MEDUSA: Minkowski functionals estimated from Delaunay tessellations of the three-dimensional large-scale structure

Minkowski functionals (MFs) are a set of statistics that characterise the geometry and topology of the cosmic density field and contain complementary information to the standard two-point analyses. We present MEDUSA, an implementation of an accurate method for estimating the MFs of three-dimensional point distributions. These estimates are inferred from triangulated isodensity surfaces that are constructed from the Delaunay tessellation of the input point sample. Contrary to previous methods, MEDUSA can account for periodic boundary conditions, which is crucial for the analysis of N-body simulations. We validate our code against several test samples with known MFs, including Gaussian random fields with a ${\Lambda}$CDM power spectrum, and find excellent agreement with the theory predictions. We use MEDUSA to measure the MFs of synthetic galaxy catalogues constructed from N-body simulations. Our results show clearly non-Gaussian signatures that arise from the non-linear gravitational evolution of the density field. We find that, although redshift-space distortions significantly change our MFs estimates, their impact is considerably reduced if these measurements are expressed as a function of the volume-filling fraction. We also show that the effect of Alcock-Paczynski (AP) distortions on the MFs can be described by scaling them with different powers of the isotropic AP parameter $q$ defined in terms of the volume-averaged distance $D_{\rm V}(z)$. Thus the MFs estimates by MEDUSA are useful probes of non-linearities in the density field, and the expansion and growth of structure histories of the Universe.