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Table B.1

Priors used for the joint LC and RV fit of TOI-1238.

Parameter Prior Unit Description
Stellar parameter
ρ (4254.2, 578.2) kg m−3 Stellar density
Photometric parameters
γTESS, S14 (0, 0.1) ppm The offset relative flux for TESS
γTESS, S15 (0, 0.1) ppm The offset relative flux for TESS
γTESS, S21 (0, 0.1) ppm The offset relative flux for TESS
γTESS, S22 (0, 0.1) ppm The offset relative flux for TESS
σTESS, S14 (1e−6, 0.03) ppm A jitter added in quadrature to the error bars of instrument
σTESS, S15 (1e−6, 0.02) ppm A jitter added in quadrature to the error bars of instrument
σTESS, S21 (1e−6, 0.02) ppm A jitter added in quadrature to the error bars of instrument
σTESS, S22 (1e−6, 0.03) ppm A jitter added in quadrature to the error bars of instrument
q1TESS (0, 1) ... Limb-darkening for photometric instrument
q2TESS (0, 1) ... Limb-darkening for photometric instrument
DTESS 1 (fixed) ... The dilution factor for the photometric instrument.
RV parameters
γ (-100, 100) m s−1 RV zero point for CARMENES
σ (0.001, 10) m s−1 A jitter added in quadrature
GP parameters
σGP,RV (0.01, 50) m s−1 Amplitude of the GP for the RVs
αGP,RV (1e−8, 1) d−2 Inverse (squared) length-scale of the external parameter
ΓGP,RV (1e−8, 10) ... Amplitude of the sine-part of the kernel
Prot, GP,RV (20, 80) d Period of the quasi-periodic kernel
Planet b parameters
P (0.764, 0.001) d Period
t0 (BJD-2,457,000) (1684.1, 0.01) d Time of periastron passage
e 0 (fixed) ... Orbital eccentricity
ω 90 (fixed) deg Periastron angle
K (0, 8) m s−1 RV semi-amplitude
r1 (0, 1) ... Parameterization for p and b
r2 (0, 1) ... Parameterization for p and b
Planet c parameters
P (3.294, 0.001) d Period
t0 (BJD-2,457,000) (1707.34, 0.01) d Time of periastron passage
e 0 (fixed) ... Orbital eccentricity
ω 90 (fixed) deg Periastron angle
K (0, 8) m s−1 RV semi-amplitude
r1 (0, 1) ... Parameterization for p and b
r2 (0, 1) ... Parameterization for p and b
External companion parameters
P (400, 1500) d Period
t0 (BJD-2,457,000) (1900, 3000) d Time of periastron passage
e 0 (fixed) ... Orbital eccentricity
ω 90 (fixed) deg Periastron angle
K (0, 300) m s−1 RV semi-amplitude

Notes. The prior labels of , , , and represent normal, uniform, Jeffreys, and log-uniform distribution, respectively. The error on the density of the star comes from the stellar mass and radius errors. The upper limit on the photometric jitter term corresponds to the dispersion of the data.

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