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Table C.1

Retrieved parameters and their uncertainties.

Parameter Description Prior} Luhman 16A Luhman 16B
Free chem. Dis-eq. Free chem. Dis-eq.
Retrieved Derived(a) Retrieved Derived(a)
log H2O H2O abundance U(−14.0,−2.0)Mathematical equation: $\mathcal{U}(-14.0,-2.0)$ −3.402−0.012+0.012Mathematical equation: $-3.402^{+0.012}_{-0.012}$ −3.397−0.015+0.016Mathematical equation: $-3.397^{+0.016}_{-0.015}$ −3.541−0.012+0.012Mathematical equation: $-3.541^{+0.012}_{-0.012}$ −3.463−0.010+0.009Mathematical equation: $-3.463^{+0.009}_{-0.010}$
log H218O H218O abundance U(−14.0,−2.0)Mathematical equation: $\mathcal{U}(-14.0,-2.0)$ −6.06−0.05+0.05Mathematical equation: $-6.06^{+0.05}_{-0.05}$ −6.06−0.06+0.06Mathematical equation: $-6.06^{+0.06}_{-0.06}$ −6.03−0.04+0.04Mathematical equation: $-6.03^{+0.04}_{-0.04}$ −5.94−0.03+0.03Mathematical equation: $-5.94^{+0.03}_{-0.03}$
log H217O H217O abundance U(−14.0,−2.0)Mathematical equation: $\mathcal{U}(-14.0,-2.0)$ <-7.53 <-7.01 <-7.00 <-6.80
log 12CO 12CO abundance U(−14.0,−2.0)Mathematical equation: $\mathcal{U}(-14.0,-2.0)$ −3.146−0.012+0.012Mathematical equation: $-3.146^{+0.012}_{-0.012}$ −3.140−0.014+0.015Mathematical equation: $-3.140^{+0.015}_{-0.014}$ −3.309−0.012+0.012Mathematical equation: $-3.309^{+0.012}_{-0.012}$ −3.245−0.010+0.009Mathematical equation: $-3.245^{+0.009}_{-0.010}$
log 13CO} 13CO abundance U(−14.0,−2.0)Mathematical equation: $\mathcal{U}(-14.0,-2.0)$ −5.01−0.02+0.02Mathematical equation: $-5.01^{+0.02}_{-0.02}$ −5.01−0.02+0.02Mathematical equation: $-5.01^{+0.02}_{-0.02}$ −5.18−0.02+0.02Mathematical equation: $-5.18^{+0.02}_{-0.02}$ −5.10−0.02+0.02Mathematical equation: $-5.10^{+0.02}_{-0.02}$
log C18O C18O abundance U(−14.0,−2.0)Mathematical equation: $\mathcal{U}(-14.0,-2.0)$ <-6.04 −6.30−0.23+0.16Mathematical equation: $-6.30^{+0.16}_{-0.23}$ <-6.22 −6.34−0.14+0.11Mathematical equation: $-6.34^{+0.11}_{-0.14}$
log C17O C17O abundance U(−14.0,−2.0)Mathematical equation: $\mathcal{U}(-14.0,-2.0)$ <-6.42 <-6.31 <-6.46 <-6.36
log CH4 CH4 abundance U(−14.0,−2.0)Mathematical equation: $\mathcal{U}(-14.0,-2.0)$ −5.22−0.02+0.02Mathematical equation: $-5.22^{+0.02}_{-0.02}$ −5.22−0.02+0.02Mathematical equation: $-5.22^{+0.02}_{-0.02}$ −5.03−0.01+0.01Mathematical equation: $-5.03^{+0.01}_{-0.01}$ −4.95−0.01+0.01Mathematical equation: $-4.95^{+0.01}_{-0.01}$
log NH3 NH3 abundance U(−14.0,−2.0)Mathematical equation: $\mathcal{U}(-14.0,-2.0)$ −6.15−0.03+0.03Mathematical equation: $-6.15^{+0.03}_{-0.03}$ −6.15−0.04+0.04Mathematical equation: $-6.15^{+0.04}_{-0.04}$ −6.03−0.02+0.02Mathematical equation: $-6.03^{+0.02}_{-0.02}$ −5.95−0.02+0.01Mathematical equation: $-5.95^{+0.01}_{-0.02}$
log H2S H2S abundance U(−14.0,−2.0)Mathematical equation: $\mathcal{U}(-14.0,-2.0)$ −4.35−0.03+0.03Mathematical equation: $-4.35^{+0.03}_{-0.03}$ −4.34−0.03+0.03Mathematical equation: $-4.34^{+0.03}_{-0.03}$ −4.49−0.03+0.03Mathematical equation: $-4.49^{+0.03}_{-0.03}$ −4.40−0.02+0.02Mathematical equation: $-4.40^{+0.02}_{-0.02}$
log HF HF abundance U(−14.0,−2.0)Mathematical equation: $\mathcal{U}(-14.0,-2.0)$ −7.30−0.02+0.02Mathematical equation: $-7.30^{+0.02}_{-0.02}$ −7.30−0.03+0.03Mathematical equation: $-7.30^{+0.03}_{-0.03}$ −7.45−0.03+0.02Mathematical equation: $-7.45^{+0.02}_{-0.03}$ −7.39−0.02+0.02Mathematical equation: $-7.39^{+0.02}_{-0.02}$
log CO2 CO2 abundance U(−14.0,−2.0)Mathematical equation: $\mathcal{U}(-14.0,-2.0)$ <-5.37 −7.09−0.03+0.03Mathematical equation: $-7.09^{+0.03}_{-0.03}$ −5.37−0.09+0.08Mathematical equation: $-5.37^{+0.08}_{-0.09}$ −7.20−0.02+0.02Mathematical equation: $-7.20^{+0.02}_{-0.02}$
log HCN HCN abundance U(−14.0,−2.0)Mathematical equation: $\mathcal{U}(-14.0,-2.0)$ <-6.28 −6.99−0.05+0.05Mathematical equation: $-6.99^{+0.05}_{-0.05}$ <-6.52 −6.97−0.01+0.02Mathematical equation: $-6.97^{+0.02}_{-0.01}$
Derived(b) Retrieved Derived(b) Retrieved
Projected(c) Projected(c) Projected(c) Projected(c)
[C/H] Carbon abundance U(−1.0,2.0)Mathematical equation: $\mathcal{U}(-1.0,2.0)$ 0.173−0.012+0.012Mathematical equation: $0.173^{+0.012}_{-0.012}$ 0.169−0.014+0.015Mathematical equation: $0.169^{+0.015}_{-0.014}$ 0.015−0.012+0.012Mathematical equation: $0.015^{+0.012}_{-0.012}$ 0.069−0.010+0.009Mathematical equation: $0.069^{+0.009}_{-0.010}$
0.175−0.009+0.009Mathematical equation: $0.175^{+0.009}_{-0.009}$ 0.166−0.011+0.011Mathematical equation: $0.166^{+0.011}_{-0.011}$ 0.161−0.009+0.010Mathematical equation: $0.161^{+0.010}_{-0.009}$ 0.128−0.007+0.007Mathematical equation: $0.128^{+0.007}_{-0.007}$
[O/H] Oxygen abundance U(−1.0,2.0)Mathematical equation: $\mathcal{U}(-1.0,2.0)$ 0.129−0.012+0.012Mathematical equation: $0.129^{+0.012}_{-0.012}$ 0.151−0.013+0.015Mathematical equation: $0.151^{+0.015}_{-0.013}$ −0.025−0.012+0.012Mathematical equation: $-0.025^{+0.012}_{-0.012}$ 0.082−0.010+0.009Mathematical equation: $0.082^{+0.009}_{-0.010}$
0.131−0.008+0.008Mathematical equation: $0.131^{+0.008}_{-0.008}$ 0.149−0.010+0.010Mathematical equation: $0.149^{+0.010}_{-0.010}$ 0.121−0.009+0.009Mathematical equation: $0.121^{+0.009}_{-0.009}$ 0.141−0.007+0.007Mathematical equation: $0.141^{+0.007}_{-0.007}$
[N/H] Nitrogen abundance U(−1.0,2.0)Mathematical equation: $\mathcal{U}(-1.0,2.0)$ −2.21−0.03+0.03Mathematical equation: $-2.21^{+0.03}_{-0.03}$ −0.43−0.10+0.09Mathematical equation: $-0.43^{+0.09}_{-0.10}$ −1.95−0.02+0.02Mathematical equation: $-1.95^{+0.02}_{-0.02}$ −0.01−0.04+0.04Mathematical equation: $-0.01^{+0.04}_{-0.04}$
−2.21−0.03+0.03Mathematical equation: $-2.21^{+0.03}_{-0.03}$ −0.43−0.10+0.09Mathematical equation: $-0.43^{+0.09}_{-0.10}$ −2.09−0.02+0.02Mathematical equation: $-2.09^{+0.02}_{-0.02}$ −0.07−0.04+0.04Mathematical equation: $-0.07^{+0.04}_{-0.04}$
[S/H] Sulphur abundance U(−1.0,2.0)Mathematical equation: $\mathcal{U}(-1.0,2.0)$ 0.30−0.03+0.03Mathematical equation: $0.30^{+0.03}_{-0.03}$ 0.31−0.03+0.03Mathematical equation: $0.31^{+0.03}_{-0.03}$ 0.16−0.03+0.03Mathematical equation: $0.16^{+0.03}_{-0.03}$ 0.25−0.02+0.02Mathematical equation: $0.25^{+0.02}_{-0.02}$
0.30−0.02+0.02Mathematical equation: $0.30^{+0.02}_{-0.02}$ 0.30−0.03+0.03Mathematical equation: $0.30^{+0.03}_{-0.03}$ 0.31−0.02+0.02Mathematical equation: $0.31^{+0.02}_{-0.02}$ 0.31−0.02+0.02Mathematical equation: $0.31^{+0.02}_{-0.02}$
[F/H] Fluorine abundance U(−1.0,2.0)Mathematical equation: $\mathcal{U}(-1.0,2.0)$ 0.07−0.02+0.02Mathematical equation: $0.07^{+0.02}_{-0.02}$ 0.07−0.03+0.03Mathematical equation: $0.07^{+0.03}_{-0.03}$ −0.08−0.03+0.02Mathematical equation: $-0.08^{+0.02}_{-0.03}$ −0.02−0.02+0.02Mathematical equation: $-0.02^{+0.02}_{-0.02}$
0.07−0.02+0.02Mathematical equation: $0.07^{+0.02}_{-0.02}$ 0.07−0.02+0.02Mathematical equation: $0.07^{+0.02}_{-0.02}$ 0.07−0.02+0.02Mathematical equation: $0.07^{+0.02}_{-0.02}$ 0.04−0.02+0.02Mathematical equation: $0.04^{+0.02}_{-0.02}$
log 12CO/13CO 12CO/13CO ratio U(0.0,5.0)Mathematical equation: $\mathcal{U}(0.0,5.0)$ 1.87−0.01+0.01Mathematical equation: $1.87^{+0.01}_{-0.01}$ 1.86−0.02+0.02Mathematical equation: $1.86^{+0.02}_{-0.02}$ 1.87−0.02+0.02Mathematical equation: $1.87^{+0.02}_{-0.02}$ 1.85−0.01+0.01Mathematical equation: $1.85^{+0.01}_{-0.01}$
log C16O/C18O C16O/C18O ratio U(0.0,5.0)Mathematical equation: $\mathcal{U}(0.0,5.0)$ >3.04 3.15−0.16+0.23Mathematical equation: $3.15^{+0.23}_{-0.16}$ >3.08 3.09−0.11+0.14Mathematical equation: $3.09^{+0.14}_{-0.11}$
log C16O/C17O C16O/C17O ratio U(0.0,5.0)Mathematical equation: $\mathcal{U}(0.0,5.0)$ >3.86 >3.35 >3.56 >3.26
log H216O/H218O H216O/H218O ratio U(0.0,5.0)Mathematical equation: $\mathcal{U}(0.0,5.0)$ 2.66−0.05+0.05Mathematical equation: $2.66^{+0.05}_{-0.05}$ 2.66−0.05+0.06Mathematical equation: $2.66^{+0.06}_{-0.05}$ 2.49−0.04+0.04Mathematical equation: $2.49^{+0.04}_{-0.04}$ 2.48−0.03+0.03Mathematical equation: $2.48^{+0.03}_{-0.03}$
log H216O/H217O H216O/H217O ratio U(0.0,5.0)Mathematical equation: $\mathcal{U}(0.0,5.0)$ >5.37 >3.97 >4.58 >3.63
log Kzz [cm2 s−1] Eddy diffusion coefficient U(5.0,15.0)Mathematical equation: $\mathcal{U}(5.0,15.0)$ − 8.70−0.21+0.25Mathematical equation: $8.70^{+0.25}_{-0.21}$ − 8.17−0.09+0.12Mathematical equation: $8.17^{+0.12}_{-0.09}$
Derived(d) Derived(d) Derived(d) Derived(d)
C/O C/O ratio − 0.651−0.002+0.002Mathematical equation: $0.651^{+0.002}_{-0.002}$ 0.613−0.002+0.002Mathematical equation: $0.613^{+0.002}_{-0.002}$ 0.646−0.002+0.002Mathematical equation: $0.646^{+0.002}_{-0.002}$ 0.572−0.003+0.004Mathematical equation: $0.572^{+0.004}_{-0.003}$
log g [cm s−2] Surface gravity NA(4.96,0.09)Mathematical equation: $\mathcal{N}_\mathrm{A}(4.96,0.09)$ 4.96−0.01+0.02Mathematical equation: $4.96^{+0.02}_{-0.01}$ 4.96−0.02+0.02Mathematical equation: $4.96^{+0.02}_{-0.02}$ 4.73−0.02+0.02Mathematical equation: $4.73^{+0.02}_{-0.02}$ 4.82−0.01+0.01Mathematical equation: $4.82^{+0.01}_{-0.01}$
NB(4.88,0.09)Mathematical equation: $\mathcal{N}_\mathrm{B}(4.88,0.09)$
v sin i [km s−1] Projected rotation velocity U(10.0,30.0)Mathematical equation: $\mathcal{U}(10.0,30.0)$ 14.76−0.03+0.03Mathematical equation: $14.76^{+0.03}_{-0.03}$ 14.80−0.03+0.03Mathematical equation: $14.80^{+0.03}_{-0.03}$ 24.79−0.04+0.05Mathematical equation: $24.79^{+0.05}_{-0.04}$ 25.34−0.04+0.04Mathematical equation: $25.34^{+0.04}_{-0.04}$
vrad [km s−1] Radial velocity U(10.0,30.0)Mathematical equation: $\mathcal{U}(10.0,30.0)$ 17.21−0.01+0.01Mathematical equation: $17.21^{+0.01}_{-0.01}$ 17.21−0.02+0.02Mathematical equation: $17.21^{+0.02}_{-0.02}$ 19.75−0.03+0.03Mathematical equation: $19.75^{+0.03}_{-0.03}$ 19.75−0.02+0.02Mathematical equation: $19.75^{+0.02}_{-0.02}$
∇1 Temperature gradient at P1 U(0.10,0.34)Mathematical equation: $\mathcal{U}(0.10,0.34)$ 0.20−0.06+0.07Mathematical equation: $0.20^{+0.07}_{-0.06}$ 0.18−0.05+0.07Mathematical equation: $0.18^{+0.07}_{-0.05}$ 0.22−0.07+0.07Mathematical equation: $0.22^{+0.07}_{-0.07}$ 0.28−0.05+0.04Mathematical equation: $0.28^{+0.04}_{-0.05}$
∇2 Temperature gradient at P2 U(0.10,0.34)Mathematical equation: $\mathcal{U}(0.10,0.34)$ 0.218−0.013+0.012Mathematical equation: $0.218^{+0.012}_{-0.013}$ 0.234−0.010+0.012Mathematical equation: $0.234^{+0.012}_{-0.010}$ 0.219−0.022+0.020Mathematical equation: $0.219^{+0.020}_{-0.022}$ 0.253−0.007+0.007Mathematical equation: $0.253^{+0.007}_{-0.007}$
∇3 Temperature gradient at P3 U(0.05,0.34)Mathematical equation: $\mathcal{U}(0.05,0.34)$ 0.051−0.001+0.001Mathematical equation: $0.051^{+0.001}_{-0.001}$ 0.052−0.001+0.002Mathematical equation: $0.052^{+0.002}_{-0.001}$ 0.091−0.002+0.002Mathematical equation: $0.091^{+0.002}_{-0.002}$ 0.057−0.003+0.004Mathematical equation: $0.057^{+0.004}_{-0.003}$
∇4 Temperature gradient at P4 U(0.0,0.34)Mathematical equation: $\mathcal{U}(0.0,0.34)$ 0.30−0.01+0.01Mathematical equation: $0.30^{+0.01}_{-0.01}$ 0.29−0.02+0.02Mathematical equation: $0.29^{+0.02}_{-0.02}$ 0.28−0.01+0.01Mathematical equation: $0.28^{+0.01}_{-0.01}$ 0.26−0.01+0.01Mathematical equation: $0.26^{+0.01}_{-0.01}$
∇5 Temperature gradient at P5 U(0.0,0.34)Mathematical equation: $\mathcal{U}(0.0,0.34)$ 0.11−0.07+0.08Mathematical equation: $0.11^{+0.08}_{-0.07}$ 0.13−0.08+0.10Mathematical equation: $0.13^{+0.10}_{-0.08}$ 0.06−0.04+0.06Mathematical equation: $0.06^{+0.06}_{-0.04}$ 0.12−0.06+0.07Mathematical equation: $0.12^{+0.07}_{-0.06}$
log P3 [bar] Pressure of central knot U(−1.0,1.0)Mathematical equation: $\mathcal{U}(-1.0,1.0)$ −0.35−0.02+0.02Mathematical equation: $-0.35^{+0.02}_{-0.02}$ −0.19−0.04+0.03Mathematical equation: $-0.19^{+0.03}_{-0.04}$ −0.24−0.03+0.03Mathematical equation: $-0.24^{+0.03}_{-0.03}$ −0.19−0.02+0.02Mathematical equation: $-0.19^{+0.02}_{-0.02}$
T3 [K] Temperature at central knot U(900,1900)Mathematical equation: $\mathcal{U}(900,1900)$ 1191−7+7Mathematical equation: $1191^{+7}_{-7}$ 1228−11+10Mathematical equation: $1228^{+10}_{-11}$ 1149−10+11Mathematical equation: $1149^{+11}_{-10}$ 1134−6+7Mathematical equation: $1134^{+7}_{-6}$
Δlog P23 [bar] Separation of P2 and P3 U(0.5,2.0)Mathematical equation: $\mathcal{U}(0.5,2.0)$ 1.01−0.07+0.07Mathematical equation: $1.01^{+0.07}_{-0.07}$ 0.77−0.06+0.08Mathematical equation: $0.77^{+0.08}_{-0.06}$ 1.60−0.26+0.23Mathematical equation: $1.60^{+0.23}_{-0.26}$ 0.72−0.04+0.05Mathematical equation: $0.72^{+0.05}_{-0.04}$
Δlog P34 [bar] Separation of P3 and P4 U(0.5,2.0)Mathematical equation: $\mathcal{U}(0.5,2.0)$ 0.60−0.05+0.06Mathematical equation: $0.60^{+0.06}_{-0.05}$ 0.90−0.12+0.12Mathematical equation: $0.90^{+0.12}_{-0.12}$ 0.54−0.03+0.05Mathematical equation: $0.54^{+0.05}_{-0.03}$ 0.62−0.05+0.07Mathematical equation: $0.62^{+0.07}_{-0.05}$
log κcl,0 [cm2 g−1] Cloud-base opacity U(−10.0,3.0)Mathematical equation: $\mathcal{U}(-10.0,3.0)$ −1.16−0.03+0.03Mathematical equation: $-1.16^{+0.03}_{-0.03}$ −1.11−0.03+0.03Mathematical equation: $-1.11^{+0.03}_{-0.03}$ −4.18−3.17+3.20Mathematical equation: $-4.18^{+3.20}_{-3.17}$ −1.39−0.03+0.03Mathematical equation: $-1.39^{+0.03}_{-0.03}$
log Pcl,0 [bar] Cloud-base pressure U(0.5,2.5)Mathematical equation: $\mathcal{U}(0.5,2.5)$ 0.52−0.01+0.01Mathematical equation: $0.52^{+0.01}_{-0.01}$ 0.52−0.01+0.02Mathematical equation: $0.52^{+0.02}_{-0.01}$ 1.58−0.57+0.53Mathematical equation: $1.58^{+0.53}_{-0.57}$ 0.52−0.01+0.01Mathematical equation: $0.52^{+0.01}_{-0.01}$
fsed Cloud-opacity decay U(1.0,20.0)Mathematical equation: $\mathcal{U}(1.0,20.0)$ 1.02−0.01+0.02Mathematical equation: $1.02^{+0.02}_{-0.01}$ 1.03−0.02+0.03Mathematical equation: $1.03^{+0.03}_{-0.02}$ 10.63−5.40+5.24Mathematical equation: $10.63^{+5.24}_{-5.40}$ 1.03−0.01+0.02Mathematical equation: $1.03^{+0.02}_{-0.01}$
log a GP amplitude U(−0.7,0.5)Mathematical equation: $\mathcal{U}(-0.7,0.5)$ 0.198−0.004+0.004Mathematical equation: $0.198^{+0.004}_{-0.004}$ 0.198−0.005+0.005Mathematical equation: $0.198^{+0.005}_{-0.005}$ 0.124−0.005+0.005Mathematical equation: $0.124^{+0.005}_{-0.005}$ 0.108−0.003+0.003Mathematical equation: $0.108^{+0.003}_{-0.003}$
log ℓ [km s−1] GP length-scale U(−3.0,−1.0)Mathematical equation: $\mathcal{U}(-3.0,-1.0)$ −1.300−0.001+0.005Mathematical equation: $-1.300^{+0.005}_{-0.001}$ −1.300−0.001+0.005Mathematical equation: $-1.300^{+0.005}_{-0.001}$ −1.351−0.004+0.010Mathematical equation: $-1.351^{+0.010}_{-0.004}$ −1.324−0.004+0.005Mathematical equation: $-1.324^{+0.005}_{-0.004}$
Δ BIC 0 −20.31 0 −305.67

Notes. (a) The disequilibrium mixing ratios are not directly retrieved but instead derived near the photosphere, at 2 bar. (b) The free-chemistry elemental abundances and isotopologue ratios are derived from the retrieved VMRs above. (c) The elemental abundances are projected onto the expected surface gravities, as described in Sect. 3.2 and shown in brackets. (d) The C/O ratios derived from the free-chemistry model trace only the gaseous carbon and oxygen, while the disequilibrium model accounts for oxygen condensation.

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