What determines the strength and the slowdown rate of bars?

Isolated barred galaxies evolve by redistributing their angular momentum, which, emitted by material in the inner disc at resonance with the bar, can be absorbed by resonant material in the outer disc, or in the halo. The amount of angular momentum that can be emitted/absorbed at a given resonance depends on the distribution function of the emitting/absorbing material. It thus depends not only on the amount of material on resonant orbits, but also on the velocity dispersion of that material. As it loses angular momentum, the bar becomes stronger and it also rotates slower. Thus the strength of the bar and the decrease of its pattern speed with time are set by the amount of angular momentum exchanged within the galaxy, which, in turn, is regulated by the mass distribution and the velocity dispersion of the material in the disc and spheroidal components. Correlations between the pattern speed of the bar, its strength and the angular momentum absorbed by the spheroid (halo plus bulge) argue strongly that it is the amount of angular momentum exchanged that determines the strength and the slowdown rate of the bar. The decrease of the bar pattern speed with time should not be used to set constraints on the halo-to-disc mass ratio, since it depends also on the velocity dispersion of the halo and disc material.