The ESO SupJup Survey - VIII. Chemical fingerprints of young L dwarf twins

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Volume 698 (May 2025)

A&A, 698 (2025) A252

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Table 2

Free parameters, prior ranges, and retrieval results for 2M0355 and 2M1425.

Parameter	Description	Prior range	2M0355		2M1425
			Free	Equ	Free	Equ
v_rad (km/s)	Radial velocity	𝒰(2,20)	${13.25}_{- 0.01}^{+ 0.01}$ $\[13.25_{-0.01}^{+0.01}\]$	${13.25}_{- 0.01}^{+ 0.01}$ $\[13.25_{-0.01}^{+0.01}\]$	${5.54}_{- 0.05}^{+ 0.05}$ $\[5.54_{-0.05}^{+0.05}\]$	${5.54}_{- 0.06}^{+ 0.06}$ $\[5.54_{-0.06}^{+0.06}\]$
v sin i (km/s)	Projected rotational velocity	𝒰(0,40)	${3.04}_{- 0.08}^{+ 0.08}$ $\[3.04_{-0.08}^{+0.08}\]$	${3.06}_{- 0.10}^{+ 0.10}$ $\[3.06_{-0.10}^{+0.10}\]$	${31.57}_{- 0.23}^{+ 0.19}$ $\[31.57_{-0.23}^{+0.19}\]$	${31.73}_{- 0.29}^{+ 0.31}$ $\[31.73_{-0.29}^{+0.31}\]$
log g (cm/s²)	Surface gravity	𝒰(3,5)	${4.75}_{- 0.03}^{+ 0.03}$ $\[4.75_{-0.03}^{+0.03}\]$	${4.73}_{- 0.04}^{+ 0.04}$ $\[4.73_{-0.04}^{+0.04}\]$	${4.98}_{- 0.01}^{+ 0.01}$ $\[4.98_{-0.01}^{+0.01}\]$	${4.88}_{- 0.02}^{+ 0.03}$ $\[4.88_{-0.02}^{+0.03}\]$
ϵ_limb	Limb-darkening coefficient	𝒰(0.2,1)	${0.72}_{- 0.16}^{+ 0.14}$ $\[0.72_{-0.16}^{+0.14}\]$	${0.73}_{- 0.21}^{+ 0.16}$ $\[0.73_{-0.21}^{+0.16}\]$	${0.74}_{- 0.05}^{+ 0.04}$ $\[0.74_{-0.05}^{+0.04}\]$	${0.76}_{- 0.06}^{+ 0.06}$ $\[0.76_{-0.06}^{+0.06}\]$

log H₂O	log₁₀ VMR of H₂O	𝒰(−12,−1)	$- {3.00}_{- 0.03}^{+ 0.03}$ $\[-3.00_{-0.03}^{+0.03}\]$	$- {3.02}_{- 0.04}^{+ 0.06}$ $\[-3.02_{-0.04}^{+0.06}\]$	$- {3.20}_{- 0.01}^{+ 0.01}$ $\[-3.20_{-0.01}^{+0.01}\]$	$- {3.26}_{- 0.01}^{+ 0.01}$ $\[-3.26_{-0.01}^{+0.01}\]$
log ¹²CO	log₁₀ VMR of ¹²CO	𝒰(−12,−1)	$- {2.74}_{- 0.03}^{+ 0.03}$ $\[-2.74_{-0.03}^{+0.03}\]$	$- {2.75}_{- 0.05}^{+ 0.04}$ $\[-2.75_{-0.05}^{+0.04}\]$	$- {2.92}_{- 0.01}^{+ 0.01}$ $\[-2.92_{-0.01}^{+0.01}\]$	$- {3.05}_{- 0.01}^{+ 0.03}$ $\[-3.05_{-0.01}^{+0.03}\]$
log ¹³CO	log₁₀ VMR of ¹³CO	𝒰(−12,−1)	$- {4.72}_{- 0.04}^{+ 0.04}$ $\[-4.72_{-0.04}^{+0.04}\]$	$- {4.74}_{- 0.07}^{+ 0.08}$ $\[-4.74_{-0.07}^{+0.08}\]$	$- {4.96}_{- 0.04}^{+ 0.04}$ $\[-4.96_{-0.04}^{+0.04}\]$	$- {5.03}_{- 0.09}^{+ 0.09}$ $\[-5.03_{-0.09}^{+0.09}\]$
log C¹⁸O	log₁₀ VMR of C¹⁸O	𝒰(−12,−1)	$- {7.96}_{- 1.91}^{+ 1.60}$ $\[-7.96_{-1.91}^{+1.60}\]$	$- {10.69}_{- 2.50}^{+ 3.47}$ $\[-10.69_{-2.50}^{+3.47}\]$	$- {9.22}_{- 1.31}^{+ 1.38}$ $\[-9.22_{-1.31}^{+1.38}\]$	$- {10.94}_{- 1.71}^{+ 1.59}$ $\[-10.94_{-1.71}^{+1.59}\]$
log C¹⁷O	log₁₀ VMR of C¹⁷O	𝒰(−12,−1)	$- {9.05}_{- 1.52}^{+ 1.39}$ $\[-9.05_{-1.52}^{+1.39}\]$	$- {9.93}_{- 2.63}^{+ 2.25}$ $\[-9.93_{-2.63}^{+2.25}\]$	$- {8.44}_{- 1.40}^{+ 1.18}$ $\[-8.44_{-1.40}^{+1.18}\]$	$- {9.27}_{- 3.14}^{+ 1.67}$ $\[-9.27_{-3.14}^{+1.67}\]$
log CH₄	log₁₀ VMR of CH₄	𝒰(−12,−1)	$- {9.30}_{- 1.19}^{+ 1.14}$ $\[-9.30_{-1.19}^{+1.14}\]$	$- {5.95}_{- 0.03}^{+ 0.05}$ $\[-5.95_{-0.03}^{+0.05}\]$	$- {5.35}_{- 0.08}^{+ 0.05}$ $\[-5.35_{-0.08}^{+0.05}\]$	$- {6.50}_{- 0.02}^{+ 0.03}$ $\[-6.50_{-0.02}^{+0.03}\]$
log NH₃	log₁₀ VMR of NH₃	𝒰(−12,−1)	$- {8.98}_{- 1.26}^{+ 1.13}$ $\[-8.98_{-1.26}^{+1.13}\]$	$- {6.34}_{- 0.02}^{+ 0.02}$ $\[-6.34_{-0.02}^{+0.02}\]$	$- {6.49}_{- 0.56}^{+ 0.25}$ $\[-6.49_{-0.56}^{+0.25}\]$	$- {6.46}_{- 0.01}^{+ 0.01}$ $\[-6.46_{-0.01}^{+0.01}\]$
log HCN	log₁₀ VMR of HCN	𝒰(−12,−1)	$- {8.70}_{- 1.54}^{+ 1.76}$ $\[-8.70_{-1.54}^{+1.76}\]$	$- {7.52}_{- 0.02}^{+ 0.02}$ $\[-7.52_{-0.02}^{+0.02}\]$	$- {8.22}_{- 1.19}^{+ 1.20}$ $\[-8.22_{-1.19}^{+1.20}\]$	$- {7.42}_{- 0.02}^{+ 0.01}$ $\[-7.42_{-0.02}^{+0.01}\]$
log HF	log₁₀ VMR of HF	𝒰(−12,−1)	$- {6.96}_{- 0.06}^{+ 0.06}$ $\[-6.96_{-0.06}^{+0.06}\]$	$- {6.77}_{- 0.04}^{+ 0.04}$ $\[-6.77_{-0.04}^{+0.04}\]$	$- {7.09}_{- 0.04}^{+ 0.04}$ $\[-7.09_{-0.04}^{+0.04}\]$	$- {7.13}_{- 0.01}^{+ 0.04}$ $\[-7.13_{-0.01}^{+0.04}\]$
log H₂S	log₁₀ VMR of H₂S	𝒰(−12,−1)	$- {4.15}_{- 0.07}^{+ 0.06}$ $\[-4.15_{-0.07}^{+0.06}\]$	$- {4.06}_{- 0.04}^{+ 0.04}$ $\[-4.06_{-0.04}^{+0.04}\]$	$- {9.00}_{- 1.27}^{+ 1.30}$ $\[-9.00_{-1.27}^{+1.30}\]$	$- {4.48}_{- 0.01}^{+ 0.03}$ $\[-4.48_{-0.01}^{+0.03}\]$
log $H_{2}^{18} O$ $\[\mathrm{H}_{2}^{18} \mathrm{O}\]$	log₁₀ VMR of $H_{2}^{18} O$ $\[\mathrm{H}_{2}^{18} \mathrm{O}\]$	𝒰(−12,−1)	$- {7.34}_{- 3.06}^{+ 1.51}$ $\[-7.34_{-3.06}^{+1.51}\]$	$- {10.94}_{- 2.49}^{+ 3.44}$ $\[-10.94_{-2.49}^{+3.44}\]$	$- {5.90}_{- 3.06}^{+ 0.20}$ $\[-5.90_{-3.06}^{+0.20}\]$	$- {11.15}_{- 1.69}^{+ 1.60}$ $\[-11.15_{-1.69}^{+1.60}\]$

C/O	Carbon-to-oxygen ratio	𝒰(0,1)	${0.65}_{- 0.01}^{+ 0.01}$ $\[0.65_{-0.01}^{+0.01}\]$	${0.52}_{- 0.00}^{+ 0.00}$ $\[0.52_{-0.00}^{+0.00}\]$	${0.66}_{- 0.00}^{+ 0.00}$ $\[0.66_{-0.00}^{+0.00}\]$	${0.57}_{- 0.01}^{+ 0.00}$ $\[0.57_{-0.01}^{+0.00}\]$
[Fe/H] or [C/H]	Metallicity	𝒰(−1.5,−1.5)	${0.58}_{- 0.03}^{+ 0.03}$ $\[0.58_{-0.03}^{+0.03}\]$	${0.60}_{- 0.04}^{+ 0.04}$ $\[0.60_{-0.04}^{+0.04}\]$	${0.40}_{- 0.01}^{+ 0.01}$ $\[0.40_{-0.01}^{+0.01}\]$	${0.26}_{- 0.01}^{+ 0.01}$ $\[0.26_{-0.01}^{+0.01}\]$
log ¹²C/¹³C	log₁₀ ratio of ¹²C to ¹³C	𝒰(1,12)	${1.98}_{- 0.03}^{+ 0.03}$ $\[1.98_{-0.03}^{+0.03}\]$	${1.97}_{- 0.04}^{+ 0.04}$ $\[1.97_{-0.04}^{+0.04}\]$	${2.04}_{- 0.04}^{+ 0.04}$ $\[2.04_{-0.04}^{+0.04}\]$	${1.99}_{- 0.05}^{+ 0.05}$ $\[1.99_{-0.05}^{+0.05}\]$
log ¹⁶O/¹⁷O	log₁₀ ratio of ¹⁶O to ¹⁷O	𝒰(1,12)	${6.31}_{- 1.40}^{+ 1.53}$ $\[6.31_{-1.40}^{+1.53}\]$	${8.03}_{- 2.21}^{+ 2.19}$ $\[8.03_{-2.21}^{+2.19}\]$	${5.52}_{- 1.17}^{+ 1.39}$ $\[5.52_{-1.17}^{+1.39}\]$	${6.50}_{- 2.57}^{+ 2.86}$ $\[6.50_{-2.57}^{+2.86}\]$
log ¹⁶O/¹⁸O	log₁₀ ratio of ¹⁶O to ¹⁸O	𝒰(1,12)	${4.34}_{- 1.51}^{+ 3.09}$ $\[4.34_{-1.51}^{+3.09}\]$	${3.20}_{- 0.20}^{+ 3.30}$ $\[3.20_{-0.20}^{+3.30}\]$	${2.71}_{- 0.20}^{+ 3.05}$ $\[2.71_{-0.20}^{+3.05}\]$	${5.99}_{- 2.59}^{+ 3.01}$ $\[5.99_{-2.59}^{+3.01}\]$

T₀ (K)	Temperature at P₀ = 10² bar	𝒰(1000,4000)	${2399.23}_{- 93.91}^{+ 113.53}$ $\[2399.23_{-93.91}^{+113.53}\]$	${2701.89}_{- 144.17}^{+ 150.57}$ $\[2701.89_{-144.17}^{+150.57}\]$	${3833.87}_{- 59.62}^{+ 62.89}$ $\[3833.87_{-59.62}^{+62.89}\]$	${3963.03}_{- 41.09}^{+ 24.85}$ $\[3963.03_{-41.09}^{+24.85}\]$
∇T₀	Gradient at P₀ = 10² bar	𝒰(0,0.4)	${0.19}_{- 0.10}^{+ 0.09}$ $\[0.19_{-0.10}^{+0.09}\]$	${0.02}_{- 0.02}^{+ 0.03}$ $\[0.02_{-0.02}^{+0.03}\]$	${0.28}_{- 0.07}^{+ 0.06}$ $\[0.28_{-0.07}^{+0.06}\]$	${0.17}_{- 0.09}^{+ 0.11}$ $\[0.17_{-0.09}^{+0.11}\]$
∇T₁	Gradient at P₁ = 10⁰ bar	𝒰(0,0.4)	${0.24}_{- 0.02}^{+ 0.02}$ $\[0.24_{-0.02}^{+0.02}\]$	${0.15}_{- 0.01}^{+ 0.01}$ $\[0.15_{-0.01}^{+0.01}\]$	${0.26}_{- 0.05}^{+ 0.05}$ $\[0.26_{-0.05}^{+0.05}\]$	${0.37}_{- 0.02}^{+ 0.02}$ $\[0.37_{-0.02}^{+0.02}\]$
∇T₂	Gradient at P₂ = 10⁻² bar	𝒰(0,0.4)	${0.04}_{- 0.00}^{+ 0.00}$ $\[0.04_{-0.00}^{+0.00}\]$	${0.04}_{- 0.00}^{+ 0.00}$ $\[0.04_{-0.00}^{+0.00}\]$	${0.05}_{- 0.01}^{+ 0.01}$ $\[0.05_{-0.01}^{+0.01}\]$	${0.05}_{- 0.00}^{+ 0.00}$ $\[0.05_{-0.00}^{+0.00}\]$
∇T₃	Gradient at P₃ = 10⁻⁴ bar	𝒰(0,0.4)	${0.05}_{- 0.00}^{+ 0.00}$ $\[0.05_{-0.00}^{+0.00}\]$	${0.05}_{- 0.00}^{+ 0.00}$ $\[0.05_{-0.00}^{+0.00}\]$	${0.08}_{- 0.00}^{+ 0.00}$ $\[0.08_{-0.00}^{+0.00}\]$	${0.09}_{- 0.00}^{+ 0.00}$ $\[0.09_{-0.00}^{+0.00}\]$
∇T₄	Gradient at P₄ = 10⁻⁶ bar	𝒰(0,0.4)	${0.15}_{- 0.02}^{+ 0.03}$ $\[0.15_{-0.02}^{+0.03}\]$	${0.22}_{- 0.03}^{+ 0.03}$ $\[0.22_{-0.03}^{+0.03}\]$	${0.29}_{- 0.01}^{+ 0.01}$ $\[0.29_{-0.01}^{+0.01}\]$	${0.28}_{- 0.01}^{+ 0.01}$ $\[0.28_{-0.01}^{+0.01}\]$

log κ_cl,0 (cm²/g)	Opacity at cloud base	𝒰(−10,3)	$- {5.78}_{- 2.12}^{+ 2.24}$ $\[-5.78_{-2.12}^{+2.24}\]$	$- {4.88}_{- 2.62}^{+ 2.90}$ $\[-4.88_{-2.62}^{+2.90}\]$	$- {4.17}_{- 1.82}^{+ 1.83}$ $\[-4.17_{-1.82}^{+1.83}\]$	$- {5.27}_{- 2.55}^{+ 2.66}$ $\[-5.27_{-2.55}^{+2.66}\]$
log P_cl,0 (bar)	Cloud base pressure	𝒰(−6,3)	$- {2.27}_{- 1.88}^{+ 2.03}$ $\[-2.27_{-1.88}^{+2.03}\]$	$- {2.09}_{- 2.09}^{+ 2.64}$ $\[-2.09_{-2.09}^{+2.64}\]$	$- {1.45}_{- 2.32}^{+ 2.52}$ $\[-1.45_{-2.32}^{+2.52}\]$	$- {1.82}_{- 2.20}^{+ 2.44}$ $\[-1.82_{-2.20}^{+2.44}\]$
f_sed	Cloud decay power	𝒰(0,20)	${11.35}_{- 4.14}^{+ 3.92}$ $\[11.35_{-4.14}^{+3.92}\]$	${10.54}_{- 5.26}^{+ 4.79}$ $\[10.54_{-5.26}^{+4.79}\]$	${8.30}_{- 4.08}^{+ 4.60}$ $\[8.30_{-4.08}^{+4.60}\]$	${11.48}_{- 5.56}^{+ 4.67}$ $\[11.48_{-5.56}^{+4.67}\]$
log a	GP amplitude	𝒰(−1,1)	${0.28}_{- 0.00}^{+ 0.00}$ $\[0.28_{-0.00}^{+0.00}\]$	${0.28}_{- 0.00}^{+ 0.00}$ $\[0.28_{-0.00}^{+0.00}\]$	${0.14}_{- 0.00}^{+ 0.00}$ $\[0.14_{-0.00}^{+0.00}\]$	${0.14}_{- 0.00}^{+ 0.00}$ $\[0.14_{-0.00}^{+0.00}\]$
log l (nm)	GP length-scale	𝒰(−3,0)	$- {1.76}_{- 0.00}^{+ 0.00}$ $\[-1.76_{-0.00}^{+0.00}\]$	$- {1.76}_{- 0.00}^{+ 0.00}$ $\[-1.76_{-0.00}^{+0.00}\]$	$- {1.91}_{- 0.01}^{+ 0.01}$ $\[-1.91_{-0.01}^{+0.01}\]$	$- {1.91}_{- 0.01}^{+ 0.01}$ $\[-1.91_{-0.01}^{+0.01}\]$

χ²	χ² of the best-fit model		49.78	49.85	17.43	17.53
ln ℒ_free − ln ℒ_equ	Log-likelihood (Eq. (7)) difference (free vs. equ)		11.88		33.01
ln B_m (σ)	Bayes factor (significance) betw. free vs. equ		−6.66 (−4.07 σ)		−2.67 (−2.82 σ)

Notes. The three columns on the left show the parameter notation, description and prior ranges. 𝒰 denotes a uniform distribution within the given range. The four rightmost columns show the retrieval results for 2M0355 and 2M1425, including their 1 σ errors, using the free and equilibrium (equ) chemistry setup. The gray cursive values were not retrieved as free parameters, but determined from the results. The abundances of the equilibrium chemistry retrievals are given at the pressure where the integrated emission contribution is maximal. The shown ¹⁶O/¹⁸O ratio for the free chemistry setup is based on H₂O. The logarithm of the Bayes factor ln B_m and significance σ are determined from the ln 𝒵 (nested importance sampling global log-evidence, outputted by PyMultiNest) with respect to the free chemistry retrieval.

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