Perturbations of C*-algebraic invariants

Kadison and Kastler introduced a metric on the set of all C*-algebras on a fixed Hilbert space. In this paper structural properties of C*-algebras which are close in this metric are examined. Our main result is that the property of having a positive answer to Kadison’s similarity problem transfers to close C*-algebras. In establishing this result we answer questions about closeness of commutants and tensor products when one algebra satisfies the similarity property. We also examine K-theory and traces of close C*-algebras, showing that sufficiently close algebras have isomorphic Elliott invariants when one algebra has the similarity property

Time-Dependence of the Mass Accretion Rate in Cluster Cooling Flows

We analyze two time-dependent cluster cooling flow models in spherical symmetry. The first assumes that the intracluster gas resides in a static external potential, and includes the effects of optically thin radiative cooling and mass deposition. This corresponds to previous steady-state cooling flow models calculated by White & Sarazin (1987). Detailed agreement is found between steady-state models and time-dependent models at fixed times in the simulations. The mass accretion rate is found either to increase or remain nearly constant once flows reach a steady state. The time rate of change of the accretion rate is strongly sensitive to the value of the mass deposition parameter q, but only mildly sensitive to the ratio beta of gravitational binding energy to gas temperature. We show that previous scaling arguments presented by Bertschinger (1988) and White (1988) are valid only for mature cooling flows with weak mass deposition (q ~< 1). The second set of models includes the effects of a secularly deepening cluster potential and secondary infall of gas from the Hubble flow. We find that such heating effects do not prevent the flows from reaching a steady state within an initial central cooling time.Comment: 22 pages (AASTeX) with 16 EPS figures; accepted for publication in The Astrophysical Journa

The RHIC Zero Degree Calorimeter

High Energy collisions of nuclei usually lead to the emission of evaporation neutrons from both ``beam'' and ``target'' nuclei. At the RHIC heavy ion collider with 100GeV/u beam energy, evaporation neutrons diverge by less than $~2$ milliradians from the beam axis Neutral beam fragments can be detected downstream of RHIC ion collisions (and a large aperture Accelerator dipole magnet) if $\theta\leq$ 4 mr but charged fragments in the same angular range are usually too close to the beam trajectory. In this 'zero degree' region produced particles and other secondaries deposit negligible energy when compared with that of beam fragmentation neutrons. The purpose of the RHIC zero degree calorimeters (ZDC's) is to detect neutrons emitted within this cone along both beam directions and measure their total energy (from which we calculate multiplicity). The ZDC coincidence of the 2 beam directions is a minimal bias selection of heavy ion collisions. This makes it useful as an event trigger and a luminosity monitor\cite{baltz} and for this reason we built identical detectors for all 4 RHIC experiments. The neutron multiplicity is also known to be correlated with event geometry \cite{appel} and will be used to measure collision centrality in mutual beam int eractions.Comment: 18 pages, 12 figure

Red Sequence Cluster Finding in the Millennium Simulation

We investigate halo mass selection properties of red-sequence cluster finders using galaxy populations of the Millennium Simulation (MS). A clear red sequence exists for MS galaxies in massive halos at redshifts z < 1, and we use this knowledge to inform a cluster-finding algorithm applied to 500 Mpc/h projections of the simulated volume. At low redshift (z=0.4), we find that 90% of the clusters found have galaxy membership dominated by a single, real-space halo, and that 10% are blended systems for which no single halo contributes a majority of a cluster's membership. At z=1, the fraction of blends increases to 22%, as weaker redshift evolution in observed color extends the comoving length probed by a fixed range of color. Other factors contributing to the increased blending at high-z include broadening of the red sequence and confusion from a larger number of intermediate mass halos hosting bright red galaxies of magnitude similar to those in higher mass halos. Our method produces catalogs of cluster candidates whose halo mass selection function, p(M|\Ngal,z), is characterized by a bimodal log-normal model with a dominant component that reproduces well the real-space distribution, and a redshift-dependent tail that is broader and displaced by a factor ~2 lower in mass. We discuss implications for X-ray properties of optically selected clusters and offer ideas for improving both mock catalogs and cluster-finding in future surveys.Comment: final version to appear in MNRAS. Appendix added on purity and completeness, small shift in red sequence due to correcting an error in finding i