Neutron Star Mergers in AGN Accretion Disks: Cocoon and Ejecta Shock
  Breakouts
  Neutron star mergers are believed to occur in accretion disks around
supermassive black holes. Here we show that a putative jet launched from the
merger of a binary neutron star (BNS) or a neutron star--black hole (NSBH)
merger occurring at the migration trap in an active galactic nucleus (AGN) disk
would be choked. The jet energy is deposited within the disk materials to power
a hot cocoon. The cocoon is energetic enough to break out from the AGN disk and
produce a bright X-ray shock breakout transient peaking at $\sim0.15\,{\rm d}$
after the merger. The peak luminosity is estimated as $\sim 10^{46}\,{\rm
erg}\,{\rm s}^{-1}$, which can be discovered by Einstein Probe from $z\lesssim
0.5$. Later on, the non-relativistic ejecta launched from the merger would
break out the disk, powering an X-ray/UV flare peaking at $\sim 0.5\,{\rm d}$
after the merger. This second shock breakout signal may be detected by UV
transient searches. The cocoon cooling emission and kilonova emission are
outshone by the disk emission and difficult to be detected. Future joint
observations of gravitational waves from BNS/NSBH mergers and associated two
shock breakout signatures can provide a strong support for the compact binary
coalescence formation channel in AGN disks.
