The ESO SupJup Survey - X. A carbon isotope contrast in the young ROXs 12 system

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Table 3

Free parameters, prior ranges, and retrieval results for ROXs 12A and ROXs 12B.

Parameter	Description	Prior range		Retrieval results
		ROXs 12A	ROXs 12B	ROXs 12A	ROXs 12B
v_rad (km/s)	Radial velocity	U(−20,20)}		$- {5.46}_{- 0.03}^{+ 0.03}$ $Mathematical equation: $-5.46^{+0.03}_{-0.03}$$	$- {5.28}_{- 0.02}^{+ 0.02}$ $Mathematical equation: $-5.28^{+0.02}_{-0.02}$$
v sin i (km/s)	Projected rotational velocity	U(0,40)}		${8.37}_{- 0.05}^{+ 0.05}$ $Mathematical equation: $8.37^{+0.05}_{-0.05}$$	${2.14}_{- 0.16}^{+ 0.21}$ $Mathematical equation: $2.14^{+0.21}_{-0.16}$$
log g (cm/s²)	Surface gravity	G(4.1,0.2)	G(4.0,0.2)	${4.45}_{- 0.04}^{+ 0.04}$ $Mathematical equation: $4.45^{+0.04}_{-0.04}$$	${4.03}_{- 0.04}^{+ 0.04}$ $Mathematical equation: $4.03^{+0.04}_{-0.04}$$
ε_limb	Limb-darkening coefficient	U(0.2,1)}		${0.63}_{- 0.05}^{+ 0.05}$ $Mathematical equation: $0.63^{+0.05}_{-0.05}$$	${0.60}_{- 0.25}^{+ 0.21}$ $Mathematical equation: $0.60^{+0.21}_{-0.25}$$
\midrule
C/O	Carbon-to-oxygen ratio	U(0.1,1)}		${0.87}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $0.87^{+0.01}_{-0.01}$$	${0.54}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $0.54^{+0.01}_{-0.01}$$
[Fe/H]	Metallicity	U(−1,1)}		$- {0.06}_{- 0.03}^{+ 0.02}$ $Mathematical equation: $-0.06^{+0.02}_{-0.03}$$	$- {0.53}_{- 0.03}^{+ 0.03}$ $Mathematical equation: $-0.53^{+0.03}_{-0.03}$$
log ¹²CO/¹³CO	log₁₀ ratio of ¹²CO to ¹³CO	U(1,6)}		${1.89}_{- 0.05}^{+ 0.06}$ $Mathematical equation: $1.89^{+0.06}_{-0.05}$$	${1.74}_{- 0.07}^{+ 0.08}$ $Mathematical equation: $1.74^{+0.08}_{-0.07}$$
log H₂¹⁶O/H₂¹⁸O	log₁₀ ratio of H₂¹⁶O to H₂¹⁸O	U(1,6)}		${4.34}_{- 1.08}^{+ 0.90}$ $Mathematical equation: $4.34^{+0.90}_{-1.08}$$	${2.53}_{- 0.33}^{+ 1.17}$ $Mathematical equation: $2.53^{+1.17}_{-0.33}$$
\midrule
T₀ (K)	Temperature at P₀=10² bar	U(1e3,3e4)	U(1e3,1e4)	${27797.57}_{- 1282.16}^{+ 1064.09}$ $Mathematical equation: $27797.57^{+1064.09}_{-1282.16}$$	${3445.75}_{- 140.52}^{+ 160.55}$ $Mathematical equation: $3445.75^{+160.55}_{-140.52}$$
∇ T₀	Gradient at P₀=10² bar	U(0,0.4)}		${0.30}_{- 0.03}^{+ 0.03}$ $Mathematical equation: $0.30^{+0.03}_{-0.03}$$	${0.03}_{- 0.02}^{+ 0.03}$ $Mathematical equation: $0.03^{+0.03}_{-0.02}$$
∇ T₁	Gradient at P₁=10⁰ bar	U(0,0.4)}		${0.33}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $0.33^{+0.01}_{-0.01}$$	${0.11}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $0.11^{+0.01}_{-0.01}$$
∇ T₂	Gradient at P₂=10⁻² bar	U(0,0.4)}		${0.00}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $0.00^{+0.01}_{-0.01}$$	${0.06}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $0.06^{+0.01}_{-0.01}$$
∇ T₃	Gradient at P₃=10⁻⁴ bar	U(0,0.4)}		${0.36}_{- 0.02}^{+ 0.02}$ $Mathematical equation: $0.36^{+0.02}_{-0.02}$$	${0.02}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $0.02^{+0.01}_{-0.01}$$
∇ T₄	Gradient at P₄=10⁻⁶ bar	U(0,0.4)}		${0.15}_{- 0.08}^{+ 0.10}$ $Mathematical equation: $0.15^{+0.10}_{-0.08}$$	${0.26}_{- 0.09}^{+ 0.07}$ $Mathematical equation: $0.26^{+0.07}_{-0.09}$$
\midrule
r_k(λ_mid)	Veiling at 2166 nm	U(0,2)}		${0.17}_{- 0.03}^{+ 0.02}$ $Mathematical equation: $0.17^{+0.02}_{-0.03}$$	${0.02}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $0.02^{+0.01}_{-0.01}$$
T_disk (K)	Disk temperature	U(300,1500)}		${915.77}_{- 81.78}^{+ 97.46}$ $Mathematical equation: $915.77^{+97.46}_{-81.78}$$	${548.81}_{- 96.87}^{+ 114.11}$ $Mathematical equation: $548.81^{+114.11}_{-96.87}$$
log κ_cl,0 (cm²/g)	Opacity at cloud base	−	U(−10,3)	−	$- {5.76}_{- 1.93}^{+ 2.24}$ $Mathematical equation: $-5.76^{+2.24}_{-1.93}$$
log P_cl,0 (bar)	Cloud base pressure	−	U(−6,3)	−	$- {0.68}_{- 2.07}^{+ 1.71}$ $Mathematical equation: $-0.68^{+1.71}_{-2.07}$$
f_sed	Cloud decay power	−	U(0,20)	−	${11.89}_{- 4.92}^{+ 3.99}$ $Mathematical equation: $11.89^{+3.99}_{-4.92}$$
\midrule
log a	GP amplitude	U(−1,1)}		${0.95}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $0.95^{+0.01}_{-0.01}$$	${0.17}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $0.17^{+0.01}_{-0.01}$$
log l (nm)	GP length-scale	U(−3,0)}		$- {1.52}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $-1.52^{+0.01}_{-0.01}$$	$- {2.01}_{- 0.01}^{+ 0.01}$ $Mathematical equation: $-2.01^{+0.01}_{-0.01}$$

Notes. The three columns on the left show the parameter notation, description, and prior ranges. U represents a uniform prior within the given range, whereas G stands for a Gaussian prior with the given mean and standard deviation. The retrieval results for ROXs 12A and ROXs 12B, including their 1-σ credible interval, are shown in the two columns on the right.

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