Mitigating stellar radial velocity jitter using orthogonal activity indices and a time-aware neural network

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Volume 710 (June 2026)

A&A, 710 (2026) A194

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Table 4

Comparison of orbital parameters for TZ Ari b.

Parameter	Prior	Keplerian	`CANSTAR`	GP
P (d)	𝒰(650, 850)	${808.28}_{- 17.57}^{+ 21.37}$ $Mathematical equation: $808.28_{ - 17.57}^{ + 21.37}$$	${789.92}_{- 9.27}^{+ 12.17}$ $Mathematical equation: $789.92_{ - 9.27}^{ + 12.17}$$	${780.61}_{- 11.66}^{+ 11.70}$ $Mathematical equation: $780.61_{ - 11.66}^{ + 11.70}$$
K (m s⁻¹)	𝒰(0, 40)	${22.09}_{- 2.97}^{+ 3.82}$ $Mathematical equation: $22.09_{ - 2.97}^{ + 3.82}$$	${19.89}_{- 1.98}^{+ 3.13}$ $Mathematical equation: $19.89_{ - 1.98}^{ + 3.13}$$	${19.91}_{- 2.59}^{+ 4.08}$ $Mathematical equation: $19.91_{ - 2.59}^{ + 4.08}$$
e	𝒰(−1, 1) ^(a)	${0.55}_{- 0.07}^{+ 0.07}$ $Mathematical equation: $0.55_{ - 0.07}^{ + 0.07}$$	${0.47}_{- 0.05}^{+ 0.05}$ $Mathematical equation: $0.47_{ - 0.05}^{ + 0.05}$$	${0.48}_{- 0.05}^{+ 0.06}$ $Mathematical equation: $0.48_{ - 0.05}^{ + 0.06}$$
ω (deg)	𝒰(−1, 1) ^(a)	$- {46.58}_{- 13.74}^{+ 12.69}$ $Mathematical equation: $ - 46.58_{ - 13.74}^{ + 12.69}$$	$- {33.63}_{- 10.86}^{+ 9.45}$ $Mathematical equation: $ - 33.63_{ - 10.86}^{ + 9.45}$$	$- {38.16}_{- 12.35}^{+ 10.97}$ $Mathematical equation: $ - 38.16_{ - 12.35}^{ + 10.97}$$
M₀ (deg)	𝒰(0, 360)	${122.30}_{- 70.01}^{+ 78.70}$ $Mathematical equation: $122.30_{ - 70.01}^{ + 78.70}$$	${42.31}_{- 39.45}^{+ 49.63}$ $Mathematical equation: $42.31_{ - 39.45}^{ + 49.63}$$	${8.99}_{- 50.68}^{+ 49.86}$ $Mathematical equation: $8.99_{ - 50.68}^{ + 49.86}$$
α (m s⁻¹)	𝒰(0, 30)	–	${12.60}_{- 0.98}^{+ 0.89}$ $Mathematical equation: $12.60_{ - 0.98}^{ + 0.89}$$	–
S_GP	𝒩(0.01, 0.005)	–	–	${0.0145}_{- 0.0036}^{+ 0.0040}$ $Mathematical equation: $0.0145_{ - 0.0036}^{ + 0.0040}$$
Q_GP	𝒰(5, 4473) ^(b)	–	–	${2347.84}_{- 1099.21}^{+ 1353.13}$ $Mathematical equation: $2347.84_{ - 1099.21}^{ + 1353.13}$$
ω_GP	𝒩(3.2, 0.01)	–	–	${3.2108}_{- 0.0016}^{+ 0.0015}$ $Mathematical equation: $3.2108_{ - 0.0016}^{ + 0.0015}$$
σ (m s⁻¹)	𝒧𝒰(0.1, 30)	${9.87}_{- 0.82}^{+ 0.92}$ $Mathematical equation: $9.87_{ - 0.82}^{ + 0.92}$$	${5.31}_{- 0.47}^{+ 0.55}$ $Mathematical equation: $5.31_{ - 0.47}^{ + 0.55}$$	${4.31}_{- 0.46}^{+ 0.55}$ $Mathematical equation: $4.31_{ - 0.46}^{ + 0.55}$$
γ (m s⁻¹)	𝒰(−10, 10)	$- {1.48}_{- 1.25}^{+ 1.27}$ $Mathematical equation: $ - 1.48_{ - 1.25}^{ + 1.27}$$	$- {0.88}_{- 0.79}^{+ 0.88}$ $Mathematical equation: $ - 0.88_{ - 0.79}^{ + 0.88}$$	$- {2.66}_{- 0.76}^{+ 0.94}$ $Mathematical equation: $ - 2.66_{ - 0.76}^{ + 0.94}$$

Notes. Values derived for CARMENES data modelling with the Keplerian alone or combining the fit with CANSTAR or with a GP fit. The prior column lists the probability distributions used in our MCMC analysis, where 𝒰(a, b) denotes a uniform distribution and 𝒧𝒰(a, b) a log-uniform distribution between a and b. ^(a)Prior applied to $\sqrt{e}$ $Mathematical equation: $\sqrt e $$ cos ω and $\sqrt{e}$ $Mathematical equation: $\sqrt e $$ sin ω. ^(b)Upper limit prior so we sample lifetimes up to two times the time baseline of the observations.

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