## 2. Model equations for a photoionization layerWe 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 The total particle flux of hydrogen and protons is conserved throughout the layer, that is where since the ionizing photon flux is assumed to be completely extingiushed at the bottom of the layer. Therefore if denotes the total incident ionizing photon flux, particle conservation can be written because . 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 Because total momentum is conserved, which in the subsonic approximation reduces to the constancy of total pressure. i.e., the collision frequencies must obey the relation, Thus the collision times are equal and can be expressed as where is thermal speed of hydrogen
() and is the cross
section ( cm 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 © European Southern Observatory (ESO) 1998 Online publication: March 10, 1998 |