Dark Photon Stars: Formation and Role as Dark Matter Substructure
  Any new vector boson with non-zero mass (a `dark photon' or `Proca boson')
that is present during inflation is automatically produced at this time from
vacuum fluctuations and can comprise all or a substantial fraction of the
observed dark matter density, as shown by Graham, Mardon, and Rajendran. We
demonstrate, utilising both analytic and numerical studies, that such a
scenario implies an extremely rich dark matter substructure arising purely from
the interplay of gravitational interactions and quantum effects. Due to a
remarkable parametric coincidence between the size of the primordial density
perturbations and the scale at which quantum pressure is relevant, a
substantial fraction of the dark matter inevitably collapses into
gravitationally bound solitons, which are fully quantum coherent objects. The
central densities of these `dark photon star', or `Proca star', solitons are
typically a factor $10^6$ larger than the local background dark matter density,
and they have characteristic masses of $10^{-16} M_\odot (10^{-5}{\rm
eV}/m)^{3/2}$, where $m$ is the mass of the vector. During and post soliton
production a comparable fraction of the energy density is initially stored in,
and subsequently radiated from, long-lived quasi-normal modes. Furthermore, the
solitons are surrounded by characteristic `fuzzy' dark matter halos in which
quantum wave-like properties are also enhanced relative to the usual virialized
dark matter expectations. Lower density compact halos, with masses a factor of
$\sim 10^5$ greater than the solitons, form at much larger scales. We argue
that, at minimum, the solitons are likely to survive to the present day without
being tidally disrupted. This rich substructure, which we anticipate also
arises from other dark photon dark matter production mechanisms, opens up a
wide range of new direct and indirect detection possibilities, as we discuss in
a companion paper.
