  We study the electrodynamics of a kinetically mixed dark photon cloud that
forms through superradiance around a spinning black hole, and design strategies
to search for the resulting multimessenger signals. A dark photon superradiance
cloud sources a rotating dark electromagnetic field which, through kinetic
mixing, induces a rotating visible electromagnetic field. Standard model
charged particles entering this field initiate a transient phase of particle
production that populates a plasma inside the cloud and leads to a system which
shares qualitative features with a pulsar magnetosphere. We study the
electrodynamics of the dark photon cloud with resistive magnetohydrodynamics
methods applicable to highly magnetized plasma, adapting techniques from
simulations of pulsar magnetospheres. We identify turbulent magnetic field
reconnection as the main source of dissipation and electromagnetic emission,
and compute the peak luminosity from clouds around solar-mass black holes to be
as large as $10^{43}$ erg/s for open dark photon parameter space. The emission
is expected to have a significant X-ray component and is potentially periodic,
with period set by the dark photon mass. The luminosity is comparable to the
brightest X-ray sources in the Universe, allowing for searches at distances of
up to hundreds of Mpc with existing telescopes. We discuss observational
strategies, including targeted electromagnetic follow-ups of solar-mass black
hole mergers and targeted continuous gravitational wave searches of anomalous
pulsars.
