Dynamical evolution of the mass function and radial profile of the Galactic globular cluster system

Evolution of the mass function (MF) and radial distribution (RD) of the Galactic globular cluster (GC) system is calculated using an advanced and a realistic Fokker-Planck (FP) model that considers dynamical friction, disc/bulge shocks and eccentric cluster orbits. We perform hundreds of FP calculations with different initial cluster conditions, and then search a wide-parameter space for the best-fitting initial GC MF and RD that evolves into the observed present-day Galactic GC MF and RD. By allowing both MF and RD of the initial GC system to vary, which is attempted for the first time in the present Letter, we find that our best-fitting models have a higher peak mass for a lognormal initial MF and a higher cut-off mass for a power-law initial MF than previous estimates, but our initial total masses in GCs, M_{T,i} = 1.5-1.8x10^8 Msun, are comparable to previous results. Significant findings include that our best-fitting lognormal MF shifts downward by 0.35 dex during the period of 13 Gyr, and that our power-law initial MF models well-fit the observed MF and RD only when the initial MF is truncated at >~10^5 Msun. We also find that our results are insensitive to the initial distribution of orbit eccentricity and inclination, but are rather sensitive to the initial concentration of the clusters and to how the initial tidal radius is defined. If the clusters are assumed to be formed at the apocentre while filling the tidal radius there, M_{T,i} can be as high as 6.9x10^8 Msun, which amounts to ~75 per cent of the current mass in the stellar halo.Comment: To appear in May 2008 issue of MNRAS, 386, L6

Nonlinear ac conductivity of one-dimensional Mott insulators

We discuss a semiclassical calculation of low energy charge transport in one-dimensional (1d) insulators with a focus on Mott insulators, whose charge degrees of freedom are gapped due to the combination of short range interactions and a periodic lattice potential. Combining RG and instanton methods, we calculate the nonlinear ac conductivity and interpret the result in terms of multi-photon absorption. We compare the result of the semiclassical calculation for interacting systems to a perturbative, fully quantum mechanical calculation of multi-photon absorption in a 1d band insulator and find good agreement when the number of simultaneously absorbed photons is large.Comment: Dedicated to Thomas Nattermann on the occasion of his 60th birthday. To appear in JSTAT. 5 pages, 2 figure

Switching between dynamic states in intermediate-length Josephson junctions

The appearance of zero-field steps (ZFS’s) in the current-voltage characteristics of intermediate-length overlap-geometry Josephson tunnel junctions described by a perturbed sine-Gordon equation (PSGE) is associated with the growth of parametrically excited instabilities of the McCumber background curve (MCB). A linear stability analysis of a McCumber solution of the PSGE in the asymptotic linear region of the MCB and in the absence of magnetic field yields a Hill’s equation which predicts how the number, locations, and widths of the instability regions depend on the junction parameters. A numerical integration of the PSGE in terms of truncated series of time-dependent Fourier spatial modes verifies that the parametrically excited instabilities of the MCB evolve into the fluxon oscillations characteristic of the ZFS’s. An approximate analysis of the Fourier mode equations in the presence of a small magnetic field yields a field-dependent Hill’s equation which predicts that the major effect of such a field is to reduce the widths of the instability regions. Experimental measurements on Nb-NbxOy-Pb junctions of intermediate length, performed at different operating temperatures in order to vary the junction parameters and for various magnetic field values, verify the physical existence of switching from the MCB to the ZFS’s. Good qualitative, and in many cases quantitative, agreement between analytic, numerical, and experimental results is obtained

Screening current effects in Josephson junction arrays

The purpose of this work is to compare the dynamics of arrays of Josephson junctions in presence of magnetic field in two different frameworks: the so called XY frustrated model with no self inductance and an approach that takes into account the screening currents (considering self inductances only). We show that while for a range of parameters the simpler model is sufficiently accurate, in a region of the parameter space solutions arise that are not contained in the XY model equations.Comment: Figures available from the author

Globular cluster systems II: On the formation of old globular clusters and their sites of formation

We studied the metal-poor globular cluster (GC) populations of a large variety of galaxies (47 galaxies spanning about 10mag in absolute brightness) and compared their mean [Fe/H] with the properties of the host galaxies. The mean [Fe/H] of the systems lie in the -1.65<[Fe/H]<-1.20 range (74% of the population). Using only GC systems with more than 6 objects detected, 85% of the population lie within -1.65<[Fe/H]<-1.20. The relation between the mean [Fe/H] of the metal-poor GC systems and the Mv of their host galaxies presents a very low slope which includes zero. An analysis of the correlation of the mean [Fe/H] with other galaxy properties also leads to the conclusion that no strong correlation exists. The lack of correlation suggests a formation of all metal-poor GC in similar gas fragments. A weak correlation might exist between mean [Fe/H] of the metal-poor GC and host galaxy metallicity. This would imply that some fragments in which metal-poor GC formed were already embedded in the larger dark matter halo of the final galaxy (as oppose to being independent satellites that were accreted later). Our result suggests a homogeneous formation of metal-poor GC in all galaxies, in typical fragments of masses around 10^9-10^10 solar masses with very similar metallicities, compatible with hierarchical formation scenarios for galaxies. We compared the mean [Fe/H] of the metal-poor GC populations with the typical metallicities of high-z objects. If we add the constraint that GC need a high column density of gas to form, DLAs are the most likely sites for the formation of metal-poor GC populations.Comment: accepted for publication in AJ, scheduled for the May 2001 issu

The Kinematics and Metallicity of the M31 Globular Cluster System

With the ultimate aim of distinguishing between various models describing the formation of galaxy halos (e.g. radial or multi-phase collapse, random mergers), we have completed a spectroscopic study of the globular cluster system of M31. We present the results of deep, intermediate-resolution, fibre-optic spectroscopy of several hundred of the M31 globular clusters using the Wide Field Fibre Optic Spectrograph (WYFFOS) at the William Herschel Telescope in La Palma, Canary Islands. These observations have yielded precise radial velocities (+/-12 km/s) and metallicities (+/-0.26 dex) for over 200 members of the M31 globular cluster population out to a radius of 1.5 degrees from the galaxy center. Many of these clusters have no previous published radial velocity or [Fe/H] estimates, and the remainder typically represent significant improvements over earlier determinations. We present analyses of the spatial, kinematic and metal abundance properties of the M31 globular clusters. We find that the abundance distribution of the cluster system is consistent with a bimodal distribution with peaks at [Fe/H] = -1.4 and -0.5. The metal-rich clusters demonstrate a centrally concentrated spatial distribution with a high rotation amplitude, although this population does not appear significantly flattened and is consistent with a bulge population. The metal-poor clusters tend to be less spatially concentrated and are also found to have a strong rotation signature.Comment: 33 pages, 20 figure