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 7

Fitting parameters of the evolution models and their constraints on the initial parameters of TOI-421 system.

Planet	Model^(a)	Fitting parameter	R_p [R_⊕]^(b)	ƒ_atm^(b)	$f_{atm}^{start}$ $f_{{\rm{atm}}}^{{\rm{start}}}$ ^(c)	$M_{p}^{start}$ $M_{\rm{p}}^{{\rm{start }}}$ ^(c)	$f_{atm}^{loss} [%]$ $f_{{\rm{atm }}}^{{\rm{loss }}}[\% ]$ ^(d)
b	`PASTA`	R_p	2.64 ± 0.08	0.0087 ± 0.0014	–	–	–
b	`PASTA`	ƒ_atm	2.32 ± 0.13	0.0038 ± 0.0013	–	–	–
c	`PASTA`	R_p	5.09 ± 0.07	0.106 ± 0.003	0.122 ± 0.010	14.4 ± 1.4	15±8
c	`PASTA`	ƒ_atm	6.47 ± 0.7	0.155 ± 0.012	0.19 ± 0.02	14.7 ± 1.5	22 ± 12
b	MESA-based	R_p	2.64 ± 0.08	0.026 ± 0.008	0.55 ± 0.15	14.5 ± 5.0	98 ± 2
b	MESA-based	ƒ_atm	2.13 ± 0.13	0.0038 ± 0.0013	0.47 ± 0.17	12.6 ± 4.2	~99
c	MESA-based	R_p	5.09 ± 0.07	0.242 ± 0.014	0.35 ± 0.08	16.4 ± 2.6	41 ± 21
c	MESA-based	ƒ_atm	4.3 ± 0.2	0.155 ± 0.012	0.23 ± 0.06	15.5 ± 2.0	39 ± 22

Notes. Unconstrained values are given as –. ^(a)PASTA models both planets and the stellar rotation history simultaneously, while MESA-based models consider each planet individually, further assuming a fixed stellar rotation history.^(b)R_p (planetary radius) and ƒ_atm (present-day atmospheric mass fraction) are constraining parameters, with the value in bold being the one used to constrain the model, while the other one is derived from the respective model, as listed in column three.^(c) $f_{atm}^{start}$ $f_{{\rm{atm }}}^{{\rm{start }}}$ (initial atmospheric mass fraction) and $M_{p}^{start}$ $M_{\rm{p}}^{{\rm{start }}}$ (planetary mass at the beginning of the evolution) are parameters retrieved from the model.^(d)Percentage of atmosphere lost during evolution given as $M_{atm}^{loss} = \frac{M_{atmm}^{start} - M_{atm}}{M_{atm}^{salm}}$ $M_{{\rm{atm}}}^{{\rm{loss }}} = {{M_{{\rm{atmm}}}^{{\rm{start }}} - {M_{{\rm{atm}}}}} \over {M_{{\rm{atm}}}^{{\rm{salm }}}}}$ .

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