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 1

Full model A parametrization prescription.

Group	Prescription A
Geometry	inc, PA, dRA, dDec

Front surface	$z_{f} = z_{1} {(r / 1^{″})}^{ψ_{z}} \exp (- {(r / r_{z})}^{ϕ_{z}})$ ${z_f} = {z_1}{\left( {r/1''} \right)^{{\psi _z}}}\exp \left( { - {{\left( {r/{r_z}} \right)}^{{\phi _z}}}} \right)$
Back surface	$z_{b} = - z_{f}$ ${z_b} = - {z_f}$

Keplerian velocity	$v_{k e p} = \sqrt{G M_{} r / {(r^{2} + z^{2})}^{3 / 2}}$ ${v_{kep}} = \sqrt {G{M_ }r/{{\left( {{r^2} + {z^2}} \right)}^{3/2}}}$
Sky velocity	$v_{sky} (r, z) = v_{kep} \cos (θ) \sin (\| i n c \|) + v_{sys}$ ${v_{{\rm{sky}}}}(r,z) = {v_{{\rm{kep}}}}\cos (\theta )\sin (\|inc\|) + {v_{{\rm{sys}}}}$

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	$τ = τ_{10} (^{r / 10 a u) ψ_{τ}} \exp (- {(r / r_{τ})}^{ϕ_{τ}})$ $\tau = {\tau _{10}}{(r/10au)^{{\psi _\tau }}}\exp \left( { - {{\left( {r/{r_\tau }} \right)}^{{\phi _\tau }}}} \right)$
Line profile	$τ_{v} = τ \exp (- {((v - v_{s k y}) / Δ v)}^{2})$ ${\tau _v} = \tau \exp \left( { - {{\left( {\left( {v - {v_{sky}}} \right)/{\rm{\Delta }}v} \right)}^2}} \right)$

Front surface brightness	I_v,f = B_v(1 − exp(−τ_v))
Back surface brightness	I_v,b = B_v(1 − exp(−τ_v)) exp(−τ_v)
Surface brightness	I_v = I_v,f + I_v,b

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