Structures like galaxies and filaments of galaxies in the Universe come about from the origami-like folding of an initially flat three-dimensional manifold in 6D phase space. The ORIGAMI method identifies these structures in a cosmological simulation
, delineating the structures according to their outer folds. Structure identification is a crucial step in comparing cosmological simulations to observed maps of the Universe. The ORIGAMI definition is objective, dynamical and geometric: filament, wall and void particles are classified according to the number of orthogonal axes along which dark-matter streams have crossed. Here, we briefly review these ideas, and speculate on how ORIGAMI might be useful to find cosmic voids.
We present the ORIGAMI method of identifying structures, particularly halos, in cosmological N-body simulations. Structure formation can be thought of as the folding of an initially flat three-dimensional manifold in six-dimensional phase space. ORIG
AMI finds the outer folds that delineate these structures. Halo particles are identified as those that have undergone shell-crossing along 3 orthogonal axes, providing a dynamical definition of halo regions that is independent of density. ORIGAMI also identifies other morphological structures: particles that have undergone shell-crossing along 2, 1, or 0 orthogonal axes correspond to filaments, walls, and voids respectively. We compare this method to a standard Friends-of-Friends halo-finding algorithm and find that ORIGAMI halos are somewhat larger, more diffuse, and less spherical, though the global properties of ORIGAMI halos are in good agreement with other modern halo-finding algorithms.
We investigate the use of a logarithmic density variable in estimating the Lagrangian displacement field, motivated by the success of a logarithmic transformation in restoring information to the matter power spectrum. The logarithmic relation is an e
xtension of the linear relation, motivated by the continuity equation, in which the density field is assumed to be proportional to the divergence of the displacement field; we compare the linear and logarithmic relations by measuring both of these fields directly in a cosmological N-body simulation. The relative success of the logarithmic and linear relations depends on the scale at which the density field is smoothed. Thus we explore several ways of measuring the density field, including Cloud-In-Cell smoothing, adaptive smoothing, and the (scale-independent) Delaunay tessellation, and we use both a Fourier space and a geometrical tessellation approach to measuring the divergence. We find that the relation between the divergence of the displacement field and the density is significantly tighter with a logarithmic density variable, especially at low redshifts and for very small (~2 Mpc/h) smoothing scales. We find that the grid-based methods are more reliable than the tessellation-based method of calculating both the density and the divergence fields, though in both cases the logarithmic relation works better in the appropriate regime, which corresponds to nonlinear scales for the grid-based methods and low densities for the tessellation-based method.
Measurements of the equation of state of dark energy from surveys of thousands of Type Ia Supernovae (SNe Ia) will be limited by spectroscopic follow-up and must therefore rely on photometric identification, increasing the chance that the sample is c
ontaminated by Core Collapse Supernovae (CC SNe). Bayesian methods for supernova cosmology can remove contamination bias while maintaining high statistical precision but are sensitive to the choice of parameterization of the contaminating distance distribution. We use simulations to investigate the form of the contaminating distribution and its dependence on the absolute magnitudes, light curve shapes, colors, extinction, and redshifts of core collapse supernovae. We find that the CC luminosity function dominates the distance distribution function, but its shape is increasingly distorted as the redshift increases and more CC SNe fall below the survey magnitude limit. The shapes and colors of the CC light curves generally shift the distance distribution, and their effect on the CC distances is correlated. We compare the simulated distances to the first year results of the SDSS-II SN survey and find that the SDSS distance distributions can be reproduced with simulated CC SNe that are ~1 mag fainter than the standard Richardson et al. (2002) luminosity functions, which do not produce a good fit. To exploit the full power of the Bayesian parameter estimation method, parameterization of the contaminating distribution should be guided by the current knowledge of the CC luminosity functions, coupled with the effects of the survey selection and magnitude-limit, and allow for systematic shifts caused by the parameters of the distance fit.
