Reduction of chemical networks. II. Analysis of the fractional ionisation in protoplanetary discs

We analyse the evolution of the fractional ionisation in a steady-state protoplanetary disc over 10⁶ yr. We consider a disc model with a vertical temperature gradient and with gas-grain chemistry including surface reactions. The ionisation due to stellar X-rays, stellar and interstellar UV radiation, cosmic rays and radionuclide decay is taken into account. Using our reduction schemes as a tool for the analysis, we isolate small sets of chemical reactions that reproduce the evolution of the ionisation degree at representative disc locations with an accuracy of 50%-100%. On the basis of fractional ionisation, the disc can be divided into three distinct layers. In the dark dense midplane the ionisation degree is sustained by cosmic rays and radionuclides only and is very low, ⪉10^-12. This region corresponds to the so-called ``dead zone'' in terms of the angular momentum transport driven by MHD turbulence. The ionisation degree can be accurately reproduced by chemical networks with about 10 species and a similar number of reactions. In the intermediate layer the chemistry of the fractional ionisation is driven mainly by the attenuated stellar X-rays and is far more complicated. For the first time, we argue that surface hydrogenation of long carbon chains can be of crucial importance for the evolution of the ionisation degree in protoplanetary discs. In the intermediate layer reduced networks contain more than a 100 species and hundreds of reactions. Finally, in the unshielded low-density surface layer of the disc the chemical life cycle of the ionisation degree comprises a restricted set of photoionisation-recombination processes. It is sufficient to keep about 20 species and reactions in reduced networks. Furthermore, column densities of key molecules are calculated and compared to the results of other recent studies and observational data. The relevance of our results to the MHD modelling of protoplanetary discs is discussed.