2. Model equations for a photoionization layer
We adopt a simple one dimensional model of a photoionization layer in the solar chromosphere in which a flux of EUV () photons incident from above ionizes neutral hydrogen flowing up with subsonic speeds from below. The photon flux J decays into the layer according to
in which z is directed upwards and J decays downwards, is the cross section ( cm2, see Allen (1976)) for photoionization by and N is the neutral hydrogen density in the layer. The decay of the photon flux is accompanied by the production of protons with density n and speed v according to
where V is the neutral hydrogen speed within the layer. At the bottom of the layer () there are no protons (n = 0) whereas at the top () there are no neutral hydrogen atoms (N = 0). The constant in (3) is then just the hydrogen flux at the bottom, , say. Eq. (1) and (2) yield the simple integral
Since the ionizing length scale ( 40 km) is much smaller than the gravitational scale height (300 km) and also because we assume the hydrogen is flowing upwards at low subsonic speeds, the momentum equations for neutral hydrogen and protons can be reasonably approximated by a balance between their pressure gradients and friction arising from collisions between protons and hydrogen atoms. Thus we can write
where is thermal speed of hydrogen () and is the cross section ( cm2, see Halsted (1972) for charge exchange collisions between hydrogen atoms and protons).
For simplicity we assume the temperatures , and are given throughout the layer (for example isothermal). Thus we have five Eqs. (1), (4), (5), (6) and (7) for the five physical variables n, N, V, and J, which determine the structure of the layer.
© European Southern Observatory (ESO) 1998
Online publication: March 10, 1998