Convection driven heating of the solar middle chromosphere by resistive dissipation of large scale electric currents

A two dimensional, steady state, resistive magnetohydrodynamic (MHD) model with flow is used to support the proposition that a major source of heating for the solar middle chromosphere is resistive dissipation of large scale electric currents driven by a convection electric field. The currents are large scale in that their scale heights range from hundreds of kilometers in the network to thousands of kilometers in the internetwork. The current is carried by protons, and flows orthogonal to the magnetic field in a weakly ionized, strongly magnetized hydrogen plasma. The flow velocity is mainly parallel to the magnetic field. The relatively small component of flow velocity orthogonal to the magnetic field generates a convection electric field which drives the current. The magnetic field is the sum of a loop shaped field, called a magnetic element, and a much stronger, larger scale potential field. All of the heating takes place in the magnetic element. Solutions to the model indicate that magnetic elements with horizontal spatial extents of about one thousand to five thousand kilometers may be confined to, and heat, the middle chromospheric network. Other solutions to the model indicate that magnetic elements with horizontal spatial extents of about ten thousand to thirty thousand kilometers may span and heat the middle chromospheric internetwork, and may be the building blocks of the chromospheric magnetic canopy. It is suggested that the middle chromosphere is highly structured over a wide range of spatial scales determined by the properties of thesemagnetic elements, and stronger, larger scale potential fields.