Abstract Double-barred galaxies exhibit sub-kiloparsec secondary stellar bars that are crucial for channeling gases towards a central massive object (CMO) such as a supermassive black hole or a nuclear star cluster. Recent N-body simulations have uncovered a novel galaxy evolution scenario wherein the mass of the CMO increases owing to the secondary bar, resulting in the eventual destruction of the latter. Consequently, the CMO mass growth halts, thus suggesting a maximum CMO mass of ≈10−3 of the stellar mass of the galaxy. This study focuses on backbone orbit families, particularly double-frequency orbits, within double-barred galaxies. Consequently, the dynamic influence of a CMO on these orbits is investigated. The results of the study reveal the emergence of a new orbital resonance within the central region of the galaxy upon the introduction of a CMO. Orbits subjected to this resonance become chaotic and fail to support the secondary bar, ultimately resulting in the destruction of the entire structure. This is partly because of the inability of the secondary bar to obtain support from the newly generated orbit families following the appearance of resonance. Through the estimation of the condition of secondary bar destruction in realistic double-bar galaxies with varying pattern speeds, the results of the study establish that such destruction occurred when the CMO mass reached ≈10−3 of the galaxy mass. Furthermore, a physical explanation of the galaxy evolution scenario is provided, thereby elucidating the interaction between the CMO and the secondary bar. The understanding of the co-evolution of the secondary bar and the CMO, based on stellar orbital motion, is a crucial step towards future observational studies of stars within the bulge of the Milky Way.
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