Spatially coherent 3D distributions of HI and CO in the Milky Way

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Table 2

Overview of the prior distributions of our parameters.

Symbol	Unit	Distribution	Mean	Standard deviation	Degrees of freedom
$g_{n}^{H I}, g_{σ}^{H I}$ $\[g_{n}^{\mathrm{HI}}, g_{\sigma}^{\mathrm{HI}}\]$	[1]	Normal	0.0	Matérn kernel (cf. Sects. 2.4 and 2.5)	388 × 49152
$g_{n}^{C O}, g_{σ}^{C O}, g_{x}^{v}, g_{y}^{v}, g_{z}^{v}$ $\[g_{n}^{\mathrm{CO}}, g_{\sigma}^{\mathrm{CO}}, g_{\mathrm{x}}^{v}, g_{\mathrm{y}}^{v}, g_{\mathrm{z}}^{v}\]$	[1]	Normal	0.0	Matérn kernel (cf. Sects. 2.4, 2.5 and 2.6)	388 × 49152
$g_{f_{r}}^{H I}, g_{f_{r}}^{C O}$ $\[g_{f_{\mathrm{r}}}^{\mathrm{HI}}, g_{f_{\mathrm{r}}}^{\mathrm{CO}}\]$	[1]	Normal	0.0	Gaussian kernel (cf. Sect. 2.4)	600
$g_{f_{L}}^{H I}, g_{f_{z}}^{C O}$ $\[g_{f_{\mathrm{L}}}^{\mathrm{HI}}, g_{f_{\mathrm{z}}}^{\mathrm{CO}}\]$	[1]	Normal	0.0	Gaussian kernel (cf. Sect. 2.4)	1200
$g_{circ}^{v}$ $\[g_{\text {circ }}^{v}\]$	[1]	Normal	0.0	Gaussian kernel (cf. Sect. 2.6)	1000

$a_{n}^{H I}$ $\[a_{n}^{\mathrm{HI}}\]$	[cm⁻³]	Log-normal	0.05	0.01	1
$a_{n}^{C O}$ $\[a_{n}^{\mathrm{CO}}\]$	[cm⁻³]	Log-normal	2.5 · 10⁻⁷	5 · 10⁻⁸	1
$a_{σ}^{H I}$ $\[a_{\sigma}^{\mathrm{HI}}\]$	[km s⁻¹]	Log-normal	4.5	0.45	1
$a_{σ}^{C O}$ $\[a_{\sigma}^{\mathrm{CO}}\]$	[km s⁻¹]	Log-normal	1.0	0.1	1

$s_{n}^{H I}$ $\[s_{n}^{\mathrm{HI}}\]$	[1]	Log-normal	0.6	0.06	1
$s_{n}^{C O}$ $\[s_{n}^{\mathrm{CO}}\]$	[1]	Log-normal	1.0	0.1	1
$s_{σ}^{H I}$ $\[s_{\sigma}^{\mathrm{HI}}\]$	[1]	Log-normal	0.2	0.02	1
$s_{σ}^{C O}$ $\[s_{\sigma}^{\mathrm{CO}}\]$	[1]	Log-normal	0.2	0.02	1
$s_{x}^{v}, s_{y}^{v}, s_{z}^{v}$ $\[s_{\mathrm{x}}^{v}, s_{\mathrm{y}}^{v}, s_{\mathrm{z}}^{v}\]$	[km s⁻¹]	Normal	7.5	0.5	1

U_⊙, V_⊙, W_⊙	[km s⁻¹]	Normal	10.0	5.0	1

R_⊙	[kpc]	Normal	8.178	0.035	1

p	[arcsec]	Normal		From data (cf. Sects. 2.1.4 and 2.1.5)	403

Notes. For the corresponding physical quantities, see also Eq. (15) (gas densities), Eq. (18) (line-widths) and Eq. (19) (velocities).

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