The 12CO gas structures of protoplanetary disks in the Upper Scorpius region

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Volume 705 (January 2026)

A&A, 705 (2026) A49

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Table 2

Full model B parametrization prescription.

Group	Prescription B
Geometry	inc, PA, dRA, dDec

Keplerian velocity	$v_{k e p} = \sqrt{G M_{} / r^{2}}$ ${v_{kep}} = \sqrt {G{M_ }/{r^2}}$
Sky velocity	$v_{sky} (r) = v_{kep} \cos (θ) \sin (∣ inc ∣) + v_{sys}$ ${v_{{\rm{sky}}}}(r) = {v_{{\rm{kep}}}}\cos (\theta )\sin (\mid {\rm{inc}}\mid ) + {v_{{\rm{sys}}}}$

Brightness temperature	$T = T_{10} (^{r / 10 au) q}$ $T = {T_{10}}{(r/10\,{\rm{au)}}^q}$
Line width	$Δ υ = \sqrt{2 k_{B} T / μ m_{H}}$ $\Delta \upsilon = \sqrt {2{k_B}T/\mu {m_H}}$

Optical depth	$τ (r) = {\begin{matrix} τ_{0}, \\ 0, \end{matrix} \begin{matrix} if & r \leq R_{O u t} \\ if & r > R_{O u t} \end{matrix}$ $\tau \left( r \right) = \left\{ {\matrix{ {{\tau _0},} \cr {0,} \cr } } \right.\,\,\,\matrix{ {{\mathop{\rm if}\nolimits} } & {r \le {R_{Out}}} \cr {{\mathop{\rm if}\nolimits} } & {r > {R_{Out}}} \cr }$
Line profile	$τ_{v} = τ \exp (- {((v - v_{s k y}) / Δ v)}^{2})$ ${\tau _v} = \tau \exp \left( { - {{\left( {\left( {v - {v_{sky}}} \right)/{\rm{\Delta }}v} \right)}^2}} \right)$

Surface brightness	I_v = B_v(1 − exp(−τ_v))

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