CHEOPS observations confirm nodal precession in the WASP-33 system

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Volume 693 (January 2025)

A&A, 693 (2025) A128

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Table 5

Parameters from transit light curve analysis, both with and without gravity darkening (GD).

Parameter	(i) no GD	(ii) GD λ free	(iii) GD λ fixed
Fitted parameters:

Orbital period P_orb (d)	1.2198747 ± 0.0000012	1.2198769 ± 0.0000011	${1.21987628}_{- 0.00000102}^{+ 0.00000095}$ $1.21987628_{ - 0.00000102}^{ + 0.00000095}$
Transit epoch T₀ (BJD_TDB − 2450000)	8792.63255 ± 0.00053	8792.63167 ± 0.00049	8792.63188 ± 0.00045
Scaled semi-major axis a/R_⋆	${3.6066282279}_{- 0.045}^{+ 0.036}$ $3.6066282279_{ - 0.045}^{ + 0.036}$	${3.551}_{- 0.035}^{+ 0.029}$ $3.551_{ - 0.035}^{ + 0.029}$	${3.512}_{- 0.024}^{+ 0.022}$ $3.512_{ - 0.024}^{ + 0.022}$
Radius ratio R_p/R_★	0.10918 ± 0.00098	${0.10712}_{- 0.00074}^{+ 0.00076}$ $0.10712_{ - 0.00074}^{ + 0.00076}$	0.10696 ± 0.00083
Transit impact parameter b	${0.10}_{- 0.08}^{+ 0.10}$ $0.10_{ - 0.08}^{ + 0.10}$	${0.070}_{- 0.056}^{+ 0.073}$ $0.070_{ - 0.056}^{ + 0.073}$	${0.064}_{- 0.058}^{+ 0.075}$ $0.064_{ - 0.058}^{ + 0.075}$
Limb-darkening coefficient и₊	${0.801}_{- 0.090}^{+ 0.087}$ $0.801_{ - 0.090}^{ + 0.087}$	${0.802}_{- 0.091}^{+ 0.086}$ $0.802_{ - 0.091}^{ + 0.086}$	${0.737}_{- 0.087}^{+ 0.090}$ $0.737_{ - 0.087}^{ + 0.090}$
Limb-darkening coefficient u₋	$- {0.63}_{- 0.16}^{+ 0.21}$ $- 0.63_{ - 0.16}^{ + 0.21}$	$- {0.53}_{- 0.22}^{+ 0.29}$ $- 0.53_{ - 0.22}^{ + 0.29}$	−0.26 ± 0.28
Longitude of ascending node Ω*	—	$238_{- 22}^{+ 17}$ $238_{ - 22}^{ + 17}$	201.5 (fixed)
Stellar inclination i_⋆ (deg)	—	$109_{- 12}^{+ 15}$ $109_{ - 12}^{ + 15}$	100.5 ± 8.4
White noise level σ_w (ppm)	214±5	214±5	214±6
Red noise level σ_r (ppm)	16517 ± 227	16468 ± 218	16471 ±247
Derived parameters:

Semi-major axis a (au)	0.02603 ± 0.00040	0.02603 ± 0.00040	0.02603 ± 0.00040
Orbital inclination angle i_p (degrees)	${88.3}_{- 1.7}^{+ 1.2}$ $88.3_{ - 1.7}^{ + 1.2}$	${88.8}_{- 1.2}^{+ 0.8}$ $88.8_{ - 1.2}^{ + 0.8}$	${88.9}_{- 1.2}^{+ 0.8}$ $88.9_{ - 1.2}^{ + 0.8}$
Transit duration T₁₄ (h)	2.893 ± 0.022	${2.943}_{- 0.022}^{+ 0.027}$ $2.943_{ - 0.022}^{ + 0.027}$	2.979 ± 0.016
Planet radius R_p (R_Jup )	1.724 ± 0.042	1.692 ± 0.039	1.689 ± 0.039
Sky-projected stellar obliquity λ (deg)	—	$- 148_{- 17}^{+ 22}$ $- 148_{ - 17}^{ + 22}$	−111.5 (fixed)
True obliquity ψ (deg)	—	$139_{- 15}^{+ 12}$ $139_{ - 15}^{ + 12}$	${111.3}_{- 0.7}^{+ 0.2}$ $111.3_{ - 0.7}^{ + 0.2}$
Relative Bayesian information criterion (BIC)	0	+4.1	–5.3

Notes. The best ephemeris for planning future observations is not listed in this table, but rather in Section 7.2.

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