Globular Cluster Luminosity Functions and the Hubble Constant from WFPC2 Imaging: Galaxies in the Coma I Cloud

The membership of some galaxies in the nearby (d ~ 12 Mpc) Coma I cloud is uncertain. Here we present globular cluster luminosity functions (GCLFs) from the HST for two bright ellipticals which may belong to this group. After fitting the GCLF, we find a turnover magnitude of m_V^0 = 23.23 +/- 0.11 for NGC 4278 and m_V^0 = 23.07 +/- 0.13 for NGC 4494. Our limiting magnitude is about two magnitudes fainter than these values, making this data among the most complete GCLFs published to date. The fitted GCLF dispersions (~ 1.1 mag.) are somewhat smaller than typical values for other ellipticals. Assuming an absolute turnover magnitude of M_V^0 = -7.62, and after applying a small metallicity correction, we derive distance modulii of (m -- M) = 30.61 +/- 0.14 for NGC 4278 and 30.50 +/- 0.15 for NGC 4494. These distance estimates are compared to other methods, and lie within the published range of values. We conclude that both galaxies lie at the same distance and are both members of the Coma I cloud.Comment: 13 pages, Latex. Full paper also available at http://www.ucolick.org/~forbes/home.htm

Globular Clusters and Galaxy Formation

Globular clusters provide a unique probe of galaxy formation and evolution. Here I briefly summarize the known observational properties of globular cluster systems. One re-occurring theme is that the globular cluster systems of spirals and ellipticals are remarkably similar. Photometry, and the limited spectra available, are consistent with metal-poor clusters forming before the main spheroid component is established and the metal-rich ones forming at the same time as the spheroid in a burst of star formation. These observations are compared to a model for globular cluster formation in a LCDM hierarchical universe. One model result reported here is that S_N is determined at early times and little affected by late epoch mergers.Comment: 2 pages, Latex, 2 figures, To appear in the proceedings of Galaxy Evolution: Theory and Observations, ed. V. Avila-Reese, C. Firmani, C. Frenk, C. Allen, RevMexA

The Globular Cluster Systems of Ellipticals and Spirals

In this overview of the key properties of globular cluster (GC) systems I show that the GCs in elliptical and spiral host galaxies have more in common than previously thought. After contrasting these properties I briefly comment on GC formation.Comment: 6 pages, Latex, 4 figures, To appear in the proceedings of IAU Symp. 207, "Extragalactic Star Clusters", eds. Grebel, Geisler, Minnit

Completing the design spectra for graphs with six vertices and eight edges

Apart from two possible exceptions, the design spectrum has been determined for every graph with six vertices and at most eight edges. The purpose of this note is to establish the existence of the two missing designs, both of order 32

Improved Soundness for QMA with Multiple Provers

We present three contributions to the understanding of QMA with multiple provers: 1) We give a tight soundness analysis of the protocol of [Blier and Tapp, ICQNM '09], yielding a soundness gap Omega(1/N^2). Our improvement is achieved without the use of an instance with a constant soundness gap (i.e., without using a PCP). 2) We give a tight soundness analysis of the protocol of [Chen and Drucker, ArXiV '10], thereby improving their result from a monolithic protocol where Theta(sqrt(N)) provers are needed in order to have any soundness gap, to a protocol with a smooth trade-off between the number of provers k and a soundness gap Omega(k^2/N), as long as k>=Omega(log N). (And, when k=Theta(sqrt(N)), we recover the original parameters of Chen and Drucker.) 3) We make progress towards an open question of [Aaronson et al., ToC '09] about what kinds of NP-complete problems are amenable to sublinear multiple-prover QMA protocols, by observing that a large class of such examples can easily be derived from results already in the PCP literature - namely, at least the languages recognized by a non-deterministic RAMs in quasilinear time.Comment: 24 pages; comments welcom

Passive laser irradiation as a tool for optical catalysis

The mechanisms of absorption, emission, and scattering of photons form the foundations of optical interactions between light and matter. In the vast majority of such interactions there is a significant interplay and energy exchange between the radiation field and the material components. In absorption for example, modes of the field are depopulated by photons whose energy is at resonance with a molecular transition producing excited material states. In all such optical phenomena, the initial state of the radiation field differs in mode occupation to its final state. However, certain optical processes can involve off-resonance laser beams that are unchanged on interaction with the material: the output light, after interaction, is identical to the laser input. Such off-resonance interactions include forward Rayleigh scattering, responsible for the wellknown gradient force in optical trapping, and the laser-induced intermolecular interaction commonly termed optical binding; in both processes, an intense beam delivers its effect without suffering change. It is possible for beams detuned from resonance to provide not only techniques for optomechanical and optical manipulation, but also to passively influence other important and functional interactions such as absorption from a resonant beam, or energy transfer. Such effects can be grouped under the banner of ‘optical catalysis’, since they can significantly influence resonant processes. Furthermore, off-resonance photonics affords a potential to impact on chemical interactions, as in the passive modification of rotational constants and phase transitions. To date, apart from optical manipulation, the potential applicability of passive photonics, particularly in the realm of chemical physics and materials science, has received little attention. Here we open up this field, highlighting the distinct and novel role that off-resonance laser beams and the ensuing photonics can play

Designs for graphs with six vertices and nine edges

The design spectrum has been determined for eleven of the 21 graphs with six vertices and nine edges. In this paper we completely solve the design spectrum problem for the remaining ten graphs