Minkowski Functionals of SDSS-III BOSS : Hints of Possible Anisotropy in
  the Density Field?
  We present measurements of the Minkowski functionals extracted from the
SDSS-III BOSS catalogs. After defining the Minkowski functionals, we describe
how an unbiased reconstruction of these statistics can be obtained from a field
with masked regions and survey boundaries, validating our methodology with
Gaussian random fields and mock galaxy snapshot data. From the BOSS galaxy data
we generate a set of four density fields in three dimensions corresponding to
the northern and southern skies of LOWZ and CMASS catalogs, smoothing over
large scales such that the field is perturbatively non-Gaussian. We extract the
Minkowski functionals from each data set separately, and measure their shapes
and amplitudes by fitting a Hermite polynomial expansion. For the shape
parameter of the Minkowski functional curves $a_0$, that is related to the
bispectrum of the field, we find that the LOWZ-South data presents a
systematically lower value of $a_0 = -0.080 \pm 0.040$ than its northern sky
counterpart $a_0 = 0.032 \pm 0.024$. Although the significance of this
discrepancy is low, it potentially indicates some systematics in the data or
that the matter density field exhibits anisotropy at low redshift. By assuming
a standard isotropic flat $\Lambda$CDM cosmology, the amplitudes of Minkowski
functionals from the combination of northern and southern sky data give the
constraints $\Omega_{\rm c} h^2 n_{\rm s} = 0.110 \pm 0.006$ and $0.111 \pm
0.008$ for CMASS and LOWZ, respectively, which is in agreement with the Planck
$\Lambda$CDM best-fit $\Omega_{\rm c}h^{2} n_{\rm s} = 0.116 \pm 0.001$.
