How can double-barred galaxies be long-lived?

Context. Double-barred galaxies account for almost one third of all barred galaxies, suggesting that secondary stellar bars, which are embedded in large-scale primary bars, are long-lived structures. However, up to now it has been hard to self-consistently simulate a disc galaxy that sustains two nested stellar bars for longer than a few rotation periods. Aims. The dynamical and physical requirements for long-lived triaxiality in the central region of galaxies still need to be clarified. Methods. N-body/hydrodynamical simulations including star formation recipes have been performed. Their properties (bar lengths, pattern speeds, age of stellar population, and gas content) have been compared with the most recent observational data in order to prove that they are representative of double-barred galaxies, even SB0. Overlaps in dynamical resonances and bar modes have been looked for using Fourier spectrograms. Results. Double-barred galaxies have been successfully simulated with lifetimes as long as 7 Gyr. The stellar and gaseous distributions in the central regions are time dependent and display many observed morphological features (circumnuclear rings, pseudo-bulges, triaxial bulges, ovals, etc.) typical of barred galaxies, even early-type. The stellar population of the secondary bar is younger on average than for the primary large-scale bar. An important feature of these simulations is the absence of any resonance overlap for several Gyr. In particular, there is no overlap between the primary bar inner Lindblad resonance and the secondary bar corotation. Therefore, mode coupling cannot sustain the secondary bar mode. Star formation is identified here as possibly being responsible for bringing energy to the nuclear mode. Star formation is also responsible for limiting the amount of gas in the central region which prevents the orbits sustaining the secondary bar from being destroyed. Therefore, the secondary bar can dissolve but reappear after approximate to 1 Gyr as the associated wave is persistent as long as central star formation is active. When star formation is switched off the dynamical perturbation associated with the secondary bar needs several Gyr to fully vanish, although the central morphological signature is almost undetectable after 2 Gyr. Conclusions. Double-bars can be long-lived in numerical simulations with a gaseous component, even in the absence of overlap of resonances or mode coupling, provided that star formation remains active, even moderately, in the central region where the nuclear bar lies.