Tidal interactions of a Maclaurin spheroid. I: Properties of free oscillation modes

We review the work of Bryan (1889) on the normal modes of a Maclaurin spheroid, carrying out numerical calculations of the frequencies and spatial forms of these modes that have not been previously published. We study all modes of degree $l \le 4$, which includes both inertial modes and surface gravity modes, with the aim of better understanding the effect of rapid rotation on tidal interactions. The inclusion of these higher degree modes greatly increases the number of frequencies at which tidal resonances may occur. We derive an expression for the decay rates of these modes to first order in viscosity and explicitly plot these for modes. We see that the equatorial bulge of the spheroid has a significant effect on the decay rates (changing some of these by a factor of 2 between an eccentricity of $e=0$ and $0.5$), and a more modest effect on the mode frequencies. This suggests that models of tidal interaction between rapidly rotating stars and giant planets that model the Coriolis force while neglecting the centrifugal distortion of the body may be in error by an order unity factor. In a subsequent paper we shall examine the case of a forced flow in this spheroid, and complete the model by considering how the tides raised by the orbiting companion change the orbital elements.Comment: 27 pages, 39 figures, 1 table, accepted for publication in MNRA

The solar cycle variation of the solar wind helium abundance

A critical survey was made of the experimental evidence for a variation of the relative abundance by number h, (n alpha/np), of helium in the solar wind. The abundance is found to vary by delta h = 0.01 + or - 0.01 from 0.035 to 0.045 over solar cycle 20. Changes in the average bulk speed during the solar activity cycle was insufficient to account for this increase in h with the solar cycle. The slope of the linear relation between h and the plasma bulk speed is also found to vary, being greatest around solar maximum. An attempt is made to explain the 30% variation in h as the result of the variation in the number of major solar flares over a solar cycle. These obvious transients are apparently not numerous enough to explain the observed variation, but the reasonable expectation remains that the transients observed recently by Skylab which may occur more frequently than major flares could augment those associated with major flares. Since the solar wind flux is not observed to increase at solar maximum, the abundance of Helium cannot be proportional to the proton flux leaving the sun unless the solar wind comes from a smaller area of the sun at maximum than at minimum

First results from the six-axis electron spectrometer on ISEE-1

A survey, using results from the first 25 orbits of ISEE-1, was made of some aspects of electrons in the dawn magnetosheath. There are indications that the flow of plasma is not uniformly turbulent over this region. The electron heat flux is observed to be directed away from the shock and to have an average value of about twice the interplanetary heat flux. Many magnetopause crossings were observed and usually resemble abrupt transitions from one well-defined plasma state to another. The ejection of plasma from flux tubes convected up against the magnetopause is observed for about half the time, and its thickness and dependance on the solar wind Mach number agrees with theoretical predictions. A full traversal of the whole forward hemisphere of the magnetosheath is required to fully confirm these deductions

Acceleration of protons by interplanetary shocks

Acceleration of protons by interplanetary shock

The evolution of a warped disc around a Kerr black hole

We consider the evolution of a warped disc around a Kerr black hole, under conditions such that the warp propagates in a wavelike manner. This occurs when the dimensionless effective viscosity, alpha, that damps the warp is less than the characteristic angular semi-thickness, H/R, of the disc. We adopt linearized equations that are valid for warps of sufficiently small amplitude in a Newtonian disc, but also account for the apsidal and nodal precession that occur in the Kerr metric. Through analytical and time-dependent studies, we confirm the results of Demianski & Ivanov, and of Ivanov & Illarionov, that such a disc takes on a characteristic warped shape. The inner part of the disc is not necessarily aligned with the equator of the hole, even in the presence of dissipation. We draw attention to the fact that this might have important implications for the directionality of jets emanating from discs around rotating black holes.Comment: 8 pages, 6 figures, to be published in MNRA

PNJL model for adjoint fermions

Recent work on QCD-like theories has shown that the addition of adjoint fermions obeying periodic boundary conditions to gauge theories on R^3 X S^1 can lead to a restoration of center symmetry and confinement for sufficiently small circumference L of S^1. At small L, perturbation theory may be used reliably to compute the effective potential for the Polyakov loop P in the compact direction. Periodic adjoint fermions act in opposition to the gauge fields, which by themselves would lead to a deconfined phase at small L. In order for the fermionic effects to dominate gauge field effects in the effective potential, the fermion mass must be sufficiently small. This indicates that chiral symmetry breaking effects are potentially important. We develop a Polyakov-Nambu-Jona Lasinio (PNJL) model which combines the known perturbative behavior of adjoint QCD models at small L with chiral symmetry breaking effects to produce an effective potential for the Polyakov loop P and the chiral order parameter psi-bar psi. A rich phase structure emerges from the effective potential. Our results are consistent with the recent lattice simulations of Cossu and D'Elia, which found no evidence for a direct connection between the small-L and large-L confining regions. Nevertheless, the two confined regions are connected indirectly if an extended field theory model with an irrelevant four-fermion interaction is considered. Thus the small-L and large-L regions are part of a single confined phase.Comment: 6 pages, 4 figures; presented at INPC 201