Stellar-activity analysis of the nearby M dwarf GJ 526 - Multi-dimensional Gaussian-process modelling of RV, FWHM, and S-index

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Volume 703 (November 2025)

A&A, 703 (2025) A245

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Table B.1

Parameter posteriors of our best model on all data, against the same set up on ESPRESSO data alone.

Parameter name	Symbol	Unit	Prior	Posterior

				All-data	ESPRESSO
LTF parameters
Period	P_cyc	d	$U (1000, 2000)$ $\mathcal{U}\left(1000, 2000\right)$	$1680_{- 40}^{+ 50}$ $1680^{+50}_{-40}$	$1720_{- 210}^{+ 190}$ $1720^{+190}_{-210}$
RV phase	ϕ_{cyc, 0}	–	$U (0, 1)$ $\mathcal{U}\left(0, 1\right)$ ^(w)	${0.843}_{- 0.129}^{+ 0.118}$ $0.843^{+0.118}_{-0.129}$	${0.872}_{- 0.177}^{+ 0.149}$ $0.872^{+0.149}_{-0.177}$
RV semi-amplitude	k_{cyc, 0}	m s^-1	$U (0, 10)$ $\mathcal{U}\left(0, 10\right)$	${0.51}_{- 0.33}^{+ 0.35}$ $0.51^{+0.35}_{-0.33}$	${0.54}_{- 0.37}^{+ 0.47}$ $0.54^{+0.47}_{-0.37}$
FWHM phase	ϕ_{cyc, 1}	–	$U (0, 1)$ $\mathcal{U}\left(0, 1\right)$ ^(w)	${0.429}_{- 0.089}^{+ 0.085}$ $0.429^{+0.085}_{-0.089}$	${0.448}_{- 0.132}^{+ 0.145}$ $0.448^{+0.145}_{-0.132}$
FWHM semi-amplitude	k_{cyc, 1}	m s^-1	$U (0, 10)$ $\mathcal{U}\left(0, 10\right)$	${2.73}_{- 1.32}^{+ 1.51}$ $2.73^{+1.51}_{-1.32}$	${2.34}_{- 1.44}^{+ 1.68}$ $2.34^{+1.68}_{-1.44}$
S-index phase	ϕ_{cyc, 2}	–	$U (0, 1)$ $\mathcal{U}\left(0, 1\right)$ ^(w)	${0.548}_{- 0.248}^{+ 0.252}$ $0.548^{+0.252}_{-0.248}$	${0.854}_{- 0.268}^{+ 0.342}$ $0.854^{+0.342}_{-0.268}$
S-index semi-amplitude	k_{cyc, 2}	–	$U (0, 0.1)$ $\mathcal{U}\left(0, 0.1\right)$	${0.019}_{- 0.013}^{+ 0.019}$ $0.019^{+0.019}_{-0.013}$	${0.023}_{- 0.016}^{+ 0.025}$ $0.023^{+0.025}_{-0.016}$
RV zero-order correction	α₀	m s^-1	$N (μ_{lm}, 200 σ_{lm})$ $\mathcal{N}(\mu_\text{lm},200\sigma_\text{lm})$	${0.47}_{- 0.83}^{+ 0.85}$ $0.47^{+0.85}_{-0.83}$	${0.60}_{- 1.27}^{+ 1.25}$ $0.60^{+1.25}_{-1.27}$
FWHM zero-order correction	α₁	m s^-1	$N (μ_{lm}, 200 σ_{lm})$ $\mathcal{N}(\mu_\text{lm},200\sigma_\text{lm})$	${3.89}_{- 3.23}^{+ 3.28}$ $3.89^{+3.28}_{-3.23}$	${4.11}_{- 5.25}^{+ 5.05}$ $4.11^{+5.05}_{-5.25}$
S-index zero-order correction	α₂	–	$N (μ_{lm}, 200 σ_{lm})$ $\mathcal{N}(\mu_\text{lm},200\sigma_\text{lm})$	$0.050 \pm 0.048$ $0.050\pm 0.048$	${0.051}_{- 0.077}^{+ 0.075}$ $0.051^{+0.075}_{-0.077}$
Dataset parameters
ESPRESSO19 RV offset	O_1,0	m s^-1	$N (0, 5 σ_{0})$ $\mathcal{N}(0,5\sigma_0)$	$- 1.06 \pm 0.74$ $-1.06\pm 0.74$	$- {1.17}_{- 0.94}^{+ 0.93}$ $-1.17^{+0.93}_{-0.94}$
HIRES RV offset	O_2,0	m s^-1	$N (0, 5 σ_{0})$ $\mathcal{N}(0,5\sigma_0)$	${0.00}_{- 1.01}^{+ 1.00}$ $0.00^{+1.00}_{-1.01}$	–
HARPS RV offset	O_3,0	m s^-1	$N (0, 5 σ_{0})$ $\mathcal{N}(0,5\sigma_0)$	$- {0.05}_{- 1.12}^{+ 1.13}$ $-0.05^{+1.13}_{-1.12}$	–
ESPRESSO19 FWHM offset	O_1,1	m s^-1	$N (0, 5 σ_{1})$ $\mathcal{N}(0,5\sigma_1)$	$- {4.63}_{- 2.21}^{+ 2.30}$ $-4.63^{+2.30}_{-2.21}$	$- {5.04}_{- 3.20}^{+ 3.02}$ $-5.04^{+3.02}_{-3.20}$
HARPS FWHM offset	O_3,1	m s^-1	$N (0, 5 σ_{1})$ $\mathcal{N}(0,5\sigma_1)$	$- {0.19}_{- 4.10}^{+ 4.30}$ $-0.19^{+4.30}_{-4.10}$	–
ESPRESSO19 S-index offset	O_1,2	–	$N (0, 5 σ_{2})$ $\mathcal{N}(0,5\sigma_2)$	$(- {6.22}_{- 3.38}^{+ 3.44}) \times 10^{- 2}$ $\left(-6.22^{+3.44}_{-3.38}\right)\times 10^{-2}$	$(- {6.57}_{- 4.84}^{+ 4.55}) \times 10^{- 2}$ $\left(-6.57^{+4.55}_{-4.84}\right)\times 10^{-2}$
HIRES S-index offset	O_2,2	–	$N (0, 5 σ_{2})$ $\mathcal{N}(0,5\sigma_2)$	$(- {4.63}_{- 5.44}^{+ 5.39}) \times 10^{- 2}$ $\left(-4.63^{+5.39}_{-5.44}\right)\times 10^{-2}$	–
HARPS S-index offset	O_3,2	–	$N (0, 5 σ_{2})$ $\mathcal{N}(0,5\sigma_2)$	$({0.07}_{- 5.77}^{+ 6.09}) \times 10^{- 2}$ $\left(0.07^{+6.09}_{-5.77}\right)\times 10^{-2}$	–
ESPRESSO18 RV jitter	J_0,0	m s^-1	$\exp [N (\ln σ_{0}, \ln σ_{0})]$ $\exp[\mathcal{N}(\ln\sigma_0,\ln\sigma_0)]$	${1.82}_{- 0.35}^{+ 0.47}$ $1.82^{+0.47}_{-0.35}$	${1.82}_{- 0.36}^{+ 0.48}$ $1.82^{+0.48}_{-0.36}$
ESPRESSO19 RV jitter	J_1,0	m s^-1	$\exp [N (\ln σ_{0}, \ln σ_{0})]$ $\exp[\mathcal{N}(\ln\sigma_0,\ln\sigma_0)]$	${0.85}_{- 0.22}^{+ 0.21}$ $0.85^{+0.21}_{-0.22}$	${1.01}_{- 0.23}^{+ 0.20}$ $1.01^{+0.20}_{-0.23}$
HIRES RV jitter	J_2,0	m s^-1	$\exp [N (\ln σ_{0}, \ln σ_{0})]$ $\exp[\mathcal{N}(\ln\sigma_0,\ln\sigma_0)]$	${1.20}_{- 0.65}^{+ 0.71}$ $1.20^{+0.71}_{-0.65}$	–
HARPS RV jitter	J_3,0	m s^-1	$\exp [N (\ln σ_{0}, \ln σ_{0})]$ $\exp[\mathcal{N}(\ln\sigma_0,\ln\sigma_0)]$	${2.21}_{- 0.36}^{+ 0.43}$ $2.21^{+0.43}_{-0.36}$	–
ESPRESSO18 FWHM jitter	J_0,1	m s^-1	$U_{\log} (10^{- 3}, 10^{3})$ $\mathcal{U}_{\log}\left(10^{-3}, 10^{3}\right)$	${1.02}_{- 0.27}^{+ 0.34}$ $1.02^{+0.34}_{-0.27}$	${1.00}_{- 0.26}^{+ 0.34}$ $1.00^{+0.34}_{-0.26}$
ESPRESSO19 FWHM jitter	J_1,1	m s^-1	$U_{\log} (10^{- 3}, 10^{3})$ $\mathcal{U}_{\log}\left(10^{-3}, 10^{3}\right)$	${1.82}_{- 0.29}^{+ 0.34}$ $1.82^{+0.34}_{-0.29}$	${1.78}_{- 0.31}^{+ 0.35}$ $1.78^{+0.35}_{-0.31}$
HARPS FWHM jitter	J_3,1	m s^-1	$U_{\log} (10^{- 3}, 10^{3})$ $\mathcal{U}_{\log}\left(10^{-3}, 10^{3}\right)$	${4.25}_{- 0.62}^{+ 0.77}$ $4.25^{+0.77}_{-0.62}$	–
ESPRESSO18 S-index jitter	J_0,2	–	$U_{\log} (10^{- 3}, 10^{3})$ $\mathcal{U}_{\log}\left(10^{-3}, 10^{3}\right)$	$({1.27}_{- 0.45}^{+ 0.55}) \times 10^{- 2}$ $\left(1.27^{+0.55}_{-0.45}\right)\times 10^{-2}$	$({1.46}_{- 0.51}^{+ 0.58}) \times 10^{- 2}$ $\left(1.46^{+0.58}_{-0.51}\right)\times 10^{-2}$
ESPRESSO19 S-index jitter	J_1,2	–	$U_{\log} (10^{- 3}, 10^{3})$ $\mathcal{U}_{\log}\left(10^{-3}, 10^{3}\right)$	$({4.77}_{- 0.54}^{+ 0.62}) \times 10^{- 2}$ $\left(4.77^{+0.62}_{-0.54}\right)\times 10^{-2}$	$({4.73}_{- 0.65}^{+ 0.66}) \times 10^{- 2}$ $\left(4.73^{+0.66}_{-0.65}\right)\times 10^{-2}$
HIRES S-index jitter	J_2,2	–	$U_{\log} (10^{- 3}, 10^{3})$ $\mathcal{U}_{\log}\left(10^{-3}, 10^{3}\right)$	$({3.14}_{- 0.59}^{+ 0.75}) \times 10^{- 2}$ $\left(3.14^{+0.75}_{-0.59}\right)\times 10^{-2}$	–
HARPS S-index jitter	J_3,2	–	$U_{\log} (10^{- 3}, 10^{3})$ $\mathcal{U}_{\log}\left(10^{-3}, 10^{3}\right)$	$({0.43}_{- 0.27}^{+ 0.64}) \times 10^{- 2}$ $\left(0.43^{+0.64}_{-0.27}\right)\times 10^{-2}$	–
Stellar-activity hyperparameters
Timescale	τ	d	$U_{\log} (20, 10^{4})$ $\mathcal{U}_{\log}\left(20, 10^{4}\right)$	$277_{- 82}^{+ 109}$ $277^{+109}_{-82}$	$227_{- 109}^{+ 281}$ $227^{+281}_{-109}$
Period	P_rot	d	$U (40.1, 64.1)$ $\mathcal{U}(40.1,64.1)$	$48.7 \pm 0.3$ $48.7\pm 0.3$	${48.5}_{- 1.0}^{+ 0.6}$ $48.5^{+0.6}_{-1.0}$
Sinescale (harmonic complexity)	η	–	$U_{\log} (10^{- 2}, 10^{2})$ $\mathcal{U}_{\log}\left(10^{-2}, 10^{2}\right)$	${0.53}_{- 0.10}^{+ 0.13}$ $0.53^{+0.13}_{-0.10}$	${0.94}_{- 0.32}^{+ 0.78}$ $0.94^{+0.78}_{-0.32}$
RV amplitude	A₀	m s^-1	$U (- 10^{3}, 10^{3})$ $\mathcal{U}(-10^3,10^3)$	${1.45}_{- 0.26}^{+ 0.30}$ $1.45^{+0.30}_{-0.26}$	${2.21}_{- 0.69}^{+ 2.05}$ $2.21^{+2.05}_{-0.69}$
RV gradient amplitude	B₀	m s^-1 d^-1	$U (- 10^{3}, 10^{3})$ $\mathcal{U}(-10^3,10^3)$	${19.9}_{- 3.2}^{+ 4.0}$ $19.9^{+4.0}_{-3.2}$	${23.1}_{- 7.3}^{+ 23.3}$ $23.1^{+23.3}_{-7.3}$
FWHM amplitude	A₁	m s^-1	$U_{\log} (10^{- 3}, 10^{3})$ $\mathcal{U}_{\log}\left(10^{-3}, 10^{3}\right)$	${7.26}_{- 0.86}^{+ 1.13}$ $7.26^{+1.13}_{-0.86}$	${9.76}_{- 2.78}^{+ 9.10}$ $9.76^{+9.10}_{-2.78}$
S-index amplitude	A₂	m s^-1	$U_{\log} (10^{- 3}, 10^{3})$ $\mathcal{U}_{\log}\left(10^{-3}, 10^{3}\right)$	${0.106}_{- 0.012}^{+ 0.015}$ $0.106^{+0.015}_{-0.012}$	${0.133}_{- 0.042}^{+ 0.137}$ $0.133^{+0.137}_{-0.042}$

Notes. ^(w)Wrapped parameter. Reported uncertainties reflect the 16^th and the 84^th percentiles. Offsets are defined relative to ESPRESSO18. The standard deviation of measurements in physical quantity j is denoted σ_j.

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