Vortices and waves in light dark matter
  In a galactic halo like the Milky Way, bosonic dark matter particles lighter
than about $30$ eV have a de Broglie wavelength larger than the average
inter-particle separation and are therefore well described as a set of
classical waves. This applies to, for instance, the QCD axion as well as to
lighter axion-like particles such as fuzzy dark matter. We show that the
interference of waves inside a halo inevitably leads to vortices, locations
where chance destructive interference takes the density to zero. The phase of
the wavefunction has non-trivial winding around these points. This can be
interpreted as a non-zero velocity circulation, so that vortices are sites
where the fluid velocity has a non-vanishing curl. Using analytic arguments and
numerical simulations, we study the properties of vortices and show they have a
number of universal features: (1) In three spatial dimensions, the generic
defects take the form of vortex rings. (2) On average there is about one vortex
ring per de Broglie volume and (3) generically only single winding ($\pm 1$)
vortices are found in a realistic halo. (4) The density near a vortex scales as
$r^2$ while the velocity goes as $1/r$, where $r$ is the distance to vortex.
(5) A vortex segment moves at a velocity inversely proportional to its
curvature scale so that smaller vortex rings move faster, allowing momentary
motion exceeding escape velocity. We discuss observational/experimental
signatures from vortices and, more broadly, wave interference. In the
ultra-light regime, gravitational lensing by interference substructures leads
to flux anomalies of $5-10 \%$ in strongly lensed systems. For QCD axions,
vortices lead to a diminished signal in some detection experiments but not in
others. We advocate the measurement of correlation functions by axion detection
experiments as a way to probe and capitalize on the expected interference
substructures.
