Bayesian analysis of the molecular emission and dust continuum of protoplanetary disks

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Table 3

Prior distributions of free parameters used for the comparison of the fast and full fitting approach.

Parameter	Prior	Parameter	Prior
q_mid	𝒰(−1,−0.1)	$Σ_{tmax}^{mol}^{(1)}$ $\Sigma {_{{\rm{tmax}}}^{{\rm{mol}}}^{\left( 1 \right)}}$	ℐ(10¹⁷,10²²)
q_sur	𝒰(−1,−0.1)	$T_{\max}^{mol (1)}$ $T_{\max }^{{\rm{mol }}(1)}$	𝒰(200,1100)
q_emis	𝒰(−1,−0.1)	$T_{\min}^{mol (1)}$ $T_{\min }^{{\rm{mol }}(1)}$	𝒰(100,500)
$Σ_{tmin}^{mol}^{(1)}$ $\Sigma {_{{\rm{tmin}}}^{{\rm{mol}}}^{\left( 1 \right)}}$	ℐ (10¹⁵, 10¹⁹)

Notes. The terms 𝒰(x, y) and ℐ(x, y) denote uniform and log-uniform priors in the range from x to y, respectively. The units of the parameters are given in Table 2. ⁽¹⁾Same prior used for CO₂ and H₂O.

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