  Many barred galaxies harbor small-scale secondary bars in the center. The
evolution of such double-barred galaxies is still not well understood, partly
because of a lack of realistic N-body models with which to study them. Here we
report the generation of such systems in the presence of rotating pseudobulges.
We demonstrate with high mass and force resolution collisionless N-body
simulations that long-lived secondary bars can form spontaneously without
requiring gas, contrary to previous claims. We find that secondary bars rotate
faster than primary ones. The rotation is not rigid: the secondary bars
pulsate, with their amplitude and pattern speed oscillating as they rotate
through the primary bars. This self-consistent study supports previous work
based on orbital analysis in the potential of two rigidly rotating bars. We
also characterize the density and kinematics of the N-body simulations of the
double-barred galaxies, compare with observations to achieve a better
understanding of such galaxies. The pulsating nature of secondary bars may have
important implications for understanding the central region of double-barred
galaxies.
