Spatially resolved spectroscopy of Coma cluster early-type galaxies IV. Completing the dataset

The long-slit spectra obtained along the minor axis, offset major axis and diagonal axis are presented for 12 E and S0 galaxies of the Coma cluster drawn from a magnitude-limited sample studied before. The rotation curves, velocity dispersion profiles and the H_3 and H_4 coefficients of the Hermite decomposition of the line of sight velocity distribution are derived. The radial profiles of the Hbeta, Mg, and Fe line strength indices are measured too. In addition, the surface photometry of the central regions of a subsample of 4 galaxies recently obtained with Hubble Space Telescope is presented. The data will be used to construct dynamical models of the galaxies and study their stellar populations.Comment: 40 pages, 7 figures, 6 tables. Accepted for publication in ApJ

Homogeneity of Stellar Populations in Early-Type Galaxies with Different X-ray Properties

We have found the stellar populations of early-type galaxies are homogeneous with no significant difference in color or Mg2 index, despite the dichotomy between X-ray extended early-type galaxies and X-ray compact ones. Since the X-ray properties reflect the potential gravitational structure and hence the process of galaxy formation, the homogeneity of the stellar populations implies that the formation of stars in early-type galaxies predat es the epoch when the dichotomy of the potential structure was established.Comment: 6 pages, 5 figures, accepted for publication in Ap

Thick brane solutions and topology change transition on black hole backgrounds

We consider static, axisymmetric, thick brane solutions on higher dimensional, spherically symmetric black hole backgrounds. It was found recently [1], that in cases when the thick brane has more than 2 spacelike dimensions, perturbative approaches break down around the corresponding thin solutions for Minkowski type topologies. This behavior is a consequence of the fact that thin solutions are not smooth at the axis, and for a general discussion of possible phase transitions in the system, one needs to use a non-perturbative approach. In the present paper we provide an exact, numerical solution of the problem both for black hole- and Minkowski type topologies with arbitrary number of brane and bulk dimensions. We also illustrate a topology change transition in the system for a 5-dimensional brane embedded in a 6-dimensional bulk.Comment: 11 pages, 10 figures, accepted for publication in Phys. Rev.

Stellar Orbits and the Interstellar Gas Temperature in Elliptical Galaxies

We draw attention to the close relationship between the anisotropy parameter beta(r) for stellar orbits in elliptical galaxies and the temperature profile T(r) of the hot interstellar gas. For nearly spherical galaxies the gas density can be accurately determined from X-ray observations and the stellar luminosity density can be accurately found from the optical surface brightness. The Jeans equation and hydrostatic equilibrium establish a connection between beta(r) and T(r) that must be consistent with the observed stellar velocity dispersion. Purely optical observations of the bright elliptical galaxy NGC 4472 indicate beta(r) < 0.35 within the effective radius. However, the X-ray gas temperature profile T(r) for NGC 4472 requires significantly larger anisotropy, beta = 0.6 - 0.7, about twice the optical value. This strong preference for radial stellar orbits must be understood in terms of the formation history of massive elliptical galaxies. Conversely, if the smaller, optically determined anisotropy is indeed correct, we are led to the important conclusion that the temperature profile T(r) of the hot interstellar gas in NGC 4472 must differ from that indicated by X-ray observations, or that the hot gas is not in hydrostatic equilibrium.Comment: 6 pages (emulateapj5) with 4 figures; accepted by The Astrophysical Journa

On the eigenproblems of PT-symmetric oscillators

We consider the non-Hermitian Hamiltonian H= -\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a polynomial of degree at most n \geq 1 with all nonnegative real coefficients (possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the eigenfunction u and its derivative u^\prime and we find some other interesting properties of eigenfunctions.Comment: 21pages, 9 figure

Harmonic oscillator well with a screened Coulombic core is quasi-exactly solvable

In the quantization scheme which weakens the hermiticity of a Hamiltonian to its mere PT invariance the superposition V(x) = x^2+ Ze^2/x of the harmonic and Coulomb potentials is defined at the purely imaginary effective charges (Ze^2=if) and regularized by a purely imaginary shift of x. This model is quasi-exactly solvable: We show that at each excited, (N+1)-st harmonic-oscillator energy E=2N+3 there exists not only the well known harmonic oscillator bound state (at the vanishing charge f=0) but also a normalizable (N+1)-plet of the further elementary Sturmian eigenstates \psi_n(x) at eigencharges f=f_n > 0, n = 0, 1, ..., N. Beyond the first few smallest multiplicities N we recommend their perturbative construction.Comment: 13 pages, Latex file, to appear in J. Phys. A: Math. Ge

The Isophotal Structure of Early-Type Galaxies in the SDSS: Dependence on AGN Activity and Environment

We study the dependence of the isophotal shape of early-type galaxies on their absolute B-band magnitude, their dynamical mass, and their nuclear activity and environment, using an unprecedented large sample of 847 early-type galaxies identified in the SDSS by Hao et al (2006). We find that the fraction of disky galaxies smoothly decreases with increasing luminosity. The large sample allows us to describe these trends accurately with tight linear relations that are statistically robust against the uncertainty in the isophotal shape measurements. There is also a host of significant correlations between the disky fraction and indicators of nuclear activity (both in the optical and in the radio) and environment (soft X-rays, group mass, group hierarchy). Our analysis shows however that these correlations can be accurately matched by assuming that the disky fraction depends only on galaxy luminosity or mass. We therefore conclude that neither the level of activity, nor group mass or group hierarchy help in better predicting the isophotal shape of early-type galaxies.Comment: 31 pages, 10 figures, accepted for publication in Ap

A photometric and kinematic study of the stars and interstellar medium in the central two kpc of NGC 3379

HST images of NGC 3379 show that the V and I luminosity profiles in the inner 13 arcsec of this E1 galaxy are represented by two different components: a stellar bulge following a Sersic Law with exponent n = 2.36, and a central core (r < 0.7 arcsec) with a characteristic "cuspy" profile. Subtraction of the underlying stellar component represented by the fitted Sersic profile revealed the presence of a small (r ~ 105 pc) dust disk of about 150 solar masses, oriented at PA = 125 degrees and inclined ~ 77 degrees with respect to the line of sight. The same absorption structure is detected in the color-index (V-I) image. The stellar rotation in the inner 20 arcsec is well represented by a parametric planar disk model, inclined ~ 26 degrees relative to the plane of the sky, and apparent major axis along PA ~ 67 degrees. The gas velocity curves in the inner 5 arcsec show a steep gradient, indicating that the gas rotates much faster than the stars, although in the same direction. The velocity field of the gaseous system, however, is not consistent with the simple model of Keplerian rotation sustained by the large (7 x 10E9 solar masses within a radius of ~ 90 pc) central mass implied by the maximum velocity observed, but the available data precludes a more detailed analysis.Comment: 23 pages, LaTeX(aaspp4.sty), 9 figures included. Figs. 1 and 5 are colour plates. Accepted for publication in The Astrophysical Journal (part 1

Student perceptions and attitudes about Community Service-Learning in the teacher training curriculum

Much of the international research on Community Service-Learning has investigated the benefits, outcomes, and learning experiences of students already engaged in service-learning projects and programmes. As there is scant research on students\' attitudes to and perceptions of Service-Learning, before this learning became integrated into an academic programme, our purpose was to determine teacher training students\' attitudes to, and perceptions of, Community Service-Learning, before integration of such a module into their academic programmes. A quantitative survey, employing a questionnaire as instrument, was used for measuring the attitudes and perceptions of third-year teacher training students (n = ±168) at a research university in South Africa. The Community Service-Learning Attitudes and Perception Scale (CSLAPS), developed specifically for this kind of investigation, was used in the analysis of the data. The findings indicated that students with prior knowledge of and/or participation in a community service project showed greater willingness to enrol for a course/ module in Community Service-Learning, especially if it would add value to their career development, bear credits, and enhance their personal and social development. The findings provided information that would enable academic staff and institutions to design curricula for academic programmes that take account of these attitudes and perceptions and address them positively to enhance the learning experience. Keywords: academic programme; attitudes; citizenship; Community Service-Learning; curricular community engagement; curriculum; perceptions;quantitative study; teacher training South African Journal of Education Vol. 27 (4) 2007: pp. 631-65

Does the complex deformation of the Riemann equation exhibit shocks?

The Riemann equation $u_t+uu_x=0$, which describes a one-dimensional accelerationless perfect fluid, possesses solutions that typically develop shocks in a finite time. This equation is \cP\cT symmetric. A one-parameter \cP\cT-invariant complex deformation of this equation, $u_t-iu(iu_x)^\epsilon= 0$ ($\epsilon$ real), is solved exactly using the method of characteristic strips, and it is shown that for real initial conditions, shocks cannot develop unless $\epsilon$ is an odd integer.Comment: latex, 8 page