CONDITIONS FOR PHOTOSPHERICALLY DRIVEN ALFVÉNIC OSCILLATIONS TO HEAT THE SOLAR CHROMOSPHERE BY PEDERSEN CURRENT DISSIPATION

Abstract

A magnetohydrodynamic model that includes a complete electrical conductivity\ntensor is used to estimate conditions for photospherically driven, linear,\nnon-plane Alfvenic oscillations extending from the photosphere to the lower\ncorona to drive a chromospheric heating rate due to Pedersen current\ndissipation that is comparable to the net chromospheric net radiative loss of\n$\\sim 10^7$ ergs-cm$^{-2}$-sec$^{-1}$. The heating rates due to electron\ncurrent dissipation in the photosphere and corona are also computed. The wave\namplitudes are computed self-consistently as functions of an inhomogeneous\nbackground (BG) atmosphere. The effects of the conductivity tensor are resolved\nnumerically using a resolution of 3.33 m. The oscillations drive a\nchromospheric heating flux $F_{Ch} \\sim 10^7 - 10^8$ ergs-cm$^{-2}$-sec$^{-1}$\nat frequencies $\\nu \\sim 10^2 - 10^3$ mHz for BG magnetic field strengths $B\n\\gtrsim 700$ G and magnetic field perturbation amplitudes $\\sim 0.01 - 0.1$\n$B$. The total resistive heating flux increases with $\\nu$. Most heating occurs\nin the photosphere. Thermalization of Poynting flux in the photosphere due to\nelectron current dissipation regulates the Poynting flux into the chromosphere,\nlimiting $F_{Ch}$. $F_{Ch}$ initially increases with $\\nu$, reaches a maximum,\nand then decreases with increasing $\\nu$ due to increasing electron current\ndissipation in the photosphere. The resolution needed to resolve the\noscillations increases from $\\sim 10$ m in the photosphere to $\\sim 10$ km in\nthe upper chromosphere, and is proportional to $\\nu^{-1/2}$. Estimates suggest\nthat these oscillations are normal modes of photospheric flux tubes with\ndiameters $\\sim 10-20$ km, excited by magnetic reconnection in current sheets\nwith thicknesses $\\sim 0.1$ km.\n