Appendix

In Dutrey et al. (1994), we use the following parametrizations for the physical laws in the type 0 model:
Kinetic temperature:

 

$$T_k = T_{\rm o} (r/r_{\rm o})^{-q}.$$ (A.1)

Velocity:

 

$$v(r) = v_{\rm o} (r/r_{\rm o})^{-v},{\rm Keplerian~case{:}\ } v = 0.5.$$ (A.2)

Surface density:

$$\Sigma(r) = \Sigma_{\rm o} (r/r_{\rm o})^{-p}.$$ (A.3)

Volume density:

$$\frac{\Sigma(r)}{\sqrt{\pi} \cdot H(r)}$$                    n(r) = (A.4)

$$n_{\rm o} (r/r_{\rm o})^{-s}$$ = (A.5)

s = h + p = 1 + v +p - q/2 (A.6)

$$n(r) {\rm e}^{-(\frac{z}{H(r)})^2}.$$ n(r,z) = (A.7)

Hydrostatic scale height:

$$\sqrt{\frac{2k r^3 T_k(r)}{G M_* m_{\rm o}}}$$                H(r) = (A.8)

$$\sqrt{\frac{2k}{m_{\rm o}}} \frac{r}{v(r)} \sqrt{T_k(r)}$$ = (A.9)

$$H_{\rm o} (r/r_{\rm o})^h$$ = (A.10)

h = 1 + v -q/2. (A.11)

This also implies that $H(r) = \sqrt{2}C_{\rm s}/\Omega$ (where $C_{\rm s}$ is the sound speed). G, M_* and $m_{\rm o}$ are the gravitational constant, the stellar mass and the mean molecular weight, respectively.

For the $m_{\rm o}$, we take the value of $2 \times 1.3 m_{\rm H}$ where $m_{\rm H}$is the hydrogen mass (Beckwith & Sargent 1993).

Note that other groups (in particular those working on theoretical dust disk modelling) usually use the following definition for $H(r) = C_{\rm s}/\Omega$, which leads to:

$$n(r,z) = n_{\rm o} {\rm e}^{-(\frac{z}{2 H(r)})^2}.$$

This is the case for the definition of H given in Chiang & Goldreich (1997) and d'Alessio et al. (1998). Therefore, comparing both scale heights imply that "our H'' is $\sqrt{2}$ larger. Note that the scale heights presented for comparison in the Fig. 9 take into account this factor.