Physics
Scientific paper
Dec 2008
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008agufmsh51c..07g&link_type=abstract
American Geophysical Union, Fall Meeting 2008, abstract #SH51C-07
Physics
7507 Chromosphere, 7524 Magnetic Fields, 7546 Transition Region, 7827 Kinetic And Mhd Theory, 7859 Transport Processes
Scientific paper
Analytic solutions of an MHD model that includes an anisotropic, inhomogeneous electrical conductivity tensor containing Hall, Pedersen, and Spitzer conductivities are used to compute resistive heating rates as a function of height z from the photosphere to the lower corona due to dissipation of driven, linear, non- plane waves. The background state of the atmosphere is assumed to be an FAL atmosphere. This state is linearly perturbed by a harmonic perturbation of frequency ν. The height dependence of the perturbation in the presence of the inhomogeneous background state is determined by solving the MHD equations given the harmonic, horizontal, driving magnetic field Bx1 at the photosphere, the constant vertical magnetic field Bz, and the magnetic field strength Bcond(z) that enters the electrical conductivity tensor. The variation of the heating rates per unit volume and mass with ν, Bx1, and Bcond(0) are determined. The heating rates are found to be ∝ Bcond(0)2 Bx12, and to increase with ν. The Pedersen resistivity is ∝ Bcond(0)2. It is several orders of magnitude greater than the Spitzer resistivity in the chromosphere, and determines the rate of heating by Pedersen current dissipation in the chromosphere. The Pedersen current is essentially a proton current in the chromosphere. The onset of Pedersen current dissipation rates large enough to balance the net radiative loss from the chromosphere occurs near the height of the FAL temperature minimum, and is triggered by the product of the electron and proton magnetizations first exceeding unity. The magnetizations and heating rate increase rapidly with height beginning near the temperature minimum. For the special case of Bz = 200 G, Bx1=140 G, and 400 ≤ Bcond(0) ≤ 1500 G the driver frequency for which the period averaged chromospheric heating flux FCh = 5 × 106 ergs-cm-2-sec-1 has the corresponding range of 91 ≥ ν ≥ 25 mHz. Larger magnetic field strengths correspond to lower frequencies for a given heating rate. At magnetic field strengths < 400 G, this value of FCh is achieved only at higher frequencies corresponding to solutions that violate the linear approximation. For the similar special case of Bz = 200 G, Bx1=140 G, and 50 ≤ Bcond(0) ≤ 1500 G the range of the maximum allowed driver frequency that is consistent with the linear approximation is 100.25 ≥ ν ≥ 92.5 mHz. The corresponding range of FCh is 2 × 106 ≤ FCh ≤ 5.4 × 107 ergs-cm-2-sec-1. This raises the possibility that linear MHD waves with periods ~ 10 seconds might make a major contribution to chromospheric heating in regions where the photospheric magnetic field strength is moderate to high. These results support the proposition of Goodman (e.g. Goodman 2000, ApJ, 533, 501; Goodman 2004, A&A, 424, 691; Kazeminezhad & Goodman 2006, ApJ, 166, 613) that the onset of electron and proton magnetization near the local temperature minimum, and their rapid increase with height causes the rate of proton Pedersen current dissipation to rapidly increase by orders of magnitude with height, creating and maintaining the solar chromosphere, and the chromospheres of solar type stars. This mechanism is not restricted to linear waves. It operates on any current generating MHD process. This work was supported by Grant ATM 0650443 from the National Science Foundation to the West Virginia High Technology Consortium Foundation.
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