**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 = n_{e}/n_{n}.
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/m^{2}. 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, l_{damp}, and
dissipation rate, [(e)\dot], depend, among others, on the degree of ionization,
R. For plages it is of order 10. If one fixes l_{damp} at 300 - 1000
km and [(e)\dot] @ 2 ·10^{-2} ergs/cm^{3}, 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.
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*
**McWhirter et al., Astron. Astrophys. 40, 63, 1975.
*

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

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