Gaia Reveals Dark Matter Correlations Across the Fornax Dwarf Spheroidal
  Galaxy: An Assessment of Dark Matter Models
  The predicted size of dark matter substructures in kilo-parsec scales is
model-dependent. Therefore, if the correlations between dark matter mass
densities, as a function of the distances between them, are measured via
observations, we can scrutinize dark matter scenarios. In this paper, we use
Gaia's data to infer the single-body phase-space density of the stars in the
Fornax dwarf spheroidal galaxy. The latter together with the Jeans equation,
after eliminating the gravitational potential using the Poisson equation,
reveals the mass density of dark matter as a function of its position in the
galaxy. We derive the correlations between dark matter mass densities as a
function of distances between them. For distances beyond 100 parsec, no
statistically significant correlation is observed. We use the results to limit
the parameter space of the Ginzburg-Landau statistical field theory of dark
matter mass densities, and subsequently shrink the parameter space of (i) a
classic gas dark matter and (ii) a superfluid dark matter. Our results can be
used to leave bounds on high-resolution N-body simulations by comparing the
correlations computed using their outputs and the measured ones via
observations.
