A new treatment of telluric and stellar features for medium-resolution spectroscopy and molecular mapping - Application to the abundance determination on β Pic b

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Volume 685 (May 2024)

A&A, 685 (2024) A120

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Table 4

MCMC results for the run.

Parameter	Unit	All uniform priors		Prior log g = 4.18 ± 0.01		Prior T_eff = 1724 ± 15 K		Prior log g and T_eff
		median ± σ_68.3%	MLE	median ± σ_68.3%	MLE	median ± σ_68.3%	MLE	median ± σ_68.3%	MLE
T_eff	K	$1555_{- 29}^{+ 22}$ $1555_{ - 29}^{ + 22}$	1525	$1746_{- 3}^{+ 4}$ $1746_{ - 3}^{ + 4}$	1746	$1748_{- 4}^{+ 3}$ $1748_{ - 4}^{ + 3}$	1749	$1745_{- 2}^{+ 3}$ $1745_{ - 2}^{ + 3}$	1746
log g	cgs	${3.12}_{- 0.09}^{+ 0.12}$ $3.12_{ - 0.09}^{ + 0.12}$	3 24	${4.185}_{- 0.010}^{+ 0.010}$ $4.185_{ - 0.010}^{ + 0.010}$	4.182	${4.216}_{- 0.031}^{+ 0.027}$ $4.216_{ - 0.031}^{ + 0.027}$	4 210	${4.183}_{- 0.010}^{+ 0.010}$ $4.183_{ - 0.010}^{ + 0.010}$	4.190
[Fe/H]	dex	$- {0.325}_{- 0.045}^{+ 0.065}$ $- 0.325_{ - 0.045}^{ + 0.065}$	−0.246	$- {0.235}_{- 0.011}^{+ 0.014}$ $- 0.235_{ - 0.011}^{ + 0.014}$	-0.226	$- {0.235}_{- 0.013}^{+ 0.015}$ $- 0.235_{ - 0.01}^{ + 0.015}$	−0 223	$- {0.237}_{- 0.010}^{+ 0.013}$ $- 0.237_{ - 0.010}^{ + 0.013}$	−0.233
C/O	–	${0.79}_{- 0.11}^{+ 0.01}$ $0.79_{ - 0.11}^{ + 0.01}$	0.68	${0.551}_{- 0.002}^{+ 0.002}$ $0.551_{ - 0.002}^{ + 0.002}$	0.550	${0.551}_{- 0.002}^{+ 0.002}$ $0.551_{ - 0.002}^{ + 0.002}$	0 550	${0.551}_{- 0.002}^{+ 0.002}$ $0.551_{ - 0.002}^{ + 0.002}$	0.550
v sin i	km s⁻¹	${31.4}_{- 5.0}^{+ 4.6}$ $31.4_{ - 5.0}^{ + 4.6}$	33 0	${27.1}_{- 5.4}^{+ 4.5}$ $27.1_{ - 5.4}^{ + 4.5}$	24.9	${24.9}_{- 6.2}^{+ 5.2}$ $24.9_{ - 6.2}^{ + 5.2}$	25 4	${26.6}_{- 5.2}^{+ 4.4}$ $26.6_{ - 5.2}^{ + 4.4}$	28.6
R_spec	–	$4018_{- 30}^{+ 30}$ $4018_{ - 30}^{ + 30}$	4042	$4019_{- 30}^{+ 30}$ $4019_{ - 30}^{ + 30}$	4024	$4018_{- 30}^{+ 30}$ $4018_{ - 30}^{ + 30}$	4032	$4019_{- 30}^{+ 30}$ $4019_{ - 30}^{ + 30}$	4020
v_r	km s⁻¹	${0.77}_{- 0.97}^{+ 1.05}$ $0.77_{ - 0.97}^{ + 1.05}$	1.20	${0.58}_{- 0.89}^{+ 0.86}$ $0.58_{ - 0.89}^{ + 0.86}$	0.30	${0.62}_{- 0.89}^{+ 0.87}$ $0.62_{ - 0.89}^{ + 0.87}$	1.03	${0.63}_{- 0.88}^{+ 0.84}$ $0.63_{ - 0.8}^{ + 0.84}$	0.28
ƒ_err	–	${1.02}_{- 0.13}^{+ 0.05}$ $1.02_{ - 0.13}^{ + 0.05}$	1.08	${0.98}_{- 0.12}^{+ 0.05}$ $0.98_{ - 0.12}^{ + 0.05}$	0.98	${0.99}_{- 0.11}^{+ 0.05}$ $0.99_{ - 0.11}^{ + 0.05}$	0 99	${0.98}_{- 0.12}^{+ 0.05}$ $0.98_{ - 0.12}^{ + 0.05}$	1.00
^(★)σ	–	<0.013	0.002	<0 013	0.007	<0.012	0.006	<0 013	0.005
a	–	${1.000}_{- 0.001}^{+ 0.001}$ $1.000_{ - 0.01}^{ + 0.001}$	1.000	${1.000}_{- 0.001}^{+ 0.001}$ $1.000_{ - 0.01}^{ + 0.001}$	1.000	${1.000}_{- 0.001}^{+ 0.001}$ $1.000_{ - 0.01}^{ + 0.001}$	1.000	${1.000}_{- 0.001}^{+ 0.001}$ $1.000_{ - 0.01}^{ + 0.001}$	1.000

Goodness-of-fit at MLE

χ²			1345		1375.1		1366.0		1340.5
$χ_{red}^{2}$ $\chi _{{\rm{red }}}^2$			1.002		1.029		1.022		1.003
log 𝓛/N_DOF			3.274		3.284		3.285		3.281
AIC			−8721.6		−8755.6		−8758.3		−8757.6

Diagnostics

^(†) N_step/max(τ_λ)		17		52		50		51
Acceptance rate		0 21		0.31		0 31		0.31
N_DOF		1335		1336		1336		1337

Notes. Unless stated otherwise, all parameters (except R_spec) follow uniform priors. We describe the posterior distribution of any parameter by the median and the deviation of the 16th and 84th percentiles to the median. The maximum likelihood estimator (MLE) is given as well, at which point the goodness-of-fit diagnostics are determined. ^(★)For σ, given the shape of the posterior distribution peaking close to 0 and compatible with 0 at less than 2-σ, we only give the upper-limit at the 84th percentile. ^(†)max(τ_λ) is the maximum auto-correlation time among all varied parameters λ.

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