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Table A.1

Retrieved parameters and their uncertainties.

Parameter Description Prior Luhman 16A Luhman 16B
1-column 2-column 1-column 2-column
log H2O H2O abundance 𝒰(−14.0, −2.0) −3.38−0.05+0.06$\[-3.38_{-0.05}^{+0.06}\]$ −3.42−0.05+0.04$\[-3.42_{-0.05}^{+0.04}\]$ −3.38−0.05+0.04$\[-3.38_{-0.05}^{+0.04}\]$ −3.48−0.03+0.03$\[-3.48_{-0.03}^{+0.03}\]$
log Na Na abundance 𝒰(−14.0, −2.0) −4.95−0.06+0.07$\[-4.95_{-0.06}^{+0.07}\]$ −4.97−0.06+0.05$\[-4.97_{-0.06}^{+0.05}\]$ −5.09−0.06+0.05$\[-5.09_{-0.06}^{+0.05}\]$ −5.15−0.04+0.05$\[-5.15_{-0.04}^{+0.05}\]$
log K K abundance 𝒰(−14.0, −2.0) −6.42−0.06+0.07$\[-6.42_{-0.06}^{+0.07}\]$ −6.44−0.06+0.05$\[-6.44_{-0.06}^{+0.05}\]$ −6.55−0.05+0.05$\[-6.55_{-0.05}^{+0.05}\]$ −6.61−0.03+0.04$\[-6.61_{-0.03}^{+0.04}\]$
log HF HF abundance 𝒰(−14.0, −2.0) −7.28−0.07+0.07$\[-7.28_{-0.07}^{+0.07}\]$ −7.32−0.07+0.06$\[-7.32_{-0.07}^{+0.06}\]$ −7.21−0.06+0.05$\[-7.21_{-0.06}^{+0.05}\]$ −7.31−0.04+0.04$\[-7.31_{-0.04}^{+0.04}\]$
log (FeH)0 FeH abundance at P ≥ PFeH,0 𝒰(−14.0, −2.0) −7.54−0.11+0.10$\[-7.54_{-0.11}^{+0.10}\]$ −11.07−1.49+1.71$\[-11.07_{-1.49}^{+1.71}\]$ −8.90−0.06+0.05$\[-8.90_{-0.06}^{+0.05}\]$ −7.97−0.09+0.10$\[-7.97_{-0.09}^{+0.10}\]$
−7.95−0.08+0.11$\[-7.95_{-0.08}^{+0.11}\]$ −9.26−0.08+0.07$\[-9.26_{-0.08}^{+0.07}\]$
log PFeH,0 FeH drop-off pressure 𝒰(−5.0, 3.0) +0.78−0.03+0.04$\[+0.78_{-0.03}^{+0.04}\]$ −1.4−1.8+2.1$\[-1.4_{-1.8}^{+2.1}\]$ −2.2−1.5+1.5$\[-2.2_{-1.5}^{+1.5}\]$ −2.1−1.5+1.7$\[-2.1_{-1.5}^{+1.7}\]$
−0.9−2.0+1.4$\[-0.9_{-2.0}^{+1.4}\]$ −2.5−1.3+1.2$\[-2.5_{-1.3}^{+1.2}\]$
αFeH FeH drop-off power 𝒰(0.0, 20.0) 9.5−3.2+4.4$\[9.5_{-3.2}^{+4.4}\]$ 9.2−4.9+5.1$\[9.2_{-4.9}^{+5.1}\]$ 9.6−5.2+5.4$\[9.6_{-5.2}^{+5.4}\]$ 9.8−4.9+5.1$\[9.8_{-4.9}^{+5.1}\]$
9.2−4.5+5.1$\[9.2_{-4.5}^{+5.1}\]$ 9.4−5.0+5.2$\[9.4_{-5.0}^{+5.2}\]$
log g Surface gravity 𝒢A(4.96, 0.09) 4.95−0.05+0.06$\[4.95_{-0.05}^{+0.06}\]$ 4.95−0.05+0.04$\[4.95_{-0.05}^{+0.04}\]$ 4.89−0.05+0.04$\[4.89_{-0.05}^{+0.04}\]$ 4.80−0.03+0.03$\[4.80_{-0.03}^{+0.03}\]$
𝒢B(4.89, 0.09)
v sin i Projected rotational velocity 𝒰(10.0, 30.0) 14.93−0.12+0.14$\[14.93_{-0.12}^{+0.14}\]$ 14.87−0.10+0.11$\[14.87_{-0.10}^{+0.11}\]$ 24.48−0.03+0.04$\[24.48_{-0.03}^{+0.04}\]$ 24.47−0.03+0.03$\[24.47_{-0.03}^{+0.03}\]$
ϵlimb Limb-darkening coefficient 𝒰(0.0, 1.0) 0.46−0.06+0.06$\[0.46_{-0.06}^{+0.06}\]$ 0.44−0.04+0.05$\[0.44_{-0.04}^{+0.05}\]$ 0.01−0.01+0.01$\[0.01_{-0.01}^{+0.01}\]$ 0.01−0.01+0.01$\[0.01_{-0.01}^{+0.01}\]$
vrad Radial velocity 𝒰(10.0, 30.0) 17.27−0.03+0.03$\[17.27_{-0.03}^{+0.03}\]$ 17.27−0.02+0.02$\[17.27_{-0.02}^{+0.02}\]$ 20.00−0.03+0.04$\[20.00_{-0.03}^{+0.04}\]$ 20.01−0.03+0.03$\[20.01_{-0.03}^{+0.03}\]$
𝒞ℱ Surface coverage fraction 𝒰(0.0, 1.0) 0.942−0.006+0.006$\[0.942_{-0.006}^{+0.006}\]$ 0.024−0.004+0.006$\[0.024_{-0.004}^{+0.006}\]$
0.058−0.006+0.006$\[0.058_{-0.006}^{+0.006}\]$ 0.976−0.006+0.004$\[0.976_{-0.006}^{+0.004}\]$
∇1 Temperature gradient at P1 𝒰(0.10, 0.34) 0.22−0.07+0.07$\[0.22_{-0.07}^{+0.07}\]$ 0.22−0.06+0.06$\[0.22_{-0.06}^{+0.06}\]$ 0.22−0.06+0.06$\[0.22_{-0.06}^{+0.06}\]$ 0.22−0.06+0.06$\[0.22_{-0.06}^{+0.06}\]$
∇2 Temperature gradient at P2 𝒰(0.10, 0.34) 0.17−0.04+0.06$\[0.17_{-0.04}^{+0.06}\]$ 0.15−0.02+0.03$\[0.15_{-0.02}^{+0.03}\]$ 0.25−0.05+0.05$\[0.25_{-0.05}^{+0.05}\]$ 0.22−0.04+0.04$\[0.22_{-0.04}^{+0.04}\]$
∇3 Temperature gradient at P3 𝒰(0.05, 0.34) 0.090−0.007+0.007$\[0.090_{-0.007}^{+0.007}\]$ 0.094−0.004+0.004$\[0.094_{-0.004}^{+0.004}\]$ 0.083−0.009+0.010$\[0.083_{-0.009}^{+0.010}\]$ 0.093−0.009+0.010$\[0.093_{-0.009}^{+0.010}\]$
∇4 Temperature gradient at P4 𝒰(0.0, 0.34) 0.15−0.02+0.02$\[0.15_{-0.02}^{+0.02}\]$ 0.16−0.02+0.03$\[0.16_{-0.02}^{+0.03}\]$ 0.30−0.03+0.02$\[0.30_{-0.03}^{+0.02}\]$ 0.29−0.03+0.03$\[0.29_{-0.03}^{+0.03}\]$
∇5 Temperature gradient at P5 𝒰(0.0, 0.34) 0.16−0.09+0.10$\[0.16_{-0.09}^{+0.10}\]$ 0.19−0.09+0.08$\[0.19_{-0.09}^{+0.08}\]$ 0.18−0.09+0.09$\[0.18_{-0.09}^{+0.09}\]$ 0.17−0.09+0.09$\[0.17_{-0.09}^{+0.09}\]$
log P3 Pressure of central knot 𝒰(−1.0, 1.0) +0.90−0.08+0.06$\[+0.90_{-0.08}^{+0.06}\]$ +0.53−0.12+0.12$\[+0.53_{-0.12}^{+0.12}\]$ +0.43−0.08+0.07$\[+0.43_{-0.08}^{+0.07}\]$ +0.38−0.08+0.08$\[+0.38_{-0.08}^{+0.08}\]$
T3 Temperature at central knot 𝒰(1200, 2200) 1644−28+23$\[1644_{-28}^{+23}\]$ 1505−43+42$\[1505_{-43}^{+42}\]$ 1444−28+27$\[1444_{-28}^{+27}\]$ 1418−31+29$\[1418_{-31}^{+29}\]$
Δ log P23 Separation between P2 and P3 𝒰(−2.0, −0.5) −1.4−0.3+0.4$\[-1.4_{-0.3}^{+0.4}\]$ −1.3−0.3+0.3$\[-1.3_{-0.3}^{+0.3}\]$ −1.6−0.2+0.3$\[-1.6_{-0.2}^{+0.3}\]$ −1.6−0.2+0.3$\[-1.6_{-0.2}^{+0.3}\]$
Δ log P34 Separation between P3 and P4 𝒰(0.5, 3.0) +2.3−0.5+0.4$\[+2.3_{-0.5}^{+0.4}\]$ +2.2−0.5+0.4$\[+2.2_{-0.5}^{+0.4}\]$ +1.0−0.3+0.4$\[+1.0_{-0.3}^{+0.4}\]$ +1.1−0.3+0.4$\[+1.1_{-0.3}^{+0.4}\]$
log κcl,0 Cloud-base opacity 𝒰(−10.0, 3.0) −1.27−0.09+0.09$\[-1.27_{-0.09}^{+0.09}\]$ +1.1−0.8+0.8$\[+1.1_{-0.8}^{+0.8}\]$ −0.05−0.41+0.72$\[-0.05_{-0.41}^{+0.72}\]$ −5.5−2.4+2.7$\[-5.5_{-2.4}^{+2.7}\]$
+1.2−1.0+0.9$\[+1.2_{-1.0}^{+0.9}\]$ +0.2−0.5+0.7$\[+0.2_{-0.5}^{+0.7}\]$
log Pcl,0 Cloud-base pressure 𝒰(0.0, 2.5) +1.12−0.04+0.04$\[+1.12_{-0.04}^{+0.04}\]$ +0.99−0.04+0.05$\[+0.99_{-0.04}^{+0.05}\]$ +1.26−0.03+0.03$\[+1.26_{-0.03}^{+0.03}\]$ +0.97−0.81+0.82$\[+0.97_{-0.81}^{+0.82}\]$
+1.56−0.09+0.10$\[+1.56_{-0.09}^{+0.10}\]$ +1.28−0.03+0.03$\[+1.28_{-0.03}^{+0.03}\]$
fsed Cloud-opacity decay 𝒰(1.0, 20.0) 1.4−0.2+0.2$\[1.4_{-0.2}^{+0.2}\]$ 10.3−2.3+2.3$\[10.3_{-2.3}^{+2.3}\]$ 6.1−1.4+2.7$\[6.1_{-1.4}^{+2.7}\]$ 10.6−5.0+4.9$\[10.6_{-5.0}^{+4.9}\]$
12.3−3.1+3.2$\[12.3_{-3.1}^{+3.2}\]$ 6.5−1.4+2.0$\[6.5_{-1.4}^{+2.0}\]$
log a GP amplitude 𝒰(−0.7, 0.3) −0.219−0.006+0.006$\[-0.219_{-0.006}^{+0.006}\]$ −0.217−0.005+0.005$\[-0.217_{-0.005}^{+0.005}\]$ −0.156−0.005+0.005$\[-0.156_{-0.005}^{+0.005}\]$ −0.158−0.005+0.005$\[-0.158_{-0.005}^{+0.005}\]$
log ℓ GP length-scale 𝒰(−3.0, −1.0) −1.376−0.012+0.012$\[-1.376_{-0.012}^{+0.012}\]$ −1.377−0.009+0.010$\[-1.377_{-0.009}^{+0.010}\]$ −1.285−0.005+0.006$\[-1.285_{-0.005}^{+0.006}\]$ −1.285−0.005+0.006$\[-1.285_{-0.005}^{+0.006}\]$
ln B −13.3 +0.67

Notes. All priors are uniform (indicated with 𝒰(min, max)), except for the surface gravity, which is retrieved using a Gaussian prior (𝒢(μ, σ)) and different between Luhman 16A and B. In the case of the FeH abundance and cloud-opacity parameters, the two-column solution shows the two values corresponding to each patch in black and grey. The surface coverage fraction is also calculated for the second column (as 1 − 𝒞ℱ), but it is only retrieved as a single parameter.

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