The Origin of Chromospheric Faculae

G. Haerendel

As so many other well-known solar phenomena also the origin of chromospheric faculae or plages has not been established beyond doubt. Actually, no quantitative theory is available. Here, two mechanisms have been considered which allow heating of the upper chromosphere to the extent needed to balance the enhanced emissions of the plages.

(1) Joule Heating by Field-aligned Currents. Ohmic dissipation is strongly dependent on the current density, j||, and the resistivity, which in turn depends on temperature and, for the partially ionized chromospheric gas, on the degree of ionization. In the upper chromosphere the plasma pressure is too weak to concentrate the magnetic field in thin flux-tubes. Therefore, it varies only slowly with height, and so does j||. Thus, the Ohmic heating rate depends mainly on the temperature, T. T is determined by the balance of heating and radiative cooling which depends, in addition, on total density and degree of ionization, R = ne/nn. All these quantities have been calculated by using Saha's equation with a non-LTE correction, McWhirter et al.'s [1975] cooling function and extra heating by Ohmic dissipation in a model chromosphere. The result is that temperature increases of ~  2000  K (which may be on the high side) at 2000 km height can be achieved with j|| = 1 A/m2. The high current density implied by this model can only be accommodated in thin current tubes of order 10 km. Otherwise the selfgenerated magnetic field would exceed the primary field of the active region. Although, conceptually as well as observationally, such concentrated filamentary currents can not be excluded, they meet another problem. The twisting or shearing that injects j|| has to proceed at time-scales of the order of 1 hour, otherwise Ohmic dissipation and current diffusion in the temperature minimum would limit j||. So, a rather efficient sub-photospheric current generator is implied.

(2) Heating by Collisional Damping of Alfvén Waves. This mechanism was proposed by Haerendel [1992] for the origin of spicules and elaborated in numerical models by De Pontieu [1996]. However, it is assumed that in plage regions the high-frequency Alfvén waves are excited in the active corona above (e.g. in reconnection events) and dominate the action of any Alfvén waves from below. Damping length, ldamp, and dissipation rate, [(e)\dot], depend, among others, on the degree of ionization, R. For plages it is of order 10. If one fixes ldamp at 300 - 1000 km and [(e)\dot] @ 2 ·10-2 ergs/cm3, one obtains frequencies between 10 and 20 Hz and velocity amplitudes of the waves of 3.5 to 2.0 km/s. A byproduct is a considerable downward directed force, even exceeding gravity. Selfconsistent height distributions have yet to be calculated. They may lead to substantial changes of the quoted magnitudes. However, this mechanism may explain why spicules appear to be absent in plages [Zirin, 1966].

De Pontieu, B., Chromospheric spicules driven by Alfvén waves, PhD Thesis, University of Ghent, 1986.

Haerendel, G., Weakly damped Alfvén waves as drivers of solar chromospheric spicules, Nature 360, 241, 1992.

McWhirter et al., Astron. Astrophys. 40, 63, 1975.

Zirin, H., The Solar Atmosphere, Blaisdale Publ. Comp.,Waltham, 1966 (p. 382).

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