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.
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