Bulge Oscillation Driven by Outflows of Active Galactic Nuclei. I. Fast Outflow Case

There is growing evidence for star formation inside outflows of active galactic nuclei (AGNs). The formed stars are injected into bulges and give rise to perturbation of bulges. In this paper, we investigate the issues of non-rotating, spherically symmetric bulges under the perturbation of fast, massive outflows with stars formed inside. We show that the potential perturbation of outflows together with injection and dynamical friction of these stars could drive bulge oscillations. Still, we find non-zero radial velocity of bulges will be driven by the episodic outflows of AGNs and after the AGN quenched, the radial velocity will tend to zero within a timescale $\sim\tau_{\rm AGN}$, which is the AGN's lifetime. For some typical values of bulges and AGNs, we find the expansion and contraction velocities are of a few $10\,\rm km\,s^{-1}$ for $10^{10}\,M_\odot$ bulges and mass outflowing rate $500\,M_\odot/\rm yr$, which would give observational signatures.