Introduction

In the present chapter we will describe the mechanisms that generate the continuum and line radiation in the solar spectrum in the UV, EUV, and soft X-ray ranges. We will first describe the processes that can excite an atom or ion from an atomic level to another level with higher energy, the decay from which generates a photon, as described in Chapter 3. We will then discuss the processes of ionization or recombination of atoms and ions. We will define the contribution function of an optically thin spectral line and its dependence on key parameters of the plasma itself. We will also describe the processes that generate the free-free (or bremsstrahlung) and free-bound continuum radiation.

For simplicity, throughout the remainder of this chapter we will refer to a neutral atom or an ion simply as an ion, regardless of its state of ionization.

Collisional excitation and de-excitation of atomic levels

One of the main assumptions that we will make in this chapter is that ionization and recombination processes can be decoupled from excitation and de-excitation processes, so that they can be treated separately. This approximation is usually accurate in the solar atmosphere, since the time scales for ionization and recombination are usually longer than those for excitation and de-excitation. However, as we will see in Section 4.9, ionization and recombination effects on excited levels may be non-negligible in several atomic systems, but they can be taken into account using an approximate method that allows us to retain the separation between ionization and recombination on the one hand, and excitation and de-excitation on the other.

Even those not engaged in solar physics will have noticed a huge increase in space observations of the solar atmosphere over the past few years. The last ten years especially have seen several notable space missions launched by NASA, the European Space Agency (ESA), the Japanese and Russian space agencies, and several other organizations, among which have been the Yohkoh and RHESSI X-ray spacecraft, SOHO, TRACE, and CORONAS-F which have on board high-resolution instruments working in the extreme ultraviolet spectrum, and most recently the Hinode and STEREO missions, both launched in late 2006, all of which are making spectacular observations in the visible, ultraviolet, and soft X-ray regions. Major contributions to our knowledge have also been made by rocket-borne instruments such as SERTS and EUNIS, working in the extreme ultraviolet.

The increase in our understanding of the solar atmosphere giving rise to this emission has been enormous as a direct result of studying the data from these instruments. We have built on the knowledge gained from previous large solar missions such as the Skylab mission and Solar Maximum Mission to develop models for the solar atmosphere and for phenomena such as flares and coronal mass ejections. However, to the dismay of some but the excitement of most, we are now presented with a picture of the solar atmosphere that is far more dynamic and complex than we ever expected from early spacecraft or ground-based telescopes. Consequently, it has really been the case that as fast as we solve some problems, others are created that will obviously need great ingenuity in finding satisfactory physical explanations.

The differentiability of functions at the mass-shedding limit

Since solutions to Poisson-like equations on domains containing corners are known to be non-analytic in general, it will come as no surprise to learn that the functions involved in describing a mass-shedding configuration are also not analytic. It is of interest, especially for the numerical methods used in this book, to be more precise. Ideally, we would be able to determine the asymptotic behaviour of the functions involved as one approaches a corner.We shall content ourselves in a first analysis, however, with determining which derivatives become singular.

The behaviour of solutions to Poisson-like equations on domains containing corners has been studied by Wigley (1970), Eisenstat (1974) and discussed in Birkhoff and Lynch (1984). In those analyses, it was always assumed that the domain boundaries are known whereas in our case, the (free) boundary arises from solving a global problem. Although we know that the cross-section of the surface of a mass-shedding body contains a corner, we do not know much, a priori, about the differentiability of its parametric representation ζb(ϱ).

Nonetheless, in order to study the behaviour of the Newtonian potential U, let us imagine that the global problem has been solved, that the surface is known, and that a cusp (i.e. mass shedding, cf. page 26) exists at the point ϱ = ϱ0.

Introduction

Studies of the properties of the solar atmosphere began with the onset of space-borne instruments working in X-rays and the ultraviolet. The first instruments had poor spatial resolution and conclusions regarding the structure were indirectly inferred from spectroscopic observations. Early ultraviolet spectrometers also had poor spectral resolution, from which the intensities of the stronger lines could give only a general idea of the distribution of emission measure with temperature (Pottasch (1964)). With assumptions of plane parallel geometry and hydrostatic equilibrium, and with neglect of any fine structure possibly present (i.e. filling factors of unity), the gross features of the solar atmosphere could be deduced. From this, various models (Athay (1976), Mariska (1992)) indicated the presence of a narrow transition region, height range less than 100 km, between the chromosphere and corona. Figure 1.1 shows the atmospheric structure according to theoretical models. A growing corpus of observations, particularly those starting from the Skylab mission, showed that the transition region had a much larger extent than was indicated in earlier models, leading to a revision of our ideas of its nature, which are discussed in this chapter.

Bray et al. (1991) state in their book that ‘coronal loops are a phenomenon of active regions and there is growing evidence that they are the dominant structure in the higher levels (inner corona) of the Sun's atmosphere’. Indeed, the existence of large-scale coronal structures in quiet Sun regions was well known from white-light images during total solar eclipses for many years. They are observed to consist of large loops tapering to cusp-like apices beyond which are the coronal streamers.