Multi-band infrared imaging reveals dusty spiral arcs around the binary B[e] star 3 Puppis

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Table D.1

Dynamical quantities evaluated at the inner rim (R_rim) and at the distance where the south-eastern asymmetry is (R_ref) in 3 Puppis’ disc.

Eq. n°	Quantity	Symbol (Unit)	Expression	Value at R_rim	Value at R_ref
0	Distance from the centre of mass	R (au)	$\frac{d_{G e D R 2} (p c) \times R (m a s)}{10^{3}}$ $\displaystyle \frac{d_\mathrm{GeDR2}\,(\mathrm{pc}) \times R\,(\mathrm{mas})}{10^{3}}$	3.6	10
1	Surface density	∑ (kg m^-2)	$\frac{M_{g a s}}{2 π R^{2}}$ $\displaystyle \frac{M_\mathrm{gas}}{2\pi\,R^2}$	38.2	8.25
2	Sound speed	c_s (m s^-1)	$\sqrt{\frac{k_{B} T_{r i m}}{μ m_{H}}}$ $\displaystyle \sqrt{\frac{k_B\,T_\mathrm{rim}}{\mu\,m_H}}$	2116	2116
3	Keplerian angular frequency	Ω (rad s^-1)	$\sqrt{\frac{G M_{t o t}}{R^{3}}}$ $\displaystyle \sqrt{\frac{G\,M_\mathrm{tot}}{R^3}}$	9.0 × 10⁻⁸	6.15 × 10⁻⁸
4	Toomre parameter	Q (...)	$\frac{c_{s} Ω}{π G Σ}$ $\displaystyle \frac{c_s\,\Omega}{\pi\,G\,\Sigma}$	2.4 × 10⁴	7.5 × 10⁵
5	Vertical scale height	H (au)	$\frac{c_{s}}{Ω}$ $\displaystyle \frac{c_s}{\Omega}$	0.157	0.23
6	Aspect ratio	ε (...)	$\frac{H}{R}$ $\epsilon$ (...)& $\displaystyle \frac{H}{R}$	0.044	0.023
7	Kinematic viscosity	ν (m²·s ¹)	α × c_s × H	4.98 × 10¹¹	7.28 × 10¹¹
8	Viscous timescale	t_visc (yrs)	$\frac{R^{2}}{ν}$ $\displaystyle \frac{R^2}{\nu}$	1.85 × 10⁴	9.75 × 10⁴
9	Clump area	A_clump (m²)	∆φ × R_ref × w	—	2.70 × 10²²
10	Gas mass within a clump	M_clump (M_⊕) M_clump (M_Jup)	Σ_ref × A_clump	— —	3.73 × 10⁻² 1.18 × 10⁻⁴

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