EDP Sciences
Free access
Volume 416, Number 3, March IV 2004
Page(s) 1159 - 1178
Section The Sun
DOI http://dx.doi.org/10.1051/0004-6361:20031719

A&A 416, 1159-1178 (2004)
DOI: 10.1051/0004-6361:20031719

On the efficiency of plasma heating by Pedersen current dissipation from the photosphere to the lower corona

M. L. Goodman

Institute for Scientific Research, 2500 Fairmont Avenue - Suite 734, Fairmont, WV 26555-2720, USA
(Received 11 June 2003 / Accepted 2 December 2003)

A model is presented that uses the electrical conductivity tensor of a multi-species plasma to estimate the efficiency Q of plasma heating by Pedersen current dissipation as a function of height from the photosphere to the lower corona. The particle densities and temperature are given by FAL model CM. Q is the efficiency with which the electric field generates thermal energy by transferring energy to the current density ${\vec J}_\perp$ perpendicular to the magnetic field. The energy is then thermalized by collisions. The projection of ${\vec J}_\perp$ on the driving electric field is the Pedersen current density. Q is the ratio of the actual heating rate due to Pedersen current dissipation to the heating rate when ${\vec J}_\perp$ is entirely a Pedersen current, which is the maximum possible heating rate for given ${\vec J}_\perp$ . It is found that Pedersen current dissipation is highly efficient throughout the chromosphere, but is highly inefficient in the transition region and corona on the spatial scales of FAL CM. In the photosphere, the electron magnetization, which is the product of the cyclotron frequency and the collision time is so small compared to unity that the conductivity tensor is almost isotropic, implying there is no essential difference between Pedersen current dissipation and magnetic field aligned current dissipation. It is the rapid increase with height of the magnetizations of electrons, protons and metallic ions from ${\lesssim} 1$ to ${\gg} 1$ beginning near the height of the FAL CM temperature minimum that causes Pedersen current dissipation to become essentially different from magnetic field aligned current dissipation, and that causes Q to rapidly increase from minimum values ${\sim} 0.1$ near the temperature minimum to ${\sim} 1$ in the lower chromosphere. Q remains ${\sim} 1$ up to the transition region in which it precipitously decreases with height to values ${\lesssim} 10^{-10}$ in the corona. It is proposed that the rapidly increasing magnetization triggers the onset of heating by Pedersen current dissipation that causes the chromospheric temperature inversion and heats the entire non-flaring chromosphere. The energy channeled by any mechanism into the generation of a center of mass (CM) electric field that drives current perpendicular to the magnetic field is thermalized by Pedersen current dissipation at the maximum possible rate throughout the chromosphere. The mechanism is damped in the chromosphere to the degree to which its energy is channeled into the creation of the CM electric field. The results of the model are consistent with previous predictions that slow magnetoacoustic waves heat network regions of the chromosphere through dissipation of Pedersen currents driven by a wave generated convection electric field, and that electric current dissipation on the spatial scales of the FAL models is insignificant for heating the transition region.

Key words: Sun: chromosphere -- Sun: transition region -- Sun: corona -- MHD -- Sun: magnetic fields -- stars: atmospheres

© ESO 2004