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Astron. Astrophys. 361, 795-802 (2000)

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1. Introduction

The ultimate motivation for this article is the problem of explaining one of the salient observational features of isolated (non-binary) pulsars, which is that comparatively long periods of continuous "spin down" of the observed frequency [FORMULA] are occasionally interrupted by small "glitches". Such a glitch consists of a sudden small increase, [FORMULA] say, that partially cancels the continuous negative variation [FORMULA] that has been accumulated since the preceding glitch.

Since very soon after its discovery in 1968, it has been generally agreed that the pulsar phenomenon is attributable to a strong magnetic field anchored in the outer crust layers of a central neutron star. The observed frequency [FORMULA] is to be interpreted as the rotation frequency of the outer crust layer, whose continuous spin down is evidently due to the continuous decrease of the angular momentum J due to radiation from the external magnetosphere. After thirty years of work, two basic problems remain.

The first is to account for the spectrum (from radio to X-ray and beyond) and the detailed pulse structure of the radiation, which are presumed to depend on the still very poorly understood workings of the magnetosphere.

The second problem - the one with which the present article is concerned - is to account for the frequency "glitches". It is generally recognised that the glitches must be explained in terms of what goes on in the interior of the neutron star, and it is also generally believed that the glitch phenomenon is essentially dependent on the property of solidity that is predicted (on the basis of simple, generally accepted theoretical considerations) to characterise the crust of the neutron star after it has fallen below the relevant extremely high melting temperature, which occurs very soon after its formation.

While there is agreement in presuming that discontinuous changes in the solid crustal structure must be responsible for the observed frequency glitches, what remains to be established is the qualitative nature of the process that is primarily responsible for such "crustquakes".

The purpose of this article is to draw attention to the potential importance, as a mechanism for this process, of the stresses induced in the crust just by the effective force arising from the deficit of centrifugal buoyancy that will be present whenever there is differential rotation.

It is to be noticed that centrifugal buoyancy is a phenomenom that has been previously considered in the context of neutron stars, at least with reference to one of its possible consequences, namely Ekman pumping. This is a mechanism that can considerably shorten the timescale needed for the redistribution of angular momentum (in comparison with viscous diffusion characterized by the timescale given by [FORMULA] where [FORMULA] is the typical kinetic viscosity coefficient and [FORMULA] is the relevant stellar radial length scale) and thus the damping of differential rotation in cases for which (as will be the case in a typical pulsar) the star is rotating fast enough for the corresponding rotation timescale [FORMULA] to be short compared with [FORMULA]. In such circumstances, "Ekman pumping" will supplement the very slow diffusive transport by more rapid convective transport propelled by centrifugal buoyancy forces. The ensuing "Ekman timescale" [FORMULA] for the effective damping of differential rotation in such cases will be given roughly by the geometric mean of the pure diffusion and rotation timescales, i.e. [FORMULA].

While it has been suggested that either Ekman pumping or magnetic coupling may be able bring the core plasma into corotation with the crust (Easson 1979), it has since been pointed out that Ekman pumping will be inhibited by density stratification (see e.g. Abney & Epstein 1995) and will therefore be inefficient. It is plausible that it also applies to the uncharged crust neutron superfluid that is believed (see e.g. Sauls 1988) to permeate the lower layers of the crust in the density range from [FORMULA] to about [FORMULA] gm/cm3. This means that the convectively accelerated Ekman timescale, [FORMULA], is too long to prevent the development of significant differential rotation. The negligibility, in such cases, of Ekman pumping is attributable to the effective negligibility of viscosity, but should not be construed as implying the negligibility of centrifugal buoyancy forces. In previous discussions of such scenarios - and in particular of the simplified strictly stationary limit in which the effective viscosity is neglected, so that no possibility of Ekman pumping can arise at all - the role of centrifugal buoyancy forces has been rather generally overlooked. The upshot of the present investigation of stationary differentially rotating configurations is to show that in such cases the general neglect of the centrifugal buoyancy effect is quite unjustified, and that on the contrary this effect is potentially capable by itself of providing the dominant contribution to the crust stresses that are ultimately released in "glitches".

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© European Southern Observatory (ESO) 2000

Online publication: October 2, 2000
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