Structure and Evolution of Barred Spiral Galaxies, III

Abstract

Some exact two-dimensional rotating non-axially symmetric collisionless self-gravitating stellar systems have been constructed. Their approximate evolution, as they lose mass and angular momentum, has been computed by using the adiabatic invariants associated with each stellar orbit. If the arms of barred spiral galaxies form from gas streaming out along the bar, the results indicate that the bar becomes more dense, more stubby, rotates more rapidly, and becomes more bound against centrifugal force. The results favour this scheme for spiral arm formation against another mechanism which has been suggested (8, 9). I. Introduction. In a previous paper (1) we summarized the observational evidence for gas flow outward along the bar in barred spiral galaxies, and described some simple uniformly rotating models of these systems. In these models gas streams out from the central region of the system, and is fed with the necessary energy and angular momentum by the gravitational torque of the bar. The gas, together with its energy and angular momentum, is lost from the ends of the bar, and forms trailing spiral arms. It was concluded that the gravitational torque is adequate to maintain outflow velocities of the observed magnitude. The mass of a barred galaxy is of order io 10 Mq (2), and the observed rate of mass loss is estimated at 1 Mq yearly (3). Therefore the timescale for mass loss is of order 10 10 years, which is comparable with the probable lifetime of a galaxy. This means that if we are to extend the simple description of barred systems to times long compared with a rotation period (~ax 10 8 years), we must consider the secular evolution of the bar as it loses mass, energy and angular momentum, according to the scheme outlined above. The bar may be represented as a collisionless stellar system. To describe the secular evolution of such a system, we would like to know a mass distribution function /, of velocity, space, and time, such that : (i) for times of the order of a rotation period,/satisfies the time-independent collisionless Boltzmann equation ; (ii) the initial spatial density distribution obtained by taking the integral of/over all velocity space is the same as the initial density distribution of the bar ; (iii) Poisson's equation is satisfied ; and (iv) the total mass, energy, and angular momentum derived from/decrease slowly, as prescribed. In this paper we consider the problem by an approach which depends on the secular nature of the evolution. The changes in the bar will be slow compared with the orbital periods of stars in the bar. The isolating integrals of the motion of a star in the non-evolving bar will therefore change very slowly as the system evolves, and there will be adiabatic invariants associated with these integrals.