@TaylorCordes93; @CordesLazio_02]. On the other hand, neither the position nor the thickness of the neutral phases agree with observations of the Milky Way ISM [@BoularesCox90; @Ferriere01; @NakanishiSofue03; @NakanishiSofue06]. Nevertheless, a central ionized region may be present in several astrophysical scenarios[^4], and therefore it is interesting to test the influence of gravity in this particular example.

The role of gravity can be assessed by comparison with the standard [[constant pressure]{}]{} solution, depicted in Figure \[figConstantP\] for a mid-plane density $n_0=0.5$ cm$^{-3}$. The vertical structure of the disk is basically the same (i.e. gravity does not play a significant role) up to the ionization front. There, the temperature decreases sharply, and the density has to rise accordingly to compensate. In the standard implementation, pressure increases in order to balance the radiative acceleration ($\Delta P_{\rm rad}>0$). The effect is very significant near the ionization front, but it rapidly decreases as photons become absorbed. Although the pressure keeps increasing monotonically with $z$, the slope is quite shallow, and the physical state of the gas in the outer region (density, chemical composition, and temperature) remains approximately constant. Thus, the main effect of gravity on a plane-parallel atmosphere is to set the extent of the molecular 