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

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4. Glitch mechanisms due to the vortices

In the context of a glitch due to differential rotation, the question that arises is what physical mechanism can increase the effective coupling between the superfluid component and the crust, in order to generate a transfer of angular momentum.

The explanations that exist in the literature are based on an important property of a superfluid neutron star, which we have not yet mentioned in this article: the existence of an array of vortex lines in the rotating neutron superfluid component, each vortex carrying a quantum of vorticity [FORMULA] (where [FORMULA] is the neutron mass). The vortex number density (per unit area) [FORMULA] is directly related to the superfluid angular velocity [FORMULA] by the expression


(for uniform rotation).

The kind of angular momentum transfer mechanism that has for many years been generally considered to offer the most likely explanation for large glitches is based on the supposition that these vortices will be "pinned" in the sense of being effectively anchored in the lower crust, either by pinning in the strict sense (Anderson & Itoh 1975) or by a sufficiently strong friction force (Alpar et al. 1984). The braking of the crust will thus have the effect of slowing down the vortices relatively to the underlying superfluid, thereby giving rise to a Magnus force tending to move them out through the superfluid layer and thus slow it down as well. However this tendency to move out will be thwarted by the same anchoring effect that gave rise to it in the first place. This conflict will cause the pinning forces to build up to a critical point at which there will be a breakdown bringing about a discontinuous readjustment of the kind described by the analysis of the preceding section, and in particular by the formula (14).

The breakdown can occur in two different manners:

(a) There can be a sudden unpinning of many vortices, due to the breaking of the pinning bonds (Anderson & Itoh 1975; Link & Epstein 1991).

(b) Another possibility is that the crust lattice breaks before vortex lines can unpin from it, as suggested by Anderson & Itoh (1975) and studied in detail by Ruderman (1976).

Finally, we would like to mention another interesting glitch mechanism due to Link & Epstein (1996), which may be relevant for the present work:

(c) their thermally driven glitch mechanism is based on the so-called vortex creep model (Alpar et al. 1984), in which the coupling between the vortices and the crust is strongly temperature dependent. A sudden local increase of the inner crust temperature, such as may be due to a crustquake, can then be shown to induce a glitch.

It must be emphasized that all these three mechanisms, even if corresponding to some breaking of the crust as in the scenarios (b) and (c), are very different from the mechanism of Sect. 2, in the sense that they all are in the context of a two-component star, with the neutron superfluid rotating faster than the crust and thus acting as a reservoir of angular momentum. In the following sections, we will consider a mechanism which is not based on the presence of vortices, but still in the context of differential rotation.

Finally, let us mention the question of how big is [FORMULA] compared with I, in other words how much of the neutron fluid is effectively free to rotate independently of the rest? In the unpinned part the vortices can move out freely so as to establish corotation, so [FORMULA] may be relatively small (Jones 1991), representing the moment of inertia just of the small fraction of the neutron fluid that interpenetrates the deeper layers of the solid crust where pinning is expected to be most effective. However effective pinning may not be confined to the solid crust: it may also be achieved by forces exerted by quantised magnetic field lines (resulting from superfluidity of the protons) in the layers below the crust, in which case the relevant value of [FORMULA] might be much larger (Sedrakian & Sedrakian 1995). Another question (which applies also to the less important spheroidality mechanism discussed above) is that of the absolute values of the discontinuous changes. The foregoing reasonning is concerned just with the ratio of [FORMULA] to [FORMULA] but does not tackle the harder problem of their absolute values.

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Online publication: October 2, 2000