Mechanisms of Solar Coronal Heating

A major problem in astrophysical plasma physics is to explain how the outer atmosphere, the corona, ofthe sun is heated to temperatures of millions of degrees Kelvin. It is accepted that the heating mechanism is magnetic, with the energy source being turbulent motions below the solar surface. Two classes of theory are proposed, according to the timescale of the driving motions in relation to the Alfvin timescale orthe coronal plasma. Fast motions gencrate MHD waves which propagate up into the corona carrying energy and can heat the corona if the waves are damped. Slow motions move the footpoints of the coronal field, generating field-aligned currents which may dissipate 10 provide heat. In each case, the main difficulty is in finding an adequate m a n s of dissipation in the highly-conducting coronal plasma. Same proposed heating mechanisms are outlined here, which present a number of interesting plasma physics problems closely related lo those arising for fusion plasma; in particular, Alfvin wave propagation and absorption in a non-uniform medium, and anomalous heating by reconnection, turbulence and relaxation. I . I N T R O D U C T I O N I , 1 , Basic properties of the solar corona The temperature of the sun declines radially outwards from the hot core (1.6 x I O 7 Kj, Faiiing to about 6000 K just above the visibie surface (the photospherej. Above this, counter to our intuitions, the temperature actually rises with height so that the outer atmosphere (the corona) has a temperature of up to 2-3 x IO6 K. It remains a major unsolved question in solar physics as to why the corona is so hot. Indeed, it has recently become apparent from the results of Einstein and other satellite missions that stars of a wide range of spectral types have similar hot coronae which emit Xrays, and analogous physical processes arise in systems such as the coronae of accretion discs, so this question is of wide significance in astrophysics. In this paper, I outline current suggestions for mechanisms to heat the solar corona. We shall see that a number of interesting plasma physics problems arise which have analogies in other situations. In particular, the physical regime of the corona is remarkably similar to a magnetically-confined fusion experiment : both are magnetized plasmas with small ion Larmor radius (hence usually well described by the magnetohydrodynamic model), low plasma beta and high electric conductivity; the parameters are compared in more detail by BROWNING (1988aj. Thus, there is potentially a lot of interest for fusion plasma physicists in the coronal heating question. The corona may be regarded as a natural laboratory for testing plasma theory, extending the range of available conditions beyond those which can be artificially created. Conversely, solar physics benefits from a comparison with detailed experimental results, and also from the application of theoretical models first developed for fusion plasmas. Of course, the differences between the two regimes must always be kept in