Characterisation of the TOI-421 planetary system using CHEOPS, TESS, and archival radial velocity data

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Volume 686 (June 2024)

A&A, 686 (2024) A301

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Table 6

Retrieved planetary and stellar parameters.

Parameters	Symbols	Priors	Values	Units
Planet b
Orbital period	P_b	𝒰(5.1975, 5.1977)	5.197576 ± 0.000005	days
Transit time	T_0,b	𝒰(2459189.7, 2459189.76)	2459189.7341 ± 0.0005	BJD
Planet-to-star radius ratio	R_b/R_⋆	𝒰(0.02, 0.04)	0.0279 ± 0.0008	-
Impact parameter	b_b	𝒰(0.0, 1.1)	0.942 ± 0.011	-
Eccentricity	e_b	𝒰(0.0, 1.0)^(b)	0.13 ± 0.05	-
Argument of periapsis	ω_b	𝒰(0, 360)^(b)	140 ± 30	^deg₁
RV semi-amplitude	K_b	𝒰(1, 4)	2.83 ± 0.18	ms⁻¹
Transit duration	dur_b	–	0.0454 ± 0.0014	days
Semi-major axis	a_b	–	0.0554 ± 0.0010	A𝒰
Radius	R_b	–	2.64 ± 0.08	R_θ
Mass	M_b	–	6.7 ± 0.6
Mean density	ρ_b	–	0.37 ± 0.05	ρ_θ
Equilibrium temperature^(a)	T_eq,b	–	922 ± 14	K

Planet c
Orbital period	P_c	𝒰(16.0672, 16.0678)	16.067541 ± 0.000004	days
Transit time	T_0,c	𝒰(2459195.305, 2459195.310)	2459195.30741 ± 0.00018	BJD
Planet-to-star radius ratio	R_c/R_⋆	𝒰(0.04, 0.07)	0.0540 ± 0.0006	-
Impact parameter	b_c	𝒰(0.0, 1.1)	0.70 ± 0.03	-
Eccentricity	e_c	𝒰(0.0, 1.0)^(b)	0.19 ± 0.04	-
Argument of periapsis	ω_c	𝒰(0, 360)^(b)	102±14	deg
RV semi-amplitude	K_c	𝒰(3, 6)	4.1 ± 0.3	ms⁻¹
Transit duration	dur_c	–	0.1148 ± 0.0009	days
Semi-major axis	a_c	–	0.1170 ± 0.0018	A𝒰
Radius	R_c	–	5.09 ± 0.07	^Rθ
Mass	M_c	–	14.1 ± 1.4	M_θ
Mean density	ρ_c	–	0.107 ± 0.012	Pθ
Equilibrium temperature ^(a)	T_eq,c	–	635 ± 9	K

Stellar parameters
Stellar density	ρ_⋆	𝒩 (1.28, 0.09)	1.28 ± 0.06
Limb darkening coefficients
CHEOPS passband	$q_{1_{CHEOPS}}$ ${q_{{1_{{\rm{CHEOPS }}}}}}$	𝒩 (0.487, 0.048)	0.44 ± 0.04	-
CHEOPS passband	$q_{2_{CHEOPS}}$ ${q_{{2_{{\rm{CHEOPS }}}}}}$	𝒩(0.359, 0.015)	0.363 ± 0.010	-
TESS passband	$q_{1_{TESS}}$ ${q_{{1_{{\rm{TESS}}}}}}$	𝒩(0.377, 0.040)	0.378 ± 0.03	-
TESS passband	$q_{2_{TESS}}$ ${q_{{2_{{\rm{TESS}}}}}}$	𝒩 (0.311, 0.015)	0.316 ± 0.011	-

Instrumental parameters
CHEOPS white-noise	σ _CHEOPS	𝒰(6, 2500)	305 ± 5	ppm
TESS white-noise	σ _TESS	𝒰(17, 6740)	722 ± 7	^ppm₁
HARPS jitter	σ _HARPS	𝒰(0.05, 135)	1.0 ± 0.4	ms⁻¹
HIRES jitter	σ _HIRES	𝒰(0.05, 135)	2.2 ± 0.4	ms⁻¹
PFS jitter	σ _PFS	𝒰(0.05, 135)	2.0 ± 0.7	ms⁻¹
FIES jitter	σ _FIES	𝒰(0.001, 135)	0.02 ± 0.16	ms⁻¹
HARPS offset	γ_HARPS	𝒰(−50, 50)	1.8 ± 0.9	ms⁻¹
HIRES offset	γ_HIRES	𝒰(−50, 50)	−0.8 ± 0.4	ms⁻¹
PFS offset	γ_PFS	𝒰(−50, 50)	2.3 ± 1.3	ms⁻¹
FIES offset	γ_FIES	𝒰(−50, 50)	−7.1 ± 1.3	ms⁻¹
HARPS amplitude of variations	log(S _0,HARPS)	𝒰(−15, −5)	−8.9 ± 0.3	-
HIRES amplitude of variations	log(S _0,HIRES)	𝒰(−15, −5)	−11.3 ± 1.1	-
PFS amplitude of variations	log(S _0,PFS)	𝒰(−15, −5)	−9.5 ± 0.8	-
FIES amplitude of variations	log(S _0,FIES)	𝒰(−15, −5)	−12.3 ± 1.6	-
RV angular frequency of variations	ω_0,RV	𝒩(0.153, 0.008)	0.159 ± 0.007	1/days
RV period of variations	P_rot,⋆	𝒩 (41.2, 2.1)	39.6 ± 1.6	days

Notes. The Gaussian priors with mean µ and standard deviation σ are displayed as 𝒩(µ, σ). 𝒰 represents an uniform bounded prior.^(a)Assuming albedo equal to zero. ^(b)The uniform priors on e_c and ω_c were imposed on $\sqrt{e_{c}} \cos (ω_{c})$ $\sqrt {{e_{\rm{c}}}} \cos \left( {{\omega _{\rm{c}}}} \right)$ and $\sqrt{e_{c}} \sin (ω_{c})$ $\sqrt {{e_{\rm{c}}}} \sin \left( {{\omega _{\rm{c}}}} \right)$ .

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