III .8 . Solar Prominence Circuit and Solar Flares
As the Sun is still outside the reach of spacecraft, detailed diagnostics of solar plasmas is impossible, and theories of solar phenomena will necessarily remain speculative, or in any case, unconfirmed by high-quality diagnostics . However, if we combine solar observations with careful extrapolations from regions which have been explored by spacecraft, we may clarify several solar physics problems.
Because of its filamentary structure, we conclude that a solar prominence is due to a current . In the photosphere, there are motions with velocity v, which are sometimes irregular (e .g ., originating from the granulations), and sometimes systematic (e .g ., from whirls around Sun-spots, or from the non-uniform rotation of the Sun) . As the photosphere is magnetized (field = B), its electric voltage V varies from point to point . If a magnetic field line above the photosphere runs between point A to another point B,
the voltage, [latex]V= \int_{A}^{B} {\bf v} \times {\bf B} d{\bf s}[/latex], between A and B is applied to this field line, and may cause an electric current along the field line . The circuit is similar to the auroral circuit, but simpler ; it consists of a magnetic flux tube intersecting the solar surface at two points, and a photospheric or subphotospheric connection between these points .
With v ~ 104 m/s , B = 10-3 T (10 G), given the distance between A and B to be of the order of 108 m, we find V = 109 V. However, if v and B are irregular (vary in a more
or less random way), V could have much smaller values . On the other hand, the values for v and B are by no means extreme . We may put 108 –109 V as typical values . According to Alfven and Carlqvist (1967), the electric current is expected to be 1011 – 1012 A (1010 – 1011 emu), a value which has been confirmed observationally by Moreton and Severny (1968) . The inductance of the circuit is 10 H, and the stored energy is 0.5 LI2 = 1023 joule (1030 erg).
The size of a prominence circuit is comparable to that of the auroral circuit . The currents are much larger, because of the higher e .m.f. and the higher conductivity (the high resistivity of the upper ionosphere is replaced by a low resistivity due to the high temperature) . As in the auroral circuit, a double layer may be produced . The auroral double layer is often rapidly fluctuating, giving rise to the rapid variability of auroral phenomena. The prominence double layer is still more variable ; indeed, it can explode, thus producing solar flares . A theory of solar flares, based on such current disruptions, has been worked out by Carlqvist (1969, 1973) . He has presented a quantitatively consistent theory of solar flares.
Much effort has been spent on attempts to explain solar flares by a magnetic field formalism (a survey of these efforts is given by Heyvaerts (1979)) . For reasons given in Chapter I (see Figure I .4), such an explanation is inadequate . To be more specific, since the boundary conditions are not correctly introduced in the magnetic merging theories of solar flares, these theories cannot explain the rapid concentration of the entire circuit's inductive energy at the point of disruption . On the other hand, there are theories which account for a solar flare as a disruption of a current, but attribute the disruption to instabilities other than exploding double layers . Such theories deserve to be taken seriously .
