Equation of continuity

For the  the equation of continuity looks as follows:

$$\frac {\partial \rho_{\rm g}}{\partial { t}}+ \frac{1}{{\rm ... ...gg( \frac{\delta \rho_{\rm g}} {\delta { t}} \bigg)_{\rm coll}$$ (39)

where, for the mass conservation, we have that, obviously,

$$\bigg( \frac{\delta \rho_{\rm g}}{\delta { t}} \bigg)_{\rm c... ...igg( \frac{\delta \rho_{\star}}{\delta { t}} \bigg)_{\rm coll}$$ (40)

We follow the same procedure as for the star continuity equation to get the equation in terms of the logarithmic variables:

$$\frac{\partial \ln \rho_{\rm g}}{\partial t} + \frac{\partia... ...( \frac{\delta \rho_{\rm g}}{\delta {\rm t}} \bigg)_{\rm coll}$$ (41)

The interaction term is in this case

$$\frac{1}{\rho_{\rm g}}\bigg( \frac{\delta \rho_{\rm g}}{\del... ...rm t}} \bigg) = -\frac{\rho_{\star}}{\rho_{\rm g}}X_{\rm coll}$$ (42)