A planetary system with a sub-Neptune planet in the habitable zone of TOI-2093

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Table A.3

Priors and posteriors of the joint transit and RV fit of TOI-2093.

Parameter	Prior	Posterior		Unit	Description
		e = 0	Free e
Stellar parameter
ρ_⋆	𝒩(2.71097, 0.45015)	${2.85}_{- 0.46}^{+ 0.49}$ $\[2.85_{-0.46}^{+0.49}\]$	${2.70}_{- 0.45}^{+ 0.43}$ $\[2.70_{-0.45}^{+0.43}\]$	g cm⁻³	Stellar density
Photometric parameters
μ_TESS	𝒩(0, 0.1)	. . .		. . .	The offset relative flux for TESS
σ_TESS	ℒ 𝒰(10⁻⁶, 0.04)	. . .		. . .	The jitter for the photometric instrument
q1_TESS	𝒰(0, 1)	${0.61}_{- 0.25}^{+ 0.24}$ $\[0.61_{-0.25}^{+0.24}\]$	${0.59}_{- 0.26}^{+ 0.25}$ $\[0.59_{-0.26}^{+0.25}\]$	. . .	Limb-darkening for photometric instrument
q2_TESS	𝒰(0, 1)	0.44 ± 0.29	${0.42}_{- 0.25}^{+ 0.28}$ $\[0.42_{-0.25}^{+0.28}\]$	. . .	Limb-darkening for photometric instrument
D_TESS	1 (fixed)	. . .		. . .	The dilution factor
RV instrumental parameters
γ	𝒰(−10, 10)	$- {0.01}_{- 0.57}^{+ 0.55}$ $\[-0.01_{-0.57}^{+0.55}\]$	$- {0.07}_{- 0.59}^{+ 0.52}$ $\[-0.07_{-0.59}^{+0.52}\]$	m s⁻¹	RV zero point for CARMENES
σ	ℒ 𝒰(0.001, 5)	${0.41}_{- 0.40}^{+ 2.22}$ $\[0.41_{-0.40}^{+2.22}\]$	${0.39}_{- 0.37}^{+ 2.02}$ $\[0.39_{-0.37}^{+2.02}\]$	m s⁻¹	A jitter added in quadrature
RV dSHO GP parameters
GP_σ	𝒰(0.00, 15.00)	${5.0}_{- 1.2}^{+ 1.1}$ $\[5.0_{-1.2}^{+1.1}\]$	${5.0}_{- 1.1}^{+ 1.2}$ $\[5.0_{-1.1}^{+1.2}\]$	m s⁻¹	Standard deviation of the GP
GP_Q₀	𝒰(2.00, 20.00)	${8.8}_{- 4.0}^{+ 6.7}$ $\[8.8_{-4.0}^{+6.7}\]$	${9.9}_{- 5.0}^{+ 5.7}$ $\[9.9_{-5.0}^{+5.7}\]$	. . .	The quality factor
GP_{star rotation}	𝒩(19.60, 1.20)	${19.57}_{- 0.39}^{+ 0.35}$ $\[19.57_{-0.39}^{+0.35}\]$	${19.46}_{- 0.35}^{+ 0.38}$ $\[19.46_{-0.35}^{+0.38}\]$	d	The primary period of variability
GP_f	𝒰(0.00, 1.00)	${0.67}_{- 0.26}^{+ 0.22}$ $\[0.67_{-0.26}^{+0.22}\]$	${0.64}_{- 0.27}^{+ 0.23}$ $\[0.64_{-0.27}^{+0.23}\]$	. . .	The fractional amplitude of the secondary mode
GP_dQ	𝒰(0.10, 30.00)	${15.4}_{- 10.0}^{+ 9.7}$ $\[15.4_{-10.0}^{+9.7}\]$	${14.9}_{- 8.8}^{+ 9.8}$ $\[14.9_{-8.8}^{+9.8}\]$	. . .	The difference between the quality factors
Planet b fit parameters
P	𝒰(12, 13.4)	12.836 ± 0.021	${12.801}_{- 0.042}^{+ 0.036}$ $\[12.801_{-0.042}^{+0.036}\]$	d	Period
T₀ (BJD–2,457,000)	𝒰(2317, 2330)	${2320.53}_{- 0.50}^{+ 0.43}$ $\[2320.53_{-0.50}^{+0.43}\]$	${2320.74}_{- 0.48}^{+ 0.57}$ $\[2320.74_{-0.48}^{+0.57}\]$	d	Time of periastron passage
e	𝒰(0, 1)	0 (fixed)	${0.17}_{- 0.12}^{+ 0.27}$ $\[0.17_{-0.12}^{+0.27}\]$	. . .	Orbital eccentricity
ω	𝒰(0, 360)	90 (fixed)	$119_{- 67}^{+ 146}$ $\[119_{-67}^{+146}\]$	deg	Periastron angle
K	𝒰(0, 15)	${3.52}_{- 0.84}^{+ 0.79}$ $\[3.52_{-0.84}^{+0.79}\]$	${3.71}_{- 0.85}^{+ 1.01}$ $\[3.71_{-0.85}^{+1.01}\]$	m s⁻¹	RV semi-amplitude
Planet c fit parameters
P	𝒩(53.81, 0.01)	53.81149 ± 0.00017	${53.81149}_{- 0.00016}^{+ 0.00019}$ $\[53.81149_{-0.00016}^{+0.00019}\]$	d	Period
T₀ (BJD–2,457,000)	𝒩(1751.62, 0.01)	${1751.6122}_{- 0.0042}^{+ 0.0040}$ $\[1751.6122_{-0.0042}^{+0.0040}\]$	${1751.6124}_{- 0.0048}^{+ 0.0044}$ $\[1751.6124_{-0.0048}^{+0.0044}\]$	d	Central transit time
e	𝒰(0, 1)	0 (fixed)	0.23 ± 0.10	. . .	Orbital eccentricity
ω	𝒰(0, 360)	90 (fixed)	148 ± 34	deg	Periastron angle
K	𝒰(0, 15)	${3.26}_{- 0.80}^{+ 0.74}$ $\[3.26_{-0.80}^{+0.74}\]$	${3.83}_{- 0.81}^{+ 0.78}$ $\[3.83_{-0.81}^{+0.78}\]$	m s⁻¹	RV semi-amplitude
r₁	𝒰(0, 1)	${0.706}_{- 0.063}^{+ 0.047}$ $\[0.706_{-0.063}^{+0.047}\]$	0.57 ± 0.15	. . .	Parameterization for p and b
r₂	𝒰(0, 1)	${0.0290}_{- 0.0011}^{+ 0.0010}$ $\[0.0290_{-0.0011}^{+0.0010}\]$	${0.0282}_{- 0.0011}^{+ 0.0013}$ $\[0.0282_{-0.0011}^{+0.0013}\]$	. . .	Parameterization for p and b

Notes. The prior labels of 𝒩, 𝒰, and ℒ 𝒰 represent normal, uniform and log-uniform distributions, respectively. The jitter was added in quadrature to the error bars of the instrument. The dilution factor was fixed to one for all TESS sectors. The offset between the different TESS sectors was modeled with a normal prior 𝒩(0, 1), and the upper limit on the photometric jitter term was set to three times the error bars of each individual sector following a log-uniform distribution.

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