The tidal deformation and atmosphere of WASP-12 b from its phase curve

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Table 2

Result of the fit to the CHEOPS and TESS phase curves.

Parameter	Symbol	Prior	Posterior

			Spherical planet	Ellipsoidal planet
Orbital period (days)	P	𝒩 (1.0914,0.0001)	1.0914185 ± 2E-7	1 .0914185 ± 2E-7
Transit time (BJD_TBD−2459000)	T₀ ^◊	𝓤(196,197)	196.624122 ± 6.6E-4	196.624121 ± 6.6E-4
Impact parameter	b	𝓤(0,l)	0.392 ± 0.011	0.369 ± 0.016
Scaled semi-major axis	a/R_★	𝓤(2.5, 3.5)	3.006 ± 0.013	3.036 ± 0.018
Love number	h₂	𝓤(0,2.5)	–	${1.55}_{- 0.49}^{+ 0.45}$ $1.55_{ - 0.49}^{ + 0.45}$
Log planet-to-star mass ratio	log Q_M	𝒩(−6.935, 0.025)	–	−6.931 ± 0.022
Planet–star radius ratio^(*)	$R_{v} / R_{⋆}_{CHEOPS}$ ${{R_{\rm{v}}}/{R_ \star }_{{\rm{CHEOPS}}}}$	𝓤(0, 0.25)	0.1177 ± 0.0002	0.1242 ± 0.0023
	$R_{v} / R_{⋆_{TESS}}$ ${{R_{\rm{v}}}/{R_{{ \star _{{\rm{TESS}}}}}}}$		0.1164 ± 0.0002	0.1226 ± 0.0023
	$R_{v} / R_{⋆}_{S p i t z e r 3.6}$ ${{R_{\rm{v}}}/{R_ \star }_{Spitzer{\rm{}}3.6}}$		0.1133 ± 0.0004	0.1188 ± 0.0020
	$R_{v} / R_{⋆}_{S p i t z e r 4.5}$ ${{R_{\rm{v}}}/{R_ \star }_{Spitzer{\rm{}}4.5}}$		0.1071 ± 0.0006	0.1115 ± 0.0017
EV semi-amplitude (ppm)	$A_{{EV}_{CHEOPS}}$ ${{A_{{\rm{E}}{{\rm{V}}_{{\rm{CHEOPS}}}}}}}$	𝓤(0,200)	69 ± 14	54±15
	$A_{{EV}_{TESS}}$ ${{A_{{\rm{E}}{{\rm{V}}_{{\rm{TESS}}}}}}}$		58 ± 14	40 ±15
DB semi-amplitude (ppm)	$A_{{DB}_{CHEOPS}}$ ${{A_{{\rm{D}}{{\rm{B}}_{{\rm{CHEOPS}}}}}}}$	𝒩(2.92, 0.2)	2.92 ± 0.17	2.91 ± 0.17
	$A_{{DB}_{TESS}}$ ${{A_{{\rm{D}}{{\rm{B}}_{{\rm{TESS}}}}}}}$	𝓤(2.32, 0.2)	2.31 ± 0.17	2.31 ± 0.17
Dayside flux (ppm) (occultation depth)	$F_{d} / F_{⋆_{CHEOPS}}$ ${{F_{\rm{d}}}/{F_{{ \star _{{\rm{CHEOPS}}}}}}}$	𝓤 (0 1000)	340 ± 24	333 ± 24
	$F_{d} / F_{⋆_{TESS}}$ ${{F_{\rm{d}}}/{F_{{ \star _{{\rm{TESS}}}}}}}$	𝓤 (0, 1000)	513 ± 29	493 ± 29
Nightside flux (ppm)	$F_{n} / F_{⋆_{CHEOPS}}$ ${{F_{\rm{n}}}/{F_{{ \star _{{\rm{CHEOPS}}}}}}}$	𝓤(−90,90)	6.2 ± 23	7.0 ± 23
	$F_{n} / F_{⋆_{TESS}}$ ${{F_{\rm{n}}}/{F_{{ \star _{{\rm{TESS}}}}}}}$		6.1 ± 21	11.8 ± 21
Hotspot offset (°)	δ_CHEOPS	𝓤(-90,90)	9.8 ± 4.5	9.3 ± 4.6
	δ_TESS		6.3 ± 2.7	5.8 ± 2.6

Derived parameters

Effective planetary radius ratio mid-occultation	$R_{p}^{eff} / R_{⋆_{CHEOPS}}$ ${R_{\rm{p}}^{{\rm{eff}}}/{R_{{ \star _{{\rm{CHEOPS}}}}}}}$	-	0.11770 ± 0.00020	0.11730 ± 0.00027
	$R_{p}^{eff} / R_{⋆}_{THSS}$ ${R_{\rm{p}}^{{\rm{eff}}}/{R_ \star }_{{\rm{THSS}}}}$		0.11640 ± 0.00020	0.11600 ± 0.00025
Ellipsoid axis ratios	$r_{1} : r_{2} : r_{3}_{_{CHEOPS}}$ ${{r_1}:{r_2}:{r_3}_{_{{\rm{CHEOPS}}}}}$	_—	–	l.23 : l.06 : l.0
	$r_{1} : r_{2} : r_{3}_{_{TESS}}$ ${{r_1}:{r_2}:{r_3}_{_{{\rm{TESS}}}}}$	-	-	l.22·: l.05 :·l.0
	$r_{1} : r_{2} : r_{3}_{_{S p i t z e r 3.6}}$ ${{r_1}:{r_2}:{r_3}_{_{Spitzer{\rm{3}}{\rm{.6}}}}}$	—	-	l.20·: l.05·l.0
	$r_{1} : r_{2} : r_{3}_{_{S p i t z e r 4.5}}$ ${{r_1}:{r_2}:{r_3}_{_{Spitzer{\rm{}}4.5}}}$	—	-	l.l6·: l.04· l.0

Planet phase variation	$A_{{atm}_{CHEOPS}}$ ${{A_{{\rm{at}}{{\rm{m}}_{{\rm{CHEOPS}}}}}}}$		170 ± 16	165±16
semi-amplitude (ppm)	$A_{{atm}_{TESS}}$ ${{A_{{\rm{at}}{{\rm{m}}_{{\rm{TESS}}}}}}}$		254 ± 14	241 ± 14
Planetary mass	$M_{p_{CHEOPS}}$ ${{M_{{p_{{\rm{CHEOPS}}}}}}}$		2.34 ± 0.48	1.89 ± 0.53
fromEV(M_JUP)	$M_{p_{TESS}}$ ${{M_{{p_{{\rm{TESS}}}}}}}$		2.09 ± 0.49	1 .49 ± 0.58
	$A_{g_{CHEOPS}}$ ${{A_{{g_{{\rm{CHEOPS}}}}}}}$		0.089 ± 0.017	0.086 ± 0.017
Geometric albedo	$A_{g_{TESS}}$ ${{A_{{g_{{\rm{TESS}}}}}}}$		0.022 ± 0.023	0.010 ± 0.023
	$T_{{day}_{CHEOPS}}$ ${{T_{{\rm{day}}{{\rm{}}_{{\rm{CHEOPS}}}}}}}$		2821 ± 25	2821 ± 25
Dayside temperature (K)	$T_{{day}_{TESS}}$ ${{T_{{\rm{day}}{{\rm{}}_{{\rm{TESS}}}}}}}$		2915 ± 25	2915 ± 25
	$T_{{night}_{CHEOPS}}$ ${{T_{{\rm{night}}{{\rm{}}_{{\rm{CHEOPS}}}}}}}$		<2025 (2σ)	<2126 (2σ)
Nightside temperature (K)	$T_{{night}_{TESS}}$ ${{T_{{\rm{night}}{{\rm{}}_{{\rm{TESS}}}}}}}$		<1890 (2σ)	<1921 (2σ)

Notes. We note that 𝒩(µ, σ) represents a Gaussian prior with mean µ and standard deviation σ while 𝓤(α, b) is a uniform prior between a and b. ^(*)For the spherical planet, this is equal to the transit radius.

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