The Ages and Abundances of the M87 Globular Clusters

A subset of 150 globular clusters in M87 has been selected on the basis of S/N ratio for abundance and age determinations from the sample of Paper I. Indices measuring the strength of the strongest spectral features were determined for the M87 GCs and from new data for twelve galactic GCs. Combining the new and existing data for the galactic GCs and comparing the $(U-R)$ colors and the line indices gives qualitative indications for the ages and abundances of the GCs. Quantitative results are obtained by applying the Worthey (1994) models for the integrated light of stellar systems of a single age, calibrated by observations of galactic GCs, to deduce abundances and ages for the objects in our sample. We find that the M87 GCs span a wide range in metallicity, from very metal poor to somewhat above solar metallicity. The mean [Fe/H] of -0.95 dex is higher than that of the galactic GC system, and there is a metal rich tail that reaches to higher [Fe/H] than one finds among the galactic GCs. The mean metallicity of the M87 GC system is about a factor of four lower than that of the M87 stellar halo at a fixed projected radius $R$. The metallicity inferred from the X-ray studies is similar to that of the M87 stellar halo, not to that of GCs. We infer the relative abundances of Na, Mg, and Fe in the M87 GCs from the strength of their spectral features. The behavior of these elements between the metal rich and metal poor M87 GCs is similar to that shown by the galactic GCs and by halo stars in the Galaxy. The pattern of chemical evolution in these disparate old stellar systems is indistinguishable. We obtain a median age for the M87 GC system of 13 Gyr, similar to that of the galactic GCs, with a small dispersion about this value.Comment: 56 pages with included postscript figures; added derived M87 GC metallicities to Table 2, a statistical analysis of possible bimodality, an appendix on the metallicity calibration of U-R and the Washington system, and other smaller changes. Accepted for publication in ApJ. (See paper for complete version of the Abstract.

The Dynamics of the M87 Globular Cluster System

We present the results from a study of the dynamics of the system of globular clusters around M87. After eliminating foreground galactic stars and background galaxies, we end up with a sample of 205 bona fide M87 globular clusters for which we have radial velocities determined from multi-slit spectra taken with the LRIS on the Keck Telescope. We find that the mean radial velocity of the M87 globular clusters agrees well with that of M87 itself, and that the velocity histogram is well represented by a Gaussian distribution. We find evidence for rotation in the globular cluster system. We find that the observed velocity dispersion of the M87 globular cluster system increases with radius from 270 \kms~ at $r$ = 9 kpc to $\approx$400 \kms~ at $r$ = 40 kpc. The inferred mass-to-light ratio in solar units increases from 5 at $r$ = 9 kpc to $\approx$30 at $r$ = 40 kpc with $M(r) \sim r^{1.7}$. The long slit optical spectroscopy near the center of M87 and the recent analysis of the ROSAT X-ray data are in good agreement with this analysis near the nucleus and in the outer parts of M87 respectively.Comment: 29 pages, TeX, with 6 Figures. Accepted for publication in the Ap

The Ages and Abundances of a Large Sample of M87 Globular Clusters

A subset of 150 globular clusters (GCs) in M87 has been selected for abundance and age determinations from the 1997 sample of Cohen & Ryzhov. This has been done solely on the basis of the signal-to-noise ratios of the spectra. Indices that measure the strength of the strongest spectral features were determined for the M87 GCs and from new data for twelve galactic GCs. Combining the new and existing data for the galactic GCs and comparing the (U-R) colors and the line indices gave qualitative indications for the ages and abundances of the M87 GC system. Quantitative results, which confirm and extend the qualitative ones, were obtained by applying the Worthey models for the integrated light of stellar systems of a single age, calibrated by observations of galactic globular clusters, to deduce abundances and ages for the objects in our sample. We find that the M87 GCs span a wide range in metallicity, from very metal-poor to somewhat above solar metallicity. The mean [Fe/H] of -0.95 dex is higher than that of the galactic GC system, and there is a metal-rich tail that reaches to higher [Fe/H] than one finds among the galactic GCs. Excluding the very metal-rich tail, there is marginal evidence for a bimodal distribution over the single one at the 89% significance level. The two "subpopulations" in this model are located at -1.3 and -0.7 dex and contain 40% and 60% of the total, respectively. The dispersion in [Fe/H] for each of the model subpopulations is σ = 0.3 dex. The mean metallicity of the M87 GC system is about a factor of 4 lower than that of the M87 stellar halo at a fixed projected radius R. The metallicity inferred from the X-ray studies is similar to that of the M87 stellar halo, not to that of the M87 GC system. We infer the relative abundances of Na, Mg, and Fe in the M87 GCs from the strength of their spectral features. The behavior of these elements between the metal-rich and metal-poor M87 GCs is similar to that shown by the galactic GCs and by halo stars in the Galaxy. The pattern of chemical evolution in these disparate old stellar systems is, as far as we can tell, identical. Superposed on a very large dispersion in abundance at all R, there is a small but real radial gradient in the mean abundance of the M87 GCs with R, but no detectable change in the Hβ index with R. We obtain a median age for the M87 GC system of 13 Gyr, similar to that found for the galactic GCs. The dispersion about that value (σ = 2 Gyr) is small

Three-Point Functions of Quarter BPS Operators in N=4 SYM

In a recent paper hep-th/0109064, quarter-BPS chiral primaries were constructed in the fully interacting four dimensional N=4 Super-Yang-Mills theory with gauge group SU(N). These operators are annihilated by four supercharges, and at order g^2 have protected scaling dimension and normalization. Here, we compute three-point functions involving these quarter-BPS operators along with half-BPS operators. The combinatorics of the problem is rather involved, and we consider the following special cases: (1) correlators of two half-BPS primaries with an arbitrary chiral primary; (2) certain classes of and < quarter quarter quarter > three-point functions; (3) three-point functions involving the Delta correlators with the special quarter-BPS operator made of single and double trace operators only. The analysis in cases (1)-(3) is valid for general N, while (4) is a large N approximation. Order g^2 corrections to all three-point functions considered in this paper are found to vanish. In the AdS/CFT correspondence, quarter-BPS chiral primaries are dual to threshold bound states of elementary supergravity excitations. We present a supergravity discussion of two- and three-point correlators involving these bound states.Comment: 44 pages, Latex, eps figures, uses epsfig.sty; references adde

Introduction to the statistical theory of differential communication based on chaotic signals

The purpose of this paper is to analyse the statistical characteristics of a Direct Chaotic Differentially Coherent communication scheme based on chaotic radio pulses in a communication channel with additive white Gaussian noise, where the chaotic signal is given by different instantaneous distributions. Methods. To achieve this goal, numerical modelling of the noise immunity of Direct Chaotic Differentially Coherent communication is conducted and compared with the results of analytical research. Results. The regularities associated with the use of chaotic signals with various statistical distributions of instantaneous values were studied. The minimum values of energy per bit to white Gaussian noise power spectral density ratio were obtained, providing the required error probabilities. Conclusion. It is shown that the proposed system works efficiently at high values of processing gain, and as the processing gain increases, the dependence of noise immunity on the specific statistical distribution of the chaotic signal is levelled out

Large N Quantum Time Evolution Beyond Leading Order

For quantum theories with a classical limit (which includes the large N limits of typical field theories), we derive a hierarchy of evolution equations for equal time correlators which systematically incorporate corrections to the limiting classical evolution. Explicit expressions are given for next-to-leading order, and next-to-next-to-leading order time evolution. The large N limit of N-component vector models, and the usual semiclassical limit of point particle quantum mechanics are used as concrete examples. Our formulation directly exploits the appropriate group structure which underlies the construction of suitable coherent states and generates the classical phase space. We discuss the growth of truncation error with time, and argue that truncations of the large-N evolution equations are generically expected to be useful only for times short compared to a ``decoherence'' time which scales like N^{1/2}.Comment: 36 pages, 2 eps figures, latex, uses revtex, epsfig, float