Left: stellar mass black holes (1M_⊙–10²M_⊙) form accretion-modified stars (AMSs) to denote them in AGN accretion disks. Right: the Bondi sphere hosts a BH undergoing hyper-Eddington accretion. Powerful outflows developed from the slim disk of the BH produce strong feedback to the Bondi sphere. The hyperaccretion is halted by the mechanical feedback at the radius r_a(∼10⁴ gravitational radii) within interval t_a, generating flares from radio to γ-rays (see the text for details). In this paper, we neglect the spins of the Bondi sphere (see a brief discussion in Section 2.2).