EMPEROR - I. Exoplanet MCMC parallel tempering for RV orbit retrieval

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Volume 704 (December 2025)

A&A, 704 (2025) A323

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Table B.1

51 Peg b model parameters.

Parameter	reddemcee	dyn-long	dyn-short	Butler et al. 2006
P (d)	${4.230782}_{- 0.000013}^{+ 0.000016}$ $4.230782_{ - 0.000013}^{ + 0.000016}$	${4.230781}_{- 0.000038}^{+ 0.000038}$ $4.230781_{ - 0.000038}^{ + 0.000038}$	${4.230784}_{- 0.000014}^{+ 0.000014}$ $4.230784_{ - 0.000014}^{ + 0.000014}$	${4.230785}_{- 0.000036}^{+ 0.000036}$ $4.230785_{ - 0.000036}^{ + 0.000036}$
K (m s⁻¹)	${55.69}_{- 0.23}^{+ 0.18}$ $55.69_{ - 0.23}^{ + 0.18}$	${55.66}_{- 0.54}^{+ 0.54}$ $55.66_{ - 0.54}^{ + 0.54}$	${55.71}_{- 0.11}^{+ 0.20}$ $55.71_{ - 0.11}^{ + 0.20}$	${55.94}_{- 0.69}^{+ 0.69}$ $55.94_{ - 0.69}^{ + 0.69}$
T₀ (d)	${1.55}_{- 0.38}^{+ 0.16}$ $1.55_{ - 0.38}^{ + 0.16}$	${0.24}_{- 1.35}^{+ 1.27}$ $0.24_{ - 1.35}^{ + 1.27}$	${1.56}_{- 0.17}^{+ 0.23}$ $1.56_{ - 0.17}^{ + 0.23}$	${1.51}_{- 0.61}^{+ 0.61}$ $1.51_{ - 0.61}^{ + 0.61}$
e	${0.0085}_{- 0.0067}^{+ 0.0108}$ $0.0085_{ - 0.0067}^{ + 0.0108}$	${0.0059}_{- 0.0043}^{+ 0.0076}$ $0.0059_{ - 0.0043}^{ + 0.0076}$	${0.0102}_{- 0.0029}^{+ 0.0032}$ $0.0102_{ - 0.0029}^{ + 0.0032}$	${0.0130}_{- 0.0120}^{+ 0.0120}$ $0.0130_{ - 0.0120}^{ + 0.0120}$
ω (rad)	${1.07}_{- 0.55}^{+ 0.24}$ $1.07_{ - 0.55}^{ + 0.24}$	${4.51}_{- 1.73}^{+ 1.46}$ $4.51_{ - 1.73}^{ + 1.46}$	${1.08}_{- 0.26}^{+ 0.34}$ $1.08_{ - 0.26}^{ + 0.34}$	1.01

$\dot{γ} ({ms}^{- 1} {yr}^{- 1})$ $\dot \gamma \left( {{\rm{m}}{{\rm{s}}^{ - 1}}{\rm{y}}{{\rm{r}}^{ - 1}}} \right)$	$- {1.62}_{- 0.05}^{+ 0.09}$ $- 1.62_{ - 0.05}^{ + 0.09}$	$- {1.60}_{- 0.19}^{+ 0.19}$ $- 1.60_{ - 0.19}^{ + 0.19}$	$- {1.60}_{- 0.07}^{+ 0.07}$ $- 1.60_{ - 0.07}^{ + 0.07}$	$- {1.64}_{- 0.16}^{+ 0.16}$ $- 1.64_{ - 0.16}^{ + 0.16}$
γ (m s^{− 1})	${5.41}_{- 0.26}^{+ 0.08}$ $5.41_{ - 0.26}^{ + 0.08}$	${5.32}_{- 0.44}^{+ 0.44}$ $5.32_{ - 0.44}^{ + 0.44}$	${5.31}_{- 0.16}^{+ 0.16}$ $5.31_{ - 0.16}^{ + 0.16}$	-
σ (m s^{− 1})	${0.64}_{- 0.59}^{+ 0.01}$ $0.64_{ - 0.59}^{ + 0.01}$	${1.034}_{- 0.709}^{+ 0.841}$ $1.034_{ - 0.709}^{ + 0.841}$	${1.05}_{- 0.27}^{+ 0.27}$ $1.05_{ - 0.27}^{ + 0.27}$	-

Notes. From left to right: parameter estimates for EMPEROR with reddemcee , dynesty random-slice (dyn-rs), and the Butler et al. (2006) solution. T₀ was substracted 2450000d for readability. In Butler 2006, ω had ill defined uncertainties, due the proximity of e to 0. The parameters displayed here are from the run with the median maximum-likelihood for each method.

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