Instabilities of a family of oblate stellar spheroids

We have examined the stability of a sequence of oblate elliptical galaxy models having the Stackel form suggested by Kuz'min & Kutuzov. We have employed the 2-integral DFs given by Dejonghe & de Zeeuw for which flattened non-rotating models are characterized by counter-streaming motion and are radially cool; we introduce net rotation in some models by changing the sign of the z-component of angular momentum for a fraction of the particles. We have found that all non-rotating and slowly rotating members of this sequence rounder than E7 are stable, and that even maximally rotating models rounder than E4 are stable. In the absence of strong rotation, the most disruptive instability, and the last to be stabilized by increasing thickness, is a lopsided (m=1) mode. This instability appears to be driven by counter-rotation in radially cool models. Its vigour is lessened as rotation is increased, but it remains strong even in models with net angular momentum 90% of that of a maximally rotating model before finally disappearing in maximally rotating models. Strongly rotating models are more unstable to bar-forming modes which afflict maximally rotating models with c/a >~ 0.5, but this mode is quickly stabilized by moderate fractions of counter-rotating particles. Bending instabilities appear not to be very important; they are detectable in the inner parts of the flatter models, but are less vigorous and more easily stabilized than the lop-sided or bar modes in every case. We briefly discuss the possible relevance of the lop-sided instability to the existence of many lop-sided disk galaxies.Comment: 18 pages including 8 figures, TeX, macro file included, to appear in Monthly Notices of RA

New views of the solar wind with the Lambert W function

This paper presents closed-form analytic solutions to two illustrative problems in solar physics that have been considered not solvable in this way previously. Both the outflow speed and the mass loss rate of the solar wind of plasma particles ejected by the Sun are derived analytically for certain illustrative approximations. The calculated radial dependence of the flow speed applies to both Parker's isothermal solar wind equation and Bondi's equation of spherical accretion. These problems involve the solution of transcendental equations containing products of variables and their logarithms. Such equations appear in many fields of physics and are solvable by use of the Lambert W function, which is briefly described. This paper is an example of how new functions can be applied to existing problems.Comment: 16 pages (revtex4), 3 figures, American J. Phys., in press (2004

The Carter Constant for Inclined Orbits About a Massive Kerr Black Hole: I. circular orbits

In an extreme binary black hole system, an orbit will increase its angle of inclination (i) as it evolves in Kerr spacetime. We focus our attention on the behaviour of the Carter constant (Q) for near-polar orbits; and develop an analysis that is independent of and complements radiation reaction models. For a Schwarzschild black hole, the polar orbits represent the abutment between the prograde and retrograde orbits at which Q is at its maximum value for given values of latus rectum (l) and eccentricity (e). The introduction of spin (S = |J|/M2) to the massive black hole causes this boundary, or abutment, to be moved towards greater orbital inclination; thus it no longer cleanly separates prograde and retrograde orbits. To characterise the abutment of a Kerr black hole (KBH), we first investigated the last stable orbit (LSO) of a test-particle about a KBH, and then extended this work to general orbits. To develop a better understanding of the evolution of Q we developed analytical formulae for Q in terms of l, e, and S to describe elliptical orbits at the abutment, polar orbits, and last stable orbits (LSO). By knowing the analytical form of dQ/dl at the abutment, we were able to test a 2PN flux equation for Q. We also used these formulae to numerically calculate the di/dl of hypothetical circular orbits that evolve along the abutment. From these values we have determined that di/dl = -(122.7S - 36S^3)l^-11/2 -(63/2 S + 35/4 S^3) l^-9/2 -15/2 S l^-7/2 -9/2 S l^-5/2. Thus the abutment becomes an important analytical and numerical laboratory for studying the evolution of Q and i in Kerr spacetime and for testing current and future radiation back-reaction models for near-polar retrograde orbits.Comment: 51 pages, 8 figures, accepted by Classical and Quantum Gravity on September 22nd, 201

Signatures of LCDM substructure in tidal debris

In the past decade, surveys of the stellar component of the Galaxy have revealed a number of streams from tidally disrupted dwarf galaxies and globular clusters. Simulations of hierarchical structure formation in LCDM cosmologies predict that the dark matter halo of a galaxy like the Milky Way contains hundreds of subhalos with masses of ~10^8 solar masses and greater, and it has been suggested that the existence of coherent tidal streams is incompatible with the expected abundance of substructure. We investigate the effects of dark matter substructure on tidal streams by simulating the disruption of a self-gravitating satellite on a wide range of orbits in different host models both with and without substructure. We find that the halo shape and the specific orbital path more strongly determine the overall degree of disruption of the satellite than does the presence or absence of substructure, i.e., the changes in the large-scale properties of the tidal debris due to substructure are small compared to variations in the debris from different orbits in a smooth potential. Substructure typically leads to an increase in the degree of clumpiness of the tidal debris in sky projection, and in some cases a more compact distribution in line-of-sight velocity. Substructure also leads to differences in the location of sections of debris compared to the results of the smooth halo model, which may have important implications for the interpretation of observed tidal streams. A unique signature of the presence of substructure in the halo which may be detectable by upcoming surveys is identified. We conclude, however, that predicted levels of substructure are consistent with a detection of a coherent tidal stream from a dwarf galaxy.Comment: 15 pages, 13 figures, accepted for publication in ApJ. Matches accepted versio

The Analysis of Large Order Bessel Functions in Gravitational Wave Signals from Pulsars

In this work, we present the analytic treatment of the large order Bessel functions that arise in the Fourier Transform (FT) of the Gravitational Wave (GW) signal from a pulsar. We outline several strategies which employ asymptotic expansions in evaluation of such Bessel functions which also happen to have large argument. Large order Bessel functions also arise in the Peters-Mathews model of binary inspiralling stars emitting GW and several problems in potential scattering theory. Other applications also arise in a variety of problems in Applied Mathematics as well as in the Natural Sciences and present a challenge for High Performance Computing(HPC).Comment: 8 pages, Uses IEEE style files: Ieee.cls, Ieee.clo and floatsty.sty. Accepted for publication in High Performance Computing Symposium, May 15-18 (HPCS 2005) Guelph, Ontario, Canad

A Study of the Gravitational Wave Pulsar Signal with orbital and spindown Effects

In this work we present analytic and numerical treatments of the gravitational wave signal from a pulsar which includes spindown. We consider phase corrections to a received monochromatic signal due to rotational and elliptical orbital motion of the Earth, as well as perturbations due to Jupiter and the Moon. We discuss the Fourier transform of such a signal, which is expressed in terms of well known special functions and lends itself to a tractable numerical analysis.Comment: 8 pages, 8 figures. Write-up of talk given at Theory Canada I, June 2005, University of British Columbi

Lamm, Valluri, Jentschura and Weniger comment on "A Convergent Series for the QED Effective Action" by Cho and Pak [Phys. Rev. Lett. vol. 86, pp. 1947-1950 (2001)]

Complete results were obtained by us in [Can. J. Phys. 71, 389 (1993)] for convergent series representations of both the real and the imaginary part of the QED effective action; these derivations were based on correct intermediate steps. In this comment, we argue that the physical significance of the "logarithmic correction term" found by Cho and Pak in [Phys. Rev. Lett. 86, 1947 (2001)] in comparison to the usual expression for the QED effective action remains to be demonstrated. Further information on related subjects can be found in Appendix A of hep-ph/0308223 and in hep-th/0210240.Comment: 1 page, RevTeX; only "meta-data" update

A unified framework for the orbital structure of bars and triaxial ellipsoids

We examine a large random sample of orbits in two self-consistent simulations of N-body bars. Orbits in these bars are classified both visually and with a new automated orbit classification method based on frequency analysis. The well-known prograde x1 orbit family originates from the same parent orbit as the box orbits in stationary and rotating triaxial ellipsoids. However, only a small fraction of bar orbits (~4%) have predominately prograde motion like their periodic parent orbit. Most bar orbits arising from the x1 orbit have little net angular momentum in the bar frame, making them equivalent to box orbits in rotating triaxial potentials. In these simulations a small fraction of bar orbits (~7%) are long-axis tubes that behave exactly like those in triaxial ellipsoids: they are tipped about the intermediate axis owing to the Coriolis force, with the sense of tipping determined by the sign of their angular momentum about the long axis. No orbits parented by prograde periodic x2 orbits are found in the pure bar model, but a tiny population (~2%) of short-axis tube orbits parented by retrograde x4 orbits are found. When a central point mass representing a supermassive black hole (SMBH) is grown adiabatically at the center of the bar, those orbits that lie in the immediate vicinity of the SMBH are transformed into precessing Keplerian orbits that belong to the same major families (short-axis tubes, long-axis tubes and boxes) occupying the bar at larger radii. During the growth of an SMBH, the inflow of mass and outward transport of angular momentum transform some x1 and long-axis tube orbits into prograde short-axis tubes. This study has important implications for future attempts to constrain the masses of SMBHs in barred galaxies using orbit-based methods like the Schwarzschild orbit superposition scheme and for understanding the observed features in barred galaxies