A bright electromagnetic counterpart to extreme mass ratio inspirals
  The extreme mass ratio inspiral (EMRI), defined as a stellar-mass compact
object inspiraling into a supermassive black hole (SMBH), has been widely
argued to be a low-frequency gravitational wave (GW) source. EMRIs providing
accurate measurements of black hole mass and spin, are one of the primary
interests for Laser Interferometer Space Antenna (LISA). However, it is usually
believed that there are no electromagnetic (EM) counterparts to EMRIs. Here we
show a new formation channel of EMRIs with tidal disruption flares as EM
counterparts. In this scenario, flares can be produced from the tidal stripping
of the helium (He) envelope of a massive star by an SMBH. The left compact core
of the massive star will evolve into an EMRI. We find that, under certain
initial eccentricity and semimajor axis, the GW frequency of the inspiral can
enter LISA band within 10 $\sim$ 20 years, which makes the tidal disruption
flare an EM precursor to EMRI. Although the event rate is just $2\times
10^{-4}~\rm Gpc^{-3}yr^{-1}$, this association can not only improve the
localization accuracy of LISA and help to find the host galaxy of EMRI, but
also serve as a new GW standard siren for cosmology.
