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We use high-resolution numerical simulations to follow the barred diskevolution in a suite of models with progressively more massive stellar bulges,with bulge-to-total (disk$+$bulge) mass ratios of $B/T\sim 0-0.25$, embedded indark matter (DM) halos with the spin $\lambda \sim 0 - 0.09$. We focus onmodels with a sequence of initial rotational support for bulges, and analyzetheir spinup and spindown. We find that (1) the presence of a bulge affects theevolution of stellar bars, i.e., the timescale of bar instability, bar patternspeed and its decay, and the vertical buckling instability. The bar strength isnearly independent of $B/T$ in halos with spin $\lambda = 0$, and is suppressedby a factor $\sim 2$ for halos with $\lambda = 0.09$; (2) The main effect ofthe bulge is the destruction of the harmonic core which affects the buckling;(3) The bulge plays a minor role in the exchange of angular momentum betweenthe barred disk and the DM halo, during its spinup and spindown; (4) Mostinterestingly, the buckling process triggers different response above/below thedisk midplane, which anti-correlates with the bulge mass; (5) In spinninghalos, the buckling process has a prolonged amplitude tail, extending by fewGyr, as verified by measuring distortions in the Laplace plane; (6)Furthermore, as verified by orbital spectral analysis, the bulge gains its spinfrom the bar mainly via the inner Lindblad resonance, while losing it via anumber of resonances lying between the outer and inner Lindblad resonance.

Evolution of Stellar Bars in Spinning Dark Matter Halos and Stellar Bulges