  About one third of early-type barred galaxies host small-scale secondary
bars. The formation and evolution of such double-barred galaxies remain far
from being well understood. In order to understand the formation of such
systems, we explore a large parameter space of isolated pure-disk simulations.
We show that a dynamically cool inner disk embedded in a hotter outer disk can
naturally generate a steady secondary bar while the outer disk forms a
large-scale primary bar. The independent bar instabilities of inner and outer
disks result in long-lived double-barred structures whose dynamical properties
are comparable with observations. This formation scenario indicates that the
secondary bar might form from the general bar instability, the same as the
primary bar. Under some circumstances, the interaction of the bars and the disk
leads to the two bars aligning or single, nuclear, bars only. Simulations that
are cool enough of the center to experience clump instabilities may also
generate steady double-barred galaxies. In this case, the secondary bars are
"fast", i.e., the bar length is close to the co-rotation radius. This is the
first time that double-barred galaxies containing a fast secondary bar are
reported. Previous orbit-based studies had suggested that fast secondary bars
are not dynamically possible.
