Revisiting the Globular Cluster System of the Merger Remnant Elliptical NGC 3610

We have obtained Keck spectra of six candidate globular clusters (GCs) in the dynamically young elliptical galaxy NGC 3610, supplementing our previous Keck spectra of eight confirmed GCs (Strader et al. 2003). Five of our new candidates are confirmed to be GCs. Of the thirteen GCs, eleven are located within the K band effective radius of 7 kpc. Two of these thirteen clusters are found to be young (~ 2 Gyr) and very metal-rich ([Z/H] ~ +0.5), three are old and metal-poor, and the remaining eight clusters are old and metal-rich. The ages of the young clusters are consistent with a recent spectroscopic age estimate of 1.6+/-0.5 Gyr for the galaxy itself (Denicolo et al. 2003) and suggest that these clusters formed in the disk-disk merger which likely created NGC 3610. Intriguingly, both young GCs have [alpha/Fe] ~ +0.3, while the majority of the old clusters are not alpha-enhanced, in contrast to Galactic and M31 GCs, and contrary to predictions of nucleosynthetic calculations. The two old subpopulations of GCs can be attributed to the merger progenitors. The relative numbers of old and new metal-rich GCs are poorly constrained because of the expected differences in radial distributions of the two subpopulations. However, based on our spectroscopic results and a comparison of the Hubble Space Telescope color magnitude diagram (Whitmore et al. 2002) with stellar population models, we argue that more than half of the metal-rich GCs are likely to be old.Comment: 21 pages, 6 figures, accepted for Jan 2004 A

Structural parameters for globular clusters in M31 and generalizations for the fundamental plane

The structures of globular clusters (GCs) reflect their dynamical states and past histories. High-resolution imaging allows the exploration of morphologies of clusters in other galaxies. Surface brightness profiles from new Hubble Space Telescope observations of 34 globular clusters in M31 are presented, together with fits of several different structural models to each cluster. M31 clusters appear to be adequately fit by standard King models, and do not obviously require alternate descriptions with relatively stronger halos, such as are needed to fit many GCs in other nearby galaxies. The derived structural parameters are combined with corrected versions of those measured in an earlier survey to construct a comprehensive catalog of structural and dynamical parameters for M31 GCs with a sample size similar to that for the Milky Way. Clusters in M31, the Milky Way, Magellanic Clouds, Fornax dwarf spheroidal and NGC 5128 define a very tight fundamental plane with identical slopes. The combined evidence for these widely different galaxies strongly reinforces the view that old globular clusters have near-universal structural properties regardless of host environment.Comment: AJ in press; 59 pages including 16 figure

Metal-Poor Globular Clusters and Galaxy Formation

We demonstrate a significant (> 5-sigma) correlation between the mean color of metal-poor globular cluster (GC) systems and parent galaxy luminosity. A Bayesian Markov Chain Monte Carlo method is introduced to find the mean color, and is easily generalizable to quantify multimodality in other astronomical datasets. We derive a GC color--galaxy luminosity relation of the form Z ~ L^ (0.15 +/- 0.03). When combined with evidence against a single primordial GC metallicity--galaxy luminosity relation for protogalactic fragments, the existence of such a correlation is evidence against both accretion and major merger scenarios as an explanation of the entire metal-poor GC systems of luminous galaxies. However, our relation arises naturally in an in situ picture of GC formation, and is consistent with the truncation of metal-poor GC formation by reionization. A further implication is that the ages of metal-poor GCs in dwarf galaxies constrain the main epoch of galaxy formation in hierarchical models. If the ages of old metal-poor GCs in Local Group dwarfs (> 11 Gyr) are typical of those in dwarfs elsewhere, then the bulk of galaxy assembly (at least in clusters and groups) must have occurred at z > 2.5, contrary to the predictions of some structure formation models.Comment: 13 pages, 1 figure, accepted for A

Moyal star product approach to the Bohr-Sommerfeld approximation

The Bohr-Sommerfeld approximation to the eigenvalues of a one-dimensional quantum Hamiltonian is derived through order $\hbar^2$ (i.e., including the first correction term beyond the usual result) by means of the Moyal star product. The Hamiltonian need only have a Weyl transform (or symbol) that is a power series in $\hbar$, starting with $\hbar^0$, with a generic fixed point in phase space. The Hamiltonian is not restricted to the kinetic-plus-potential form. The method involves transforming the Hamiltonian to a normal form, in which it becomes a function of the harmonic oscillator Hamiltonian. Diagrammatic and other techniques with potential applications to other normal form problems are presented for manipulating higher order terms in the Moyal series.Comment: 27 pages, no figure

Restoring observed classical behavior of the carbon nanotube field emission enhancement factor from the electronic structure

Experimental Fowler-Nordheim plots taken from orthodoxly behaving carbon nanotube (CNT) field electron emitters are known to be linear. This shows that, for such emitters, there exists a characteristic field enhancement factor (FEF) that is constant for a range of applied voltages and applied macroscopic fields $F_\text{M}$. A constant FEF of this kind can be evaluated for classical CNT emitter models by finite-element and other methods, but (apparently contrary to experiment) several past quantum-mechanical (QM) CNT calculations find FEF-values that vary with $F_\text{M}$. A common feature of most such calculations is that they focus only on deriving the CNT real-charge distributions. Here we report on calculations that use density functional theory (DFT) to derive real-charge distributions, and then use these to generate the related induced-charge distributions and related fields and FEFs. We have analysed three carbon nanostructures involving CNT-like nanoprotrusions of various lengths, and have also simulated geometrically equivalent classical emitter models, using finite-element methods. We find that when the DFT-generated local induced FEFs (LIFEFs) are used, the resulting values are effectively independent of macroscopic field, and behave in the same qualitative manner as the classical FEF-values. Further, there is fair to good quantitative agreement between a characteristic FEF determined classically and the equivalent characteristic LIFEF generated via DFT approaches. Although many issues of detail remain to be explored, this appears to be a significant step forwards in linking classical and QM theories of CNT electrostatics. It also shows clearly that, for ideal CNTs, the known experimental constancy of the FEF value for a range of macroscopic fields can also be found in appropriately developed QM theory.Comment: A slightly revised version has been published - citation below - under a title different from that originally used. The new title is: "Restoring observed classical behavior of the carbon nanotube field emission enhancement factor from the electronic structure

Minimax Current Density Coil Design

'Coil design' is an inverse problem in which arrangements of wire are designed to generate a prescribed magnetic field when energized with electric current. The design of gradient and shim coils for magnetic resonance imaging (MRI) are important examples of coil design. The magnetic fields that these coils generate are usually required to be both strong and accurate. Other electromagnetic properties of the coils, such as inductance, may be considered in the design process, which becomes an optimization problem. The maximum current density is additionally optimized in this work and the resultant coils are investigated for performance and practicality. Coils with minimax current density were found to exhibit maximally spread wires and may help disperse localized regions of Joule heating. They also produce the highest possible magnetic field strength per unit current for any given surface and wire size. Three different flavours of boundary element method that employ different basis functions (triangular elements with uniform current, cylindrical elements with sinusoidal current and conic section elements with sinusoidal-uniform current) were used with this approach to illustrate its generality.Comment: 24 pages, 6 figures, 2 tables. To appear in Journal of Physics D: Applied Physic