Conditions for Bar Formation in Disk Galaxies with Halo and Bulge

While bars are common in disk galaxies, their formation conditions are not well understood. We use N-body simulations to study the formation and evolution of a bar in isolated galaxies consisting of a stellar disk, a classical bulge, and a dark halo. We consider 24 galaxy models that are similar to the Milky Way but differ in the mass and compactness of the classical bulge and halo concentration. We find that the bar formation requires (Q_T,min /1.2)² + (CMC/0.05)² < 1, where Q_T,min and CMC refer to the minimum value of the Toomre stability parameter and the central mass concentration, respectively. Bars tend to be stronger and longer, and to rotate more slowly, in galaxies with a less massive and less compact bulge and halo. All bars formed in our models correspond to slow bars. A model with the bulge mass of ∼10%–20% of the disk under a concentrated halo produces a bar similar to that of the Milky Way. We discuss our findings in relation to other bar formation criteria suggested by previo