Cuspy Dark-Matter Haloes and the Galaxy

The microlensing optical depth to Baade's Window constrains the minimum total mass in baryonic matter within the Solar circle to be greater than 3.9 x 10^{10} solar masses, assuming the inner Galaxy is barred with viewing angle of roughly 20 degrees. From the kinematics of solar neighbourhood stars, the local surface density of dark matter is about 30 +/- 15 solar masses per square parsec. We construct cuspy haloes normalised to the local dark matter density and calculate the circular-speed curve of the halo in the inner Galaxy. This is added in quadrature to the rotation curve provided by the stellar and ISM discs, together with a bar sufficiently massive so that the baryonic matter in the inner Galaxy reproduces the microlensing optical depth. Such models violate the observational constraint provided by the tangent-velocity data in the inner Galaxy (typically at radii 2-4 kpc). The high baryonic contribution required by the microlensing is consistent with implications from hydrodynamical modelling and the pattern speed of the Galactic bar. We conclude that the cuspy haloes favoured by the Cold Dark Matter cosmology (and its variants) are inconsistent with the observational data on the Galaxy.Comment: 5 pages, 1 figures, MNRAS (submitted

Majority-vote model on (3,4,6,4) and (3^4,6) Archimedean lattices

On Archimedean lattices, the Ising model exhibits spontaneous ordering. Two examples of these lattices of the majority-vote model with noise are considered and studied through extensive Monte Carlo simulations. The order/disorder phase transition is observed in this system. The calculated values of the critical noise parameter are q_c=0.091(2) and q_c=0.134(3) for (3,4,6,4) and (3^4,6) Archimedean lattices, respectively. The critical exponents beta/nu, gamma/nu and 1/nu for this model are 0.103(6), 1.596(54), 0.872(85) for (3,4,6,4) and 0.114(3), 1.632(35), 0.978(104) for (3^4,6) Archimedean lattices. These results differs from the usual Ising model results and the majority-vote model on so-far studied regular lattices or complex networks. The effective dimensionality of the system [D_{eff}(3,4,6,4)=1.802(55) and D_{eff}(3^4,6)=1.860(34)] for these networks are reasonably close to the embedding dimension two.Comment: 6 pages, 7 figures in 12 eps files, RevTex

The Planetary Nebula System and Dynamics in the Outer Halo of NGC 5128

The halos of elliptical galaxies are faint and difficult to explore, but they contain vital clues to both structure and formation. We present the results of an imaging and spectroscopic survey for planetary nebulae (PNe) in the nearby elliptical NGC 5128. We extend the work of Hui et al.(1995) well into the halo of the galaxy--out to distances of 100 and 50 kpc along the major and minor axes. We now know of 1141 PNe in NGC 5128, 780 of which are confirmed. Of these 780 PNe, 349 are new from this survey, and 148 are at radii beyond 20 kpc. PNe exist at distances up to 80 kpc (~15 r_e), showing that the stellar halo extends to the limit of our data. This study represents by far the largest kinematic study of an elliptical galaxy to date, both in the number of velocity tracers and in radial extent. We confirm the large rotation of the PNe along the major axis, and show that it extends in a disk-like feature into the halo. The rotation curve of the stars flattens at ~100 km/s with V/sigma between 1 and 1.5, and with the velocity dispersion of the PNe falling gradually at larger radii. The two-dimensional velocity field exhibits a zero-velocity contour with a pronounced twist, showing that the galaxy potential is likely triaxial in shape, tending toward prolate. The total dynamical mass of the galaxy within 80 kpc is ~5 x 10^{11} M_sun, with M/L_B ~ 13. This mass-to-light ratio is much lower than what is typically expected for elliptical galaxies.Comment: 21 pages, 13 figures (figures 3-8 best viewed in color), accepted for publication in the Astrophysical Journa

The proper motion of the Arches cluster with Keck Laser-Guide Star Adaptive Optics

We present the first measurement of the proper motion of the young, compact Arches cluster near the Galactic center from near-infrared adaptive optics (AO) data taken with the recently commissioned laser-guide star (LGS) at the Keck 10-m telescope. The excellent astrometric accuracy achieved with LGS-AO provides the basis for a detailed comparison with VLT/NAOS-CONICA data taken 4.3 years earlier. Over the 4.3 year baseline, a spatial displacement of the Arches cluster with respect to the field population is measured to be 24.0 +/- 2.2 mas, corresponding to a proper motion of 5.6 +/- 0.5 mas/yr or 212 +/- 29 km/s at a distance of 8 kpc. In combination with the known line-of-sight velocity of the cluster, we derive a 3D space motion of 232 +/- 30 km/s of the Arches relative to the field. The large proper motion of the Arches cannot be explained with any of the closed orbital families observed in gas clouds in the bar potential of the inner Galaxy, but would be consistent with the Arches being on a transitional trajectory from x1 to x2 orbits. We investigate a cloud-cloud collision as the possible origin for the Arches cluster. The integration of the cluster orbit in the potential of the inner Galaxy suggests that the cluster passes within 10 pc of the supermassive black hole only if its true GC distance is very close to its projected distance. A contribution of young stars from the Arches cluster to the young stellar population in the inner few parsecs of the GC thus appears increasingly unlikely. The measurement of the 3D velocity and orbital analysis provides the first observational evidence that Arches-like clusters do not spiral into the GC. This confirms that no progenitor clusters to the nuclear cluster are observed at the present epoch.Comment: 22 pdflatex pages including 12 figures, reviewed version accepted by Ap

Reconstructing Three-dimensional Structure of Underlying Triaxial Dark Halos From Xray and Sunyaev-Zel'dovich Effect Observations of Galaxy Clusters

While the use of galaxy clusters as {\it tools} to probe cosmology is established, their conventional description still relies on the spherical and/or isothermal models that were proposed more than 20 years ago. We present, instead, a deprojection method to extract their intrinsic properties from X-ray and Sunyaev--Zel'dovich effect observations in order to improve our understanding of cluster physics. First we develop a theoretical model for the intra-cluster gas in hydrostatic equilibrium in a triaxial dark matter halo with a constant axis ratio. In this theoretical model, the gas density profiles are expressed in terms of the intrinsic properties of the dark matter halos. Then, we incorporate the projection effect into the gas profiles, and show that the gas surface brightness profiles are expressed in terms of the eccentricities and the orientation angles of the dark halos. For the practical purpose of our theoretical model, we provide several empirical fitting formulae for the gas density and temperature profiles, and also for the surface brightness profiles relevant to X-ray and Sunyaev--Zel'dovich effect observations. Finally, we construct a numerical algorithm to determine the halo eccentricities and orientation angles using our model, and demonstrate that it is possible in principle to reconstruct the 3D structures of the dark halos from the X-ray and/or Sunyaev-Zel'dovich effect cluster data alone without requiring priors such as weak lensing informations and without relying on such restrictive assumptions as the halo axial symmetry about the line-of-sight.Comment: Accepted version, new discussions added, typos and minor mistakes corrected, ApJ in press (2004, Feb. 1 scheduled, Vol. 601, No. 2 issue),26 pages, 7 postscript figure

On the Ionisation of Warm Opaque Interstellar Clouds and the Intercloud Medium

In this paper we use a number of observations to construct an integrated picture of the ionisation in the interiors of quiescent warm opaque interstellar clouds and in the intercloud medium (ICM) outside dense HII regions and hot dilute bubbles. Our main conclusion is that within $\sim$ 1kpc of the sun the ionisation rate of hydrogen per unit volume in both the interiors of such clouds and in the ICM is independent of the local density of neutral hydrogen, and varies with position by less than $\sim$ 20 per cent. These conclusions strongly favour the decaying neutrino hypothesis for the ionisation of the interstellar medium in these regions. Our analysis is based on a variety of observations, of which the most remarkable is the discovery by Spitzer and Fitzpatrick (1993) that, in the four slowly moving clouds along the line of sight to the halo star HD93521, the column densities of both SII and CII$^*$, which individually range over a factor $\sim$4, are proportional to the column density of HI to within $\sim$20 per cent. This proportionality is used to show that the free electrons exciting the CII to CII$^*$ are located mainly in the interiors of the clouds, rather than in their skins, despite the large opacity of the clouds to Lyman continuum radiation. The same conclusion also follows more unambiguously from the low value of the H$\alpha$ flux in this direction which was found by Reynolds (1996) in unpublished observations. These results are then used, in conjunction with observations of three pulsar parallaxes and dispersion measures, and with data on HeI, NII and OI line emissions, to constrain the ionisation of H, He, N and O and the flux of Lyman continuum photons from O stars in the ICM.Comment: 16 pages, no figures, Latex fil

Hill's Equation with Random Forcing Parameters: The Limit of Delta Function Barriers

This paper considers random Hill's equations in the limit where the periodic forcing function becomes a Dirac delta function. For this class of equations, the forcing strength $q_k$, the oscillation frequency \af_k, and the period are allowed to vary from cycle to cycle. Such equations arise in astrophysical orbital problems in extended mass distributions, in the reheating problem for inflationary cosmologies, and in periodic Schr{\"o}dinger equations. The growth rates for solutions to the periodic differential equation can be described by a matrix transformation, where the matrix elements vary from cycle to cycle. Working in the delta function limit, this paper addresses several coupled issues: We find the growth rates for the $2 \times 2$ matrices that describe the solutions. This analysis is carried out in the limiting regimes of both large $q_k \gg 1$ and small $q_k \ll 1$ forcing strength parameters. For the latter case, we present an alternate treatment of the dynamics in terms of a Fokker-Planck equation, which allows for a comparison of the two approaches. Finally, we elucidate the relationship between the fundamental parameters (\af_k,q_k) appearing in the stochastic differential equation and the matrix elements that specify the corresponding discrete map. This work provides analytic -- and accurate -- expressions for the growth rates of these stochastic differential equations in both the $q_k \gg1$ and the $q_k \ll 1$ limits.Comment: 29 pages, 3 figures, accepted to Journal of Mathematical Physic

Self-determination theory and needs satisfaction in marketing education : are we meeting the needs of students in large marketing classes?

The aim of this study is to assess whether universities are meeting the needs of students in large marketing classes. In so doing the study investigates the application of self determination theory and psychological needs satisfaction. The basic needs scale, comprising of three constructs; Control, Competence and Caring was adapted and used to evaluate students&rsquo; perception of an introductory marketing subject. The study used a multi-method approach consisting of a literature review, a qualitative phase involving in-depth interviews with marketing teaching staff and focus groups with marketing students and a survey of students about introductory level marketing. An adapted version of the basic psychological needs scale was included in a questionnaire that was administered to a convenience sample of 366 students. MANOVA, ANOVA and descriptive statistics were used to analyse the data. The results show that the psychological needs satisfaction of many students are not being fully realised. It was also found that marketing degree students enjoyed the challenges and were more stimulated by the subject. The higher achieving students enjoyed the challenge of the subject more than the lower achieving students. As a result of this study, there are three suggestions for further research. Firstly, further study should compare subjects, with relatively small enrolments, to those with large enrolments to corroborate the value of this method of assessing student satisfaction. Secondly, the use of a larger sample across other universities would confirm whether these findings hold for other institutions. Finally, it is suggested that a structural model should be developed to extend this investigation of student satisfaction and the constructs used in the study.<br /

Modelling elliptical galaxies: phase-space constraints on two-component (gamma1,gamma2) models

In the context of the study of the properties of the mutual mass distribution of the bright and dark matter in elliptical galaxies, present a family of two-component, spherical, self-consistent galaxy models, where one density distribution follows a gamma_1 profile, and the other a gamma_2 profile [(gamma_1,gamma_2) models], with different total masses and ``core'' radii. A variable amount of Osipkov-Merritt (radial) orbital anisotropy is allowed in both components. For these models, I derive analytically the necessary and sufficient conditions that the model parameters must satisfy in order to correspond to a physical system. Moreover, the possibility of adding a black hole at the center of radially anisotropic gamma models is discussed, determining analytically a lower limit of the anisotropy radius as a function of gamma. The analytical phase-space distribution function for (1,0) models is presented, together with the solution of the Jeans equations and the quantities entering the scalar virial theorem. It is proved that a globally isotropic gamma=1 component is consistent for any mass and core radius of the superimposed gamma=0 model; on the contrary, only a maximum value of the core radius is allowed for the gamma=0 model when a gamma=1 density distribution is added. The combined effects of mass concentration and orbital anisotropy are investigated, and an interesting behavior of the distribution function of the anisotropic gamma=0 component is found: there exists a region in the parameter space where a sufficient amount of anisotropy results in a consistent model, while the structurally identical but isotropic model would be inconsistent.Comment: 29 pages, LaTex, plus 5 .eps figures and macro aaspp4.sty - accepted by ApJ, main journa

Probing anisotropies of gravitational-wave backgroundswith a space-based interferometer II: Perturbative reconstruction of a low-frequency skymap

We present a perturbative reconstruction method to make a skymap of gravitational-wave backgrounds (GWBs) observed via space-based interferometer. In the presence of anisotropies in GWBs, the cross-correlated signals of observed GWBs are inherently time-dependent due to the non-stationarity of the gravitational-wave detector. Since the cross-correlated signal is obtained through an all-sky integral of primary signals convolving with the antenna pattern function of gravitational-wave detectors, the non-stationarity of cross-correlated signals, together with full knowledge of antenna pattern functions, can be used to reconstruct an intensity map of the GWBs. Here, we give two simple methods to reconstruct a skymap of GWBs based on the perturbative expansion in low-frequency regime. The first one is based on harmonic-Fourier representation of data streams and the second is based on "direct" time-series data. The latter method enables us to create a skymap in a direct manner. The reconstruction technique is demonstrated in the case of the Galactic gravitational wave background observed via planned space interferometer, LISA. Although the angular resolution of low-frequency skymap is rather restricted, the methodology presented here would be helpful in discriminating the GWBs of galactic origins by those of the extragalactic and/or cosmological origins.Comment: 23 pages, 12 figures, Phys.Rev.D (2005) in pres