Topology of Large-Scale Structure by Galaxy Type: Hydrodynamic Simulations

The topology of large scale structure is studied as a function of galaxy type using the genus statistic. In hydrodynamical cosmological CDM simulations, galaxies form on caustic surfaces (Zeldovich pancakes) then slowly drain onto filaments and clusters. The earliest forming galaxies in the simulations (defined as ``ellipticals") are thus seen at the present epoch preferentially in clusters (tending toward a meatball topology), while the latest forming galaxies (defined as ``spirals") are seen currently in a spongelike topology. The topology is measured by the genus (= number of ``donut" holes - number of isolated regions) of the smoothed density-contour surfaces. The measured genus curve for all galaxies as a function of density obeys approximately the theoretical curve expected for random-phase initial conditions, but the early forming elliptical galaxies show a shift toward a meatball topology relative to the late forming spirals. Simulations using standard biasing schemes fail to show such an effect. Large observational samples separated by galaxy type could be used to test for this effect.Comment: Princeton University Observatory, submitted to The Astrophysical Journal, figures can be ftp'ed from ftp://astro.princeton.edu/cen/TOP

Topology of COBE Microwave Background Fluctuations

We have measured the topology (genus) of the fluctuations in the cosmic microwave background seen in the recently completed (four-year) data set produced by the COBE satellite. We find that the genus is consistent with that expected from a random-phase Gaussian distribution, as might be produced naturally in inflationary models.Comment: 2 pages, one Post-Script figure, MNRAS LaTeX Style (mn.sty), submitted to MNRA

Static Einstein-Maxwell Solutions in 2+1 dimensions

We obtain the Einstein-Maxwell equations for (2+1)-dimensional static space-time, which are invariant under the transformation $q_0=i\,q_2,q_2=i\,q_0,\alpha \rightleftharpoons \gamma$. It is shown that the magnetic solution obtained with the help of the procedure used in Ref.~\cite{Cataldo}, can be obtained from the static BTZ solution using an appropriate transformation. Superpositions of a perfect fluid and an electric or a magnetic field are separately studied and their corresponding solutions found.Comment: 8 pages, LaTeX, no figures, to appear in Physical Review