Some of barred galaxies, including the Milky Way, host a boxy/peanut/X-shaped bulge (BPX-shaped bulge). Previous studiessuggested that the BPX-shaped bulge can either be developed by bar buckling or by vertical inner Lindblad resonance (vILR)heating without buckling. In this paper, we study the observable consequence of an BPX-shaped bulge built up quickly after barformation via vILR heating without buckling, using anN-body/hydrodynamics simulation of an isolated Milky Way-like galaxy.We found that the BPX-shaped bulge is dominated by stars born prior to bar formation. This is because the bar suppresses starformation, except for the nuclear stellar disc (NSD) region and its tips. The stars formed near the bar ends have higher Jacobienergy, and when these stars lose their angular momentum, their radial action increases to conserve Jacobi energy. This preventsthem from reaching the vILR to be heated to the BPX region. By contrast, the NSD forms after the bar formation. From thissimulation and general considerations, we expect that the age distributions of the NSD and BPX-shaped bulge formed withoutbar buckling do not overlap each other. Then, the transition age between these components betrays the formation time of the bar, and is testable in future observations of the Milky Way and extra-galactic barred galaxies
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