Harmonics in the Dark-Matter Sky: Directional Detection in the
  Fourier-Bessel Basis
  Details about the velocity distribution of weakly interacting massive
particle (WIMP) dark matter in our galaxy may be revealed by nuclear-recoil
detectors with directional sensitivity. Previous studies have assumed that the
velocity distribution takes a simple functional form characterized by a small
number of parameters. More recent work has shown that basis-function expansions
may allow for more general parameterization; such an approach has been
considered for both the one-dimensional speed and momentum distributions, and
also for three-dimensional velocity distributions obeying certain equilibrium
conditions. In this work, I extend this basis-function approach to allow for
arbitrary velocity distributions by working in the Fourier-Bessel basis,
deriving an analytic expression for the directional recoil spectrum. Such an
approach is completely general, and may be useful if the velocity distribution
is too complex to be characterized by simple functional forms or is not
completely virialized. Results concerning the three-dimensional Radon transform
of the Fourier-Bessel basis functions may be of general interest for
tomographic applications.
