On the Formation of Boxy and Disky Elliptical Galaxies

The origin of boxy and disky elliptical galaxies is investigated. The results of two collisionless N-body simulations of spiral-spiral mergers with mass ratios of 1:1 and 3:1 are discussed and the projected properties of the merger remnants are investigated. It is shown that the equal-mass merger leads to an anisotropic, slowly rotating system with preferentially boxy isophotes and significant minor axis rotation. The unequal-mass merger results in the formation of a rotationally supported elliptical with disky isophotes and small minor axis rotation. The observed scatter in the kinematical and isophotal properties of both classes of elliptical galaxies can be explained by projection effects.Comment: 12 pages, incl. 5 figures, accepted by ApJ Letter

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

Extending PT symmetry from Heisenberg algebra to E2 algebra

The E2 algebra has three elements, J, u, and v, which satisfy the commutation relations [u,J]=iv, [v,J]=-iu, [u,v]=0. We can construct the Hamiltonian H=J^2+gu, where g is a real parameter, from these elements. This Hamiltonian is Hermitian and consequently it has real eigenvalues. However, we can also construct the PT-symmetric and non-Hermitian Hamiltonian H=J^2+igu, where again g is real. As in the case of PT-symmetric Hamiltonians constructed from the elements x and p of the Heisenberg algebra, there are two regions in parameter space for this PT-symmetric Hamiltonian, a region of unbroken PT symmetry in which all the eigenvalues are real and a region of broken PT symmetry in which some of the eigenvalues are complex. The two regions are separated by a critical value of g.Comment: 8 pages, 7 figure

Eigenvalue Integro-Differential Equations for Orthogonal Polynomials on the Real Line

The one-dimensional harmonic oscillator wave functions are solutions to a Sturm-Liouville problem posed on the whole real line. This problem generates the Hermite polynomials. However, no other set of orthogonal polynomials can be obtained from a Sturm-Liouville problem on the whole real line. In this paper we show how to characterize an arbitrary set of polynomials orthogonal on $(-\infty,\infty)$ in terms of a system of integro-differential equations of Hartree-Fock type. This system replaces and generalizes the linear differential equation associated with a Sturm-Liouville problem. We demonstrate our results for the special case of Hahn-Meixner polynomials.Comment: 28 pages, Latex, U. Texas at Austin/ Washington University preprin

Pairing correlations beyond the mean field

We discuss dynamical pairing correlations in the context of configuration mixing of projected self-consistent mean-field states, and the origin of a divergence that might appear when such calculations are done using an energy functional in the spirit of a naive generalized density functional theory.Comment: Proceedings of the XIII Nuclear Physics Workshop ``Maria and Pierre Curie'' on ``Pairing and beyond - 50 years of the BCS model'', held at Kazimierz Dolny, Poland, September 27 - October 1, 2006. Int. J. Mod. Phys. E, in prin

Constraints on galaxy formation from alpha-enhancement in luminous elliptical galaxies

We explore the formation of alpha-enhanced and metal-rich stellar populations in the nuclei of luminous ellipticals under the assumption of two extreme galaxy formation scenarios based on hierarchical clustering, namely a fast clumpy collapse and the merger of two spirals. We investigate the parameter space of star formation time-scale, IMF slope, and stellar yields. In particular, the latter add a huge uncertainty in constraining time-scales and IMF slopes. We find that -- for Thielemann, Nomoto & Hashimoto nucleosynthesis -- in a fast clumpy collapse scenario an [alpha/Fe] overabundance of approx. 0.2 dex in the high metallicity stars can be achieved with a Salpeter IMF and star formation time-scales of the order 10^9 yr. The scenario of two merging spirals which are similar to our Galaxy, instead, fails to reproduce alpha-enhanced abundance ratios in the metal-rich stars, unless the IMF is flattened during the burst ignited by the merger. This result is independent of the burst time-scale. We suggest that abundance gradients give hints to distinguish between the two extreme formation scenarios considered in this paper.Comment: Accepted for publication in MNRAS, LaTex 2.09 with mn.sty, 13 pages, 5 figure

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

Generating Survival Times to Simulate Cox Proportional Hazards Models

This paper discusses techniques to generate survival times for simulation studies regarding Cox proportional hazards models. In linear regression models, the response variable is directly connected with the considered covariates, the regression coefficients and the simulated random errors. Thus, the response variable can be generated from the regression function, once the regression coefficients and the error distribution are specified. However, in the Cox model, which is formulated via the hazard function, the effect of the covariates have to be translated from the hazards to the survival times, because the usual software packages for estimation of Cox models require the individual survival time data. A general formula describing the relation between the hazard and the corresponding survival time of the Cox model is derived. It is shown how the exponential, the Weibull and the Gompertz distribution can be used to generate appropriate survival times for simulation studies. Additionally, the general relation between hazard and survival time can be used to develop own distributions for special situations and to handle flexibly parameterized proportional hazards models. The use of other distributions than the exponential distribution only is indispensable to investigate the characteristics of the Cox proportional hazards model, especially in non-standard situations, where the partial likelihood depends on the baseline hazard