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

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2. Glitches driven by the spheroidality mechanism

In the first years after the problem of accounting for neutron star "crustquakes" was posed, attention was concentrated on what is describable as the "spheroidality mechanism" (Ruderman 1969). This mechanism depends on the supposition that the solidity forces will not be strong enough to allow the stellar equilibrium configuration to differ very much from a perfectly fluid equilibrium state, which would be spherical in the absence of rotation, but which will actually have the form of an oblate spheroid with ellipticity proportional to [FORMULA]. The moment of inertia, defined as the ratio [FORMULA], will be given for a slowly rotating fluid by an expression of the form

[EQUATION]

where [FORMULA] is its spherical limit value and [FORMULA] is a constant characterising the rather high angular frequency needed for relative deviations from spherical symmetry to be of order unity. A more accurate formula involving higher order corrections would be needed for a star with angular velocity near the critical value [FORMULA], but the cases in which glitches have been observed so far are all characterised by

[EQUATION]

For a perfectly fluid star model, a continuous angular momentum variation [FORMULA] would bring about a corresponding momentum of inertia variation [FORMULA] that would be given by

[EQUATION]

Due to the solidity of the crust, which tends to preserve the more highly elliptic initial configuration, the actual change in the moment of inertia will fall short of what is predicted by this formula, but at some stage the strain will build up to the point at which the solid structure will break down (see Fig. 1). It is predicted that there will then be a "crustquake" in which the solid structure suddenly changes towards what the perfect fluid structure would have been, thereby changing the moment of inertia by an amount

[EQUATION]

where [FORMULA] is an efficiency factor that should presumably lie somewhere in the range

[EQUATION]

[FIGURE] Fig. 1. Qualitative sketch indicating direction of force expected to act on (magnetically slowed down) crust due to spheroidality mechanism , in absence of differential rotation. Solid lines indicate outer and inner boundaries of crust. Vertical shading indicates the alignement of the vortices in the region occupied by neutron superfluid, which is not confined to the core but interpenetrates the greater part of the solid crust as well. Note that the vortices represented here are not physically relevant in this particular mechanism.

Since the amount of angular momentum loss during the very short duration of the glitch will be negligible, the corresponding discontinuous angular velocity change will be given by

[EQUATION]

Its value will therefore be expressible in terms of the order of unity efficiency factor [FORMULA] by

[EQUATION]

in which it is to be recalled that [FORMULA] denotes the continuous (negative) change in angular velocity since the preceding glitch. This mechanism must presumably operate, and may account for some observed glitches, but it soon became clear (Baym & Pines 1971) that even if this mechanism is maximally efficient, with

[EQUATION]

the magnitude predicted by (7) is much too low for such a mechanism to be able to account for the comparatively large glitches that are frequently observed in cases such as that of the Vela pulsar.

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© European Southern Observatory (ESO) 2000

Online publication: October 2, 2000
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