Characterising WASP-43b’s interior structure: Unveiling tidal decay and apsidal motion

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Volume 694 (February 2025)

A&A, 694 (2025) A233

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Table 6

Results of the complete fit.

Parameter		Symbol (units)	Fit	Value	Priors
Assumed parameters
Stellar rotation		V sin i (km s^–1)		2.26
Stellar mass		Μ_* (M_⊙)		0.717
Planet-to-star radius ratio		r_p/R_★		0.15940
Semi-major axis		a₀ (AU)		0.01526
First transit epoch		T₀ (BJD_TDB-2 454 000)		5528.86823
Adjusted parameters
Jitters	ID 1	jit₁ (m s^–1)	RV	2.1
	ID 2	jit₂ (m s^–1)	RV	0.0
	ID 3	jit₃ (m s^–1)	RV	11.4
	ID 4	jit₄ (m s^–1)	RV	13.8
	ID 5	jit₅ (m s^–1)	RV	18.4
	ID 5	jit₆ (m s^–1)	RV	17.1
	ID 6	jit₇ (m s^–1)	RV	4.5
	ID 7	jit₈ (m s^–1)	RV	6.1
	Transits	jit_tr (d)	Tr	0.00104
	Occultations	jit_occ (d)	Occ	0.00023
Fitted parameters
Offset velocity of the system	I	V_γ (km s^–1)	RV	−3.602 ± 0.013	𝒰 [–∞,+ ∞]
Long-trend acceleration		V_γ (km s^–2)	RV	(1.05 ± 1.48) ⋅ 10-¹⁰	𝒰 [–∞,+ ∞]
RV semi-amplitude		K₀ (km s^–1)	RV	0.5543 ± 0.0017	𝒰 [–∞,+ ∞]
Offset instrumental	ID 2	V_instr,2 (km s^–1)	RV	−0.00011 ± 0.01731	𝒰 [–∞,+ ∞]
velocity	ID 3	V_instr,3 (km s^–1)	RV	+0.017 ± 0.014	𝒰 [–∞,+ ∞]
	ID 4	V_instr,4 (km s^–1)	RV	+0.0011 ± 0.0192	𝒰 [–∞,+ ∞]
	ID 5	V_instr,5 (km s^–1)	RV	+0.038 ± 0.029	𝒰 [–∞,+ ∞]
	ID 6	V_instr,5 (km s^–1)	RV	+0.0035 ± 0.029	𝒰 [–∞,+ ∞]
	ID 7	V_instr,6 (km s^–1)	RV	+0.00082 ± 0.02888	𝒰 [–∞,+ ∞]
	ID 8	V_instr,7 (km s^–1)	RV	+0.0023 ± 0.0425	𝒰 [–∞,+ ∞]
		$\sqrt{e} \cdot \sin ω_{0}$ $\sqrt e \cdot \sin {\omega _0}$	RV, Tr/Occ	$- {0.031}_{- 0.014}^{+ 0.010}$ $- 0.031_{ - 0.014}^{ + 0.010}$	𝒰 [–1,+1]
		$\sqrt{e} \cdot \cos ω_{0}$ $\sqrt e \cdot \cos {\omega _0}$	RV, Tr/Occ	$- {0.024}_{- 0.011}^{+ 0.014}$ $- 0.024_{ - 0.011}^{ + 0.014}$	𝒰 [–1,+1]
Anomalistic period		P_a,0 (d)	RV, Tr/Occ	${0.813792}_{- 0.000017}^{+ 0.000011}$ $0.813792_{ - 0.000017}^{ + 0.000011}$	𝒰 (0.81;0.1)
Tidal decay rate		${\dot{P}}_{a} ({ms yr}^{- 1})$ ${\dot P_{\rm{a}}}\left( {{\rm{msy}}{{\rm{r}}^{ - 1}}} \right)$	RV, Tr/Occ	–1.99 ± 0.50, ± 0.99	𝒰 [–∞,+ ∞]
Periastron precession rate		$\dot{ω} (^{°} d^{- 1})$ $\dot \omega \left( {^^\circ {{\rm{d}}^{ - 1}}} \right)$	RV, Tr/Occ	${0.1727}_{- 0.0089}^{+ 0.0083}$ $0.1727_{ - 0.0089}^{ + 0.0083}$
		(″ d^–1)		${621.72}_{- 32.04}^{+ 29.88}$ $621.72_{ - 32.04}^{ + 29.88}$
Stellar Love number		k_2,*	RV	0.020 ± 0.011	𝒩 (0.020; 0.004)
Stellar temperature		T_eff,* (K)	RV	4523.79 ± 270.51	𝒩 (4500 K; 100 K)
Planet-to-star mass ratio		^q	RV	0.00273 ± 0.00027	𝒩 (0.00273; 9.9·⋅ 10^–5)
Rotational stellar period¹¹¹		P_rot,* (d)	RV	${13.24}_{- 5.85}^{+ 6.11}$ $13.24_{ - 5.85}^{ + 6.11}$	𝒩 (15.0; 10.0)
Orbital inclination		i (°)	RV, Tr/Occ	82.32 ± 1.08	𝒩 (82.3°; 1.0°)
Derived parameters
Eccentricity		e		0.00188 ± 0.00035, ± 0.00070, ± 0.00160
Periastron angle		ω₀ (º)		47.09 ± 23.89
Sidereal period		P_s (d)		0.81347489 ± 9.9e-8
RV semi-amplitude increase		$\dot{K} (m s^{- 1} {yr}^{- 1})$ $\dot K\left( {{\rm{m}}{{\rm{s}}^{ - 1}}{\rm{y}}{{\rm{r}}^{ - 1}}} \right)$		(1.58 ± 0.39)⋅ 10^–5

Notes. The table shows the assumed, adjusted, and fitted parameters with their priors and the derived parameters. The third column states whether the fitted parameter is used to model radial velocity (“RV”) and/or mid-transit and mid-occultation times (“Tr/Occ”. Error bars are reported with 1σ confidence level for all parameters, while for e, $\dot{ω}$ $\dot \omega$ , and ${\dot{P}}_{a}$ ${\dot P_a}$ , they are reported also with 2σ confidence level. For e, we also report the 5σ confidence level to strengthen the findings.^(†) The stellar rotational period is fitted as in Equation (10) in Bernabò et al. (2024).

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