Title:

Instabilities in interstellar space

This thesis is a partial investigation of instabilities in the interstellar gas which are driven by a coupling between the ambient radiation field and the gas, and which do not arise when this coupling is missed out. The modes of couplings considered are, firstly, the attenuation of the radiation with the concomitant effects on the temperature, density and composition of the gas, in various combinations. Secondly, velocity dependent effects are examined in various circumstances and thirdly, radiation pressure, not included in the other two, is looked at in the simple case in which temperature and compositional changes are excluded. The explanation of why these instabilities may be of interest, and an outline of the extent to which similar instabilities have been investigated, is given in Chapter 1. Chapter 2 gives details of the basic equations used in the case in which the absorption line shape is ignored. Many of the equations are used in the other chapters. The equations are linearised in perturbations of the density, temperature, radiation field and composition, and the resulting dispersion relationship is found for a harmonic perturbation. Because of the attenuation term in the radiative transfer equation, the polynomial has complex coefficients. In Chapter 3 we investigate the properties of the roots of a complex polynomial by an extension of Routh's methods, and derive a set of criteria to determine the number of roots which have positive real part. These roots correspond to exponentially growing perturbations, or, in other words, they correspond to instabilities. Later in the chapter we apply these methods to Field's dispersion relationship for thermal instabilities and derive many of his conclusions in a fairly simple way. By a slight extension the method yields estimates of the growth times of the instabilities. Some related situations are also examined in a similar way. After the detour of Chapter 3, Chapter 4 gives details of some models of the heating and cooling of the interstellar gas as well as of the reactions to be considered, namely the formation and destruction of H_{2} and of carbon ions. Some of the limitations of the models are also discussed and the roots of the dispersion relation are given for different values of the parameters. New instabilities do appear; for H_{2} their timescales of growth are rather too long to be of interest; for carbon no short timescale instabilities are discovered. Chapter 5 gives similar details for a system of pure hydrogen gas which may be of interest in studies of the formation of the first generation of stars. In Chapter 6 there is a criticism of an earlier work by Schatzman on a similar subject, in which it is shown that his analysis was wrong. Chapter 7 deals with a new possibility, namely that, as the gas moves, photons will be seen to be shifted in frequency and so the molecules will be exposed to a new set of destructive photons at frequencies which have not been selectively absorbed in the unperturbed gas. First the simplest case, that in which the temperature is unperturbed, is treated analytically. The attenuation of the radiation field is not considered. The effectiveness of this dopplerinduced effect depends upon both the absorption profile and the radiation spectrum; these factors as well as temperature perturbations are included next. Both line absorption and continuum absorption are considered. The former is used to investigate the stability of the interstellar gas and of pure hydrogen gas, where hydrogen molecules are dissociated by line absorption; the latter is used in connection with HII regions and also the interstellar gas where the photodissociated species are hydrogen atoms and neutral carbon respectively. Radiation pressure was not included in the previous chapters but in Chapter 8 a modified version of Field's theory of instabilities driven by radiation pressure is presented. The new feature is that the frequency dependence of the absorption coefficient is included in the equations and this, in the case of a flat radiation spectrum, leads to an exact cancellation of the dominant term in Field's equation. Several restrictive features of Field's conclusions are thus modified and seem to make this instability rather more useful in the study of instabilities in the interstellar gas than it appeared in Field's work.
