01}_{- 0.01}^{+ 0.00}$ $0.01_{ - 0.01}^{ + 0.00}$	${0.26}_{- 0.01}^{+ 0.01}$ $0.26_{ - 0.01}^{ + 0.01}$	${0.13}_{- 0.02}^{+ 0.01}$ $0.13_{ - 0.02}^{ + 0.01}$	${0.09}_{- 0.02}^{+ 0.02}$ $0.09_{ - 0.02}^{ + 0.02}$	${0.32}_{- 0.03}^{+ 0.03}$ $0.32_{ - 0.03}^{ + 0.03}$
x₁ ^(deg)	–	$- {8.23}_{- 3.19}^{+ 3.55}$ $- 8.23_{ - 3.19}^{ + 3.55}$	$- {29.44}_{- 5.51}^{+ 6.95}$ $- 29.44_{ - 5.51}^{ + 6.95}$	–	$- {21.03}_{- 3.89}^{+ 3.44}$ $- 21.03_{ - 3.89}^{ + 3.44}$
x₂ ^(deg)	–	${56.76}_{- 4.10}^{+ 5.24}$ $56.76_{ - 4.10}^{ + 5.24}$	${38.80}_{- 4.34}^{+ 4.50}$ $38.80_{ - 4.34}^{ + 4.50}$	–	${12.77}_{- 6.81}^{+ 5.72}$ $12.77_{ - 6.81}^{ + 5.72}$
C₁₁	${0.05}_{- 0.03}^{+ 0.05}$ $0.05_{ - 0.03}^{ + 0.05}$	${0.06}_{- 0.04}^{+ 0.07}$ $0.06_{ - 0.04}^{ + 0.07}$	${0.07}_{- 0.05}^{+ 0.06}$ $0.07_{ - 0.05}^{ + 0.06}$	${0.14}_{- 0.02}^{+ 0.02}$ $0.14_{ - 0.02}^{ + 0.02}$	${0.10}_{- 0.02}^{+ 0.02}$ $0.10_{ - 0.02}^{ + 0.02}$
f	${0.71}_{- 0.01}^{+ 0.01}$ $0.71_{ - 0.01}^{ + 0.01}$	${0.71}_{- 0.01}^{+ 0.01}$ $0.71_{ - 0.01}^{ + 0.01}$	${0.71}_{- 0.01}^{+ 0.01}$ $0.71_{ - 0.01}^{ + 0.01}$	${0.70}_{- 0.01}^{+ 0.01}$ $0.70_{ - 0.01}^{ + 0.01}$	${0.70}_{- 0.01}^{+ 0.01}$ $0.70_{ - 0.01}^{ + 0.01}$

Derived quantities
Reflected light phase offset (deg)	–	${34.42}_{- 4.14}^{+ 2.38}$ $34.42_{ - 4.14}^{ + 2.38}$	${2.00}_{- 1.21}^{+ 1.40}$ $2.00_{ - 1.21}^{ + 1.40}$	–	$- {1.24}_{- 0.43}^{+ 0.32}$ $- 1.24_{ - 0.43}^{ + 0.32}$
Reflected light amplitude (ppm)	${2.21}_{- 0.98}^{+ 1.24}$ $2.21_{ - 0.98}^{ + 1.24}$	${11.71}_{- 0.59}^{+ 0.61}$ $11.71_{ - 0.59}^{ + 0.61}$	${5.20}_{- 0.85}^{+ 0.62}$ $5.20_{ - 0.85}^{ + 0.62}$	${47.76}_{- 9.02}^{+ 11.63}$ $47.76_{ - 9.02}^{ + 11.63}$	${14.21}_{- 1.67}^{+ 0.25}$ $14.21_{ - 1.67}^{ + 0.25}$
Thermal emission amplitude (ppm)	${1.61}_{- 0.51}^{+ 1.05}$ $1.61_{ - 0.51}^{ + 1.05}$	${1.19}_{- 0.44}^{+ 1.24}$ $1.19_{ - 0.44}^{ + 1.24}$	${6.44}_{- 2.89}^{+ 6.35}$ $6.44_{ - 2.89}^{ + 6.35}$	${20.27}_{- 3.72}^{+ 5.17}$ $20.27_{ - 3.72}^{ + 5.17}$	${51.14}_{- 8.50}^{+ 8.48}$ $51.14_{ - 8.50}^{ + 8.48}$
T_d (K)	$1653_{- 50}^{+ 70}$ $1653_{ - 50}^{ + 70}$	$1730_{- 67}^{+ 108}$ $1730_{ - 67}^{ + 108}$	$1925_{- 102}^{+ 127}$ $1925_{ - 102}^{ + 127}$	$2408_{- 55}^{+ 62}$ $2408_{ - 55}^{ + 62}$	$2812_{- 64}^{+ 56}$ $2812_{ - 64}^{ + 56}$
T_n (K)	$1510_{- 69}^{+ 49}$ $1510_{ - 69}^{ + 49}$	$1531_{- 108}^{+ 65}$ $1531_{ - 108}^{ + 65}$	$1652_{- 126}^{+ 100}$ $1652_{ - 126}^{ + 100}$	$2138_{- 63}^{+ 53}$ $2138_{ - 63}^{ + 53}$	$2289_{- 55}^{+ 64}$ $2289_{ - 55}^{ + 64}$

Notes. For prior distributions, see Table 1. The first section gives results from model comparison with leave one out cross validation (LOO-CV) and model stacking. Models are marked “Hom.” when LOO-CV prefers the homogeneous reflected light model, “Inhom.” when LOO-CV prefers the inhomogeneous model. The scattering phase function is included when preferred by LOO-CV with the same criteria. The posterior distributions for the reflected light and thermal emission parameters are in the second section, excluding g which was consistent with the prior for all planets. The derived quantities include the phase offset of the reflected light phase curve, the amplitudes of the reflected light and thermal emission components, and the dayside and nightside temperatures. See Sect. 2.10 for discussion on the uncertainties derived from these degenerate posterior distribution.

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