David Galloway

Pulsar braking indices revisited

Using the standard equation for the slowdown of a neutron star, we derive a formula for the braking index via integration rather than the conventional differentiation. The new formula negates the need to measure the second time derivative of the rotation frequency, . We show that the method gives similar braking indices for PSR B1509−58 and the Crab pulsar to those already in the literature. We point out that our method is useful for obtaining the braking indices of moderate-aged pulsars without the need for long, phase-connected timing solutions. We applied the method to 20 pulsars and discuss the implications of the results. We find that virtually all the derived braking indices are dominated by the effects of (unseen) glitches, the recovery from which corrupts the value of . However, any real, large, positive braking index has implications for magnetic field decay and offers support to recent models of pulsar evolution.

Compressible convection in the presence of rotation and a magnetic field

Abstract The onset of convection in a polytropic atmosphere with rotation and magnetic field is considered in a geometry such that rotation, magnetic field and gravity are mutually perpendicular. The anelastic approximation is used together with the low diffusion magnetogeostrophic approximation. The factors determining the pattern of convection are discussed, with particular reference to the question of whether convection rolls are primarily aligned with the rotation axis or the magnetic field. As in the Boussinesq problem, the global Elsasser number ℬ2/2μρΩη plays a key role. It is shown that the onset of convection in this system cannot be steady, but must occur in the form of travelling waves. In compressible convection the pressure fluctuations contribute to the buoyancy force as well as the temperature fluctuations: in rotating systems these pressure fluctuations are out-of-phase with the temperature fluctuations, and this phase difference gives rise to the travelling waves. Growth rates and frequen...

ABC flows then and now

We review cellular space-periodic dynamos without scale separation, starting with early work in the 1980s on ABC flows with prescribed steady velocity fields u  = (A sin z + C cos y, B sin x + A cos z, C sin y + B cos x). These naturally led to work done in the 1990s together with Mike Proctor on 2-D time-dependent versions which gave strong numerical evidence for the existence of fast dynamos growing on the flow turnover timescale. Similar calculations were subsequently performed for a spherical shell geometry jointly with Rainer Hollerbach. Also in the 1990s other studies began to take into account the back reaction of the Lorentz force when the flow rather than being prescribed was instead allowed to evolve in response to a forcing of the above ABC form. The dynamos that resulted were mostly filamentary and showed a disconcerting tendency to equilibrate with total magnetic energy much less than total kinetic energy in the low diffusivity limit relevant for astrophysics. The remarkable discovery by Archontis in 1999 of a non-filamentary dynamo with almost equal magnetic and kinetic energies showed that the unfavourable scalings for the filamentary case can be overcome; this dynamo used an ABC forcing with the cosines left out. Since then several authors have been struggling with partial success to understand just how this state of affairs comes about. Most recently efforts have been made to produce other examples of this type of dynamo, to investigate why the Archontis case is robust over a wide range of magnetic Prandtl numbers ν/η, and above all to understand its remarkable stability at very low diffusivities when non-magnetic flows are almost always unstable.

Dynamo action in christopherson hexagonal flow

Abstract Kinematic dynamo action is investigated for the Chiistopherson flow consisting of a horizontally periodic layer of identical hexagonal cells. In each cell a conducting fluid ascends at its centre and descends at its periphery. Boundary conditions are chosen so that the layer has a perfectly conducting base and is overlaid by a current-free atmosphere. By numerically solving the eigenvalue problem for the induction equation, it is found that a dynamo operates when the magnetic Reynolds number R m exceeds 515. According to recent theoretical results, this dynamo is expected to be slow, though our results show the growth rate is still increasing at R m= 1000. The magnetic structure is concentrated around stagnation points and their associated heteroclinic orbits.

On the adjustment to the Bondi-Gold theorem in a spherical-shell fast dynamo

Abstract We present a numerical solution of the magnetic induction equation in a spherical fluid shell, with an insulator inside and outside. Prescribing an axisymmetric, time-dependent, chaotic flow, we find that the magnetic field appears to grow on the fast advective, rather than on the slow diffusive time scale. We demonstrate how this may be reconciled with the theorem of Bondi and Gold (1950), that the potential field in these insulators inside and outside the shell cannot be amplified on the fast time scale, by having the field become increasingly contained within the shell with increasing magnetic Reynolds number. Thus, as the Bondi-Gold theorem becomes more and more applicable, there is indeed less and less external field being amplified. This is in precise agreement with the conjecture of Radler (1982) that the resolution would be to have an “invisible dynamo,” one having no external field. Finally, we consider some of the implications of this adjustment for the different symmetries of the field...

Generation of Coronal Currents by the Solar Convection Zone

Solar flares are thought to be caused by reconnection of magnetic fields and their associated electric currents in the solar corona. The currents have to be there to provide available energy over and above the current-free minimum energy state, but what generates them has been little discussed. This paper investigates the idea that twisting motions in the turbulent convection zone below may provide a natural source for the currents and explain some of their properties. The twists generate upward-propagating Alfven waves with a Poynting flux of the right order of magnitude to power a flare. Depending on the depth it takes place, the twisting event that initiates a particular flare may occur hours, days or even months before the flare itself.

A review of: “Stellar magnetism”

by Leon Mestel (Oxford University Press, International Series of Monographs on Physics Volume 99) 1999, XX + 636pp., £ 85.00 (hardbound; ISBN 0 19852761 0).

Braking Indices for Twenty Pulsars

We have derived a formula for the braking index of pulsars via integration rather than the conventional differentiation method. We applied the method to 20 pulsars and find that virtually all the derived braking indices are dominated by the effects of (unseen) glitches, the recovery from which corrupts the value of . However, any real, large, positive braking index has implications for magnetic field decay and offers support to recent models of pulsar evolution.