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 $\Omega_{\rm c}h^{2} n_{\rm s} = 0.116 \pm 0.001$.