Stability and Secular Heating of Galactic Discs

The secular evolution of galactic discs, of which the increase of the stellar velocity dispersion with age is the most striking expression from a kinematical point of view, is closely related to their stability properties because of the collective nature of such systems. In this context, however, the crucial role of collective effects is often underestimated or not properly taken into account. We propose a global collective heating mechanism leading to a self-regulation process of the kind suggested by the spiral structure theory, when both the linear effects of wave-wave interactions and the quasi-linear effects of wave-particle interactions at the relevant resonances are taken into account. The cold interstellar gas is expected to play a crucial role in ensuring selfregulation together with the internal excitation and feedback mechanisms invoked for the maintenance of global spiral modes. As a result, the planar and vertical components of the stellar velocity dispersion are expected to have a different age-dependence. Some observational evidences in support of this qualitative prediction are also discussed. Quantitative predictions can only be made provided a deep understanding of both local and global self-regulation mechanisms acting in galactic discs is attained. This is not an easy task at all, and in turn it requires a scrupulous investigation into their stability properties. Our contribution is thus aimed at clarifying the role of certain effects, namely those related to the presence of the cold interstellar gas and to the finite thickness of galactic discs, which are generally neglected for mathematical convenience. Most theoretical investigations into the spiral structure of galaxies p,re based on one-component models, because only low-velocity dispersion stars seem to play a fundamental role. However, it has long been recognized that in some cases also the contribution of the cold interstellar gas can be important because of its low turbulent velocity dispersion, although it represents a small fraction of the total mass in normal spiral galaxies. Our analysis is devoted to such cases. We first perform a local linear stability analysis. It is found that in some regimes of astrophysical interest the role of the cold interstellar gas can even be dominant at short wavelengths. The results obtained in this context are used to investigate global spiral modes in regimes which are expected to be associated with normal spiral structure. We use two-component equilibrium models which incorporate the essential features of the cold interstellar gas, as suggested by some recent observational surveys. Appreciable modifications to the structure of the modes, with respect to the corresponding one-component cases, are present only when a peaked distribution of molecular hydrogen is simulated. However, even in the cases where no qualitative modifi~ations are present, the basic states which support these modes are characterized by relatively high stellar planar velocity dispersions, i.e. by values of the local stability parameter Q larger than unity. Finally, some qualitative predictions concerning the expected structure of global spiral modes in peculiar gas-dominated regimes (where a more complicated global analysis is required) are made. The crucial role that the cold interstellar gas can play in the dynamics and structure of early normal spiral galaxies has been shown in Chapter 7, where finite-thickness effects have not been taken into account. In view of the importance that such effects might have in the self-regulation mechanisms which are expected to operate in galactic discs and to be at the basis of their secular heating, we have tried to evaluate them. This can be done only after that their vertical structure at equilibrium has carefully been investigated. An asymptotic analysis has thus been carried out to study the thicknessscales relevant to both the equilibrium and stability of two-component galactic discs in regimes of astrophysical interest. Two parametrizations have been introduced and examined in view of their relevance to the stability analy$is which we shall perform in Chapter 9. The results obtained in Chapter 8 as regards the vertical structure at equilibrium of two-component galactic discs are used to investigate their local linear stability properties. Under reasonable assumptions finite-thickness corrections to the local dispersion relation can be expressed in terms of two reduction factors lowering the response of the two components or, equivalently, their equilibrium surface densities. Different ansatz for such reduction factors, justified by extending the analysis performed for one-component purely stellar discs, are compared by studying the corresponding two-fluid margi.nal stability curves in standard star-dominated and peculiar gas-dominated regimes. It is found that the stabilizing role of finite-thickness effects can partially counterbalance the destabilizing role of the cold interstellar gas in linear regimes.