Plasma Heating by Pedersen Current Dissipation From the Photosphere to the Upper Chromosphere

An MHD model is used to estimate the contribution of Pedersen current dissipation, as a function of height z, to plasma heating from the photosphere to the upper chromosphere. The model computes the particle diffusion velocities, normalized to the local drift velocity, transverse to a vertical magnetic field for a seven species plasma of electrons, protons, a proxy heavy ion, HeI, HeII, HeIII, and H. The proxy heavy ion is a single species representation of singly ionized C, Si, Al, Mg, Fe, Na, and Ca. The temperature and particle densities as functions of z are given by VAL model C. Collisions between all unlike particle species are taken into account. The diffusion velocities are used to compute the heating rate per unit volume Q(z), normalized to the maximum possible heating rate per unit volume at height z, due to Pedersen current dissipation. Q is the fraction of energy in the current density perpendicular to the magnetic field that is dissipated by collisions. Solutions to the model suggest that: (i) The solar chromosphere above photospheric magnetic fields with strengths ~ 10² - 10³ G is heated by Pedersen current dissipation; (ii) This heating mechanism first becomes effective at heights corresponding to the lower chromosphere as defined by VAL; (iii) It is the rapid increase of charged particle magnetization with height in the lower chromosphere that triggers the rapid onset of intense heating by Pedersen current dissipation, where the magnetization is the ratio of the cyclotron frequency to the total collision frequency with unlike particles; (iv) Q(z) rapidly decreases to zero for z > ~ 2100 km due to strong magnetization transforming the current perpendicular to the magnetic field into a Hall current, which is not dissipative; (v) The protons and the proxy heavy ions carry essentially all of the Pedersen current. These results suggest that network and internetwork regions of the chromosphere are heated by Pedersen current dissipation. The model does not assume or predict any form for the mechanism that drives the heating. However, the results of the model are consistent with previous predictions that magnetoacoustic waves heat network regions of the chromosphere through Pedersen current dissipation driven by a wave generated convection electric field. It is proposed that this wave heating mechanism also makes a major contribution to heating internetwork regions of the chromosphere. This work was supported by National Science Foundation grant ATM 9816335.