We have explored the consequences of our previous work where we showed that a initial classical bulge (ICB) may be spun-up and "hidden" within a barred galaxies similar to the Milky Way. In this work we investigated the impact of an rotating ICB on the formation and secular evolution of the bar. We use a series of models containing both a spinning classical bulge, and a disk, which from a Boxy/peanut (BP) bulge. In all the models we show that a strong bar forms and transfers angular momentum to the ICB. However, rotation in the ICB limits the emission of the bar's angular momentum, which in turn changes the size and growth of the bar, and of the BP bulge formed from the disc. We also find that deviations from the cylindrical rotation, which is typically characteristic of BP bulges, during the early phases of secular evolution. These may correspond to similar deviations observed in some bulges. We provide a simple criterion to quantify deviations from pure cylindrical rotation, apply it to all our model bulges, and also illustrate its use for two galaxies: NGC 7332 and NGC 4570.
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