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Register a new userHigh-order 3D Voronoi tessellation for identifying Isolated galaxies, Pairs and Triplets
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Geometric method based on the high-order 3D Voronoi tessellation is proposed for identifying the single galaxies, pairs and triplets. This approach allows to select small galaxy groups and isolated galaxies in different environment and find the isolated systems. The volume-limited sample of galaxies from the SDSS DR5 spectroscopic survey was used. We conclude that in such small groups as pairs and triplets the segregation by luminosity is clearly observed: galaxies in the isolated pairs and triplets are on average two times more luminous than isolated galaxies. We consider the dark matter content in different systems. The median values of mass-to-luminosity ratio are 12 M_sol/L_sol for the isolated pairs and 44 M_sol/L_sol for the isolated triplets; 7 (8) M_sol/L_sol for the most compact pairs (triplets). We found also that systems in the denser environment have greater rms velocity and mass-to-luminosity ratio.
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The construction of catalogues of galaxies and the a posteriori study of galaxy properties in relation to their environment have been hampered by scarce redshift information. The new 3-dimensional (3D) surveys permit small, faint, physically bound satellites to be distinguished from a background-projected galaxy population. We aim to provide representative samples of isolated galaxies, isolated pairs, and isolated triplets for testing galaxy evolution and secular processes in low density regions of the local Universe, as well as to characterise their local and large-scale environments. We used spectroscopic data from the tenth data release of the SDSS-DR10 to automatically and homogeneously compile catalogues of 3702 isolated galaxies, 1240 isolated pairs, and 315 isolated triplets in the local Universe. To quantify the effects of their local and large-scale environments, we computed the projected density and the tidal strength for the brightest galaxy in each sample. We find evidence of isolated pairs and isolated triplets that are physically bound at projected separations up to $d leq 450$ kpc with radial velocity difference $Delta v leq 160$ km s$^{-1}$, where the effect of the companion typically accounts for more than 98% of the total tidal strength affecting the central galaxy. For galaxies in the catalogues, we provide their positions, redshifts, and degrees of relation with their physical and large-scale environments. The catalogues are publicly available to the scientific community. For isolated galaxies, isolated pairs, and isolated triplets, there is no difference in their degree of interaction with the large-scale structure, which may suggest that they have a common origin in their formation and evolution. We find that most of them belong to the outer parts of filaments, walls, and clusters, and generally differ from the void population of galaxies.
We present a new open source code for massive parallel computation of Voronoi tessellations(VT hereafter) in large data sets. The code is focused for astrophysical purposes where VT densities and neighbors are widely used. There are several serial Voronoi tessellation codes, however no open source and parallel implementations are available to handle the large number of particles/galaxies in current N-body simulations and sky surveys. Parallelization is implemented under MPI and VT using Qhull library. Domain decomposition takes into account consistent boundary computation between tasks, and includes periodic conditions. In addition, the code computes neighbors list, Voronoi density, Voronoi cell volume, density gradient for each particle, and densities on a regular grid.
A homogeneous Poisson-Voronoi tessellation of intensity $gamma$ is observed in a convex body $W$. We associate to each cell of the tessellation two characteristic radii: the inradius, i.e. the radius of the largest ball centered at the nucleus and included in the cell, and the circumscribed radius, i.e. the radius of the smallest ball centered at the nucleus and containing the cell. We investigate the maximum and minimum of these two radii over all cells with nucleus in $W$. We prove that when $gammarightarrowinfty$, these four quantities converge to Gumbel or Weibull distributions up to a rescaling. Moreover, the contribution of boundary cells is shown to be negligible. Such approach is motivated by the analysis of the global regularity of the tessellation. In particular, consequences of our study include the convergence to the simplex shape of the cell with smallest circumscribed radius and an upper-bound for the Hausdorff distance between $W$ and its so-called Poisson-Voronoi approximation.
The Sloan Digital Sky Survey has obtained 450 square degrees of photometric scan data, in five bands (u,g,r,i,z), which we use to identify clusters of galaxies. We illustrate how we do star-galaxy separation, and present a simple and elegant method of detecting overdensities in the galaxy distribution, using the Voronoi Tessellation.
A jammed packing of frictionless spheres at zero temperature is perfectly specified by the network of contact forces from which mechanical properties can be derived. However, we can alternatively consider a packing as a geometric structure, characterized by a Voronoi tessellation which encodes the local environment around each particle. We find that this local environment characterizes systems both above and below jamming and changes markedly at the transition. A variety of order parameters derived from this tessellation carry signatures of the jamming transition, complete with scaling exponents. Furthermore, we define a real space geometric correlation function which also displays a signature of jamming. Taken together, these results demonstrate the validity and usefulness of a purely geometric approach to jamming.
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