Accretion-modified Stars in Accretion Disks of Active Galactic Nuclei:
  Slowly Transient Appearance
  Compact objects are expected to exist in the accretion disks of supermassive
black holes (SMBHs) in active galactic nuclei (AGNs), and in the presence of
such a dense environment ($\sim 10^{14}\,{\rm cm^{-3}}$), they will form a new
kind of stellar population denoted as Accretion-Modified Stars (AMSs). This
hypothesis is supported by recent LIGO/Virgo detection of the mergers of very
high-mass stellar binary black holes (BHs). We show that the TZOs will be
trapped by the SMBH-disk within a typical AGN lifetime. In the context of
SMBH-disks, the rates of Bondi accretion onto BHs are $\sim 10^{9}L_{\rm
Edd}/c^{2}$, where $L_{\rm Edd}$ is the Eddington luminosity and $c$ is the
speed of light. Outflows developed from the hyper-Eddington accretion strongly
impact the Bondi sphere and induce episodic accretion. We show that the
hyper-Eddington accretion will be halted after an accretion interval of $t_{\rm
a}\sim 10^{5}m_{1}\,$s, where $m_{1}=m_{\bullet}/10\sunm$ is the BH mass. The
kinetic energy of the outflows accumulated during $t_{\rm a}$ is equivalent to
10 supernovae driving an explosion of the Bondi sphere and developing blast
waves. We demonstrate that a synchrotron flare from relativistic electrons
accelerated by the blast waves peaks in the soft X-ray band ($\sim 0.1\,$keV),
significantly contributing to the radio, optical, UV, and soft X-ray emission
of typical radio-quiet quasars. External inverse Compton scattering of the
electrons peaks around $40\,$GeV and is detectable through {\it Fermi}-LAT. The
flare, decaying with $t^{-6/5}$ with a few months, will appear as a slowly
varying transient. The flares, occurring at a rate of a few per year in
radio-quiet quasars, provide a new mechanism for explaining AGN variability.
