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

3. Glitches driven by differential rotation

Soon after the empirical discovery of glitches too large to be accounted for by the "spheroidality" mechanism, it came to be recognised by theorists (Anderson & Itoh 1975) that a plausible explanation involved the superfluid property of the deeper layers of sufficiently cool neutron stars. This property makes it possible to conceive that an interior neutron superfluid layer with moment of inertia, say, can rotate with an angular velocity, say, that may differ from the externally observable angular velocity that characterises the part of the star that corotates with the crust, with its own moment of inertia

In such a case it can be supposed that when an external braking mechanism causes the corotating crust component to undergo an angular velocity change , the angular velocity of the independently rotating neutron superfluid layer may in the short run be unaffected, with negligible variation expressible by

but that, when the ensuing angular velocity difference between the corotating crust component and the neutron superfluid layer exceeds some critical value there will be a discontinuous adjusment whereby this angular velocity difference is reduced by some process involving a transfer of angular momentum between the two components. Such a process will evidently entail a negative adjustment of the angular velocity of the neutron superfluid layer and an accompanying positive adjustment of the (observable) angular velocity of the corotating crust component, whereby the latter increases its angular momentum by an amount that is equal to the amount that is lost by the neutron superfluid component, so that the total angular momentum change during the discontinuous `glitch' process is zero, i.e.

If this adjustment process were a hundred per cent efficient, the net variation of the corotating crust angular velocity would be exactly matched by the net neutron superfluid angular velocity variation, which by (10) will be simply given by , so that one would have

with . In practice one would expect that there would typically be an incomplete adjustment, still expressible by a relation of the form (12), but with an efficiency factor having some lower value in the range (5). By substituting (11) in (12) it can be seen that the observable glitch magnitude will be given by

and hence, by (9), that for an efficiency factor with any value in the range (5) the glitch magnitude will satisfy the inequality

By comparing (14) with (7), it can be seen that, for a given assumed value of the efficiency factor , the differential rotation adjustment mechanism characterised by (14) can give rise to a much larger glitch magnitude than is possible by the spheroidality adjusment mechanism characterised by (7), because the factor in (14) can be of order unity, whereas the corresponding factor in (7), namely is very small compared to unity in even the most rapidly rotating pulsars. Thus, unlike the spheroidality mechanism, mechanisms involving angular momentum transfer between differentially rotating components can plausibly be considered as candidates for explaining the frequent large glitches observed in the Vela pulsar.

© European Southern Observatory (ESO) 2000

Online publication: October 2, 2000
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