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

## 5. Potential importance of the centrifugal buoyancy mechanism

So far we have only been summarising what has long been well known to workers in this field. We now come to what seems to us to be an important point that has been overlooked, which is that independently of vortex pinning there is another, comparably powerful mechanism, that can also cause discontinuous angular momentum transfer to a solid crust from an independently rotating superfluid layer. This mechanism does not depend on superfluidity in the strict sense but merely requires perfect fluidity in the sense that the effective viscosity should be low enough for the slowdown of the neutron fluid to lag behind the slowdown (due to its coupling with the radiating magnetosphere) of the solid outer layers. The point is that if the outer layers were also effectively fluid, there would be a convective readjustment, in which annular rings of fluid would change their relative positions, each retaining its separate angular momentum, in such a way that those with less angular momentum per unit mass, and thus with less "centrifugal buoyancy" would move towards the axis while those with more would move out so as to establish a state of equilibrium in which, provided the pressure depends only on the density, the angular velocity would decrease outwards as a function just of cylindrical radius, in accordance with the well known Taylor-Proudman theorem (see, e.g., Greenspan 1968). The effect of crust solidity will be to temporarily postpone such readjustments, by the development of the anisotropic stresses needed to balance the centrifugal buoyancy forces. However when such stresses have built up to the critical point at which the solid structure breaks down, the pent up centrifugal buoyancy forces will produce a "starquake" in which the convective readjustment that would have occurred continuously in the fluid case, is finally achieved in a discontinuous transition.

It is to be noticed that in contrast with the vortex pinning effect (in the following, for easier comparison, we will have in mind the scenario (b) of Sect. 4), which tends to pull the more slowly rotating crust material outwards from the axis towards the equator (see Fig. 2), the effect of the centrifugal buoyancy deficit in the crust is to pull the crust material inwards towards the axis of the star, where it will finally be subducted into the fluid interior (see Fig. 3). Although the centrifugal buoyancy effect produces convective circulation in just the opposite direction to that produced by vortex pinning (which if it were strong enough would lead to subduction at the equator rather than the axis (Ruderman 1991)) its effect on the angular momentum distribution would be similar, i.e. the net effect of a centrifugal buoyancy crustquake will be a discontinuous transfer of angular momentum to the crust from the more rapidly rotating fluid layer. This means that the crude quantitative estimate given by Eq. (14) is applicable just as well to the effect of a centrifugal buoyancy crustquake as to a vortex pinning crustquake.

 Fig. 2. Qualitative sketch indicating direction of force expected to act on (magnetically slowed down) down on crust due to vortex pinning mechanism , if it is effective, when the (interpenetrating) neutron superfluid retains a higher rotation rate.

 Fig. 3. Qualitative sketch indicating direction of force expected to act on (magnetically slowed down) crust, even if vortex pinning is ineffective, due to the centrifugal buoyancy mechanism when the (interpenetrating) neutron superfluid retains a higher rotation rate.

The main point we want to emphasise is that whereas vortex pinning may indeed be the main driving force for the build up of the stress that is relaxed in crustquakes, the extent to which it really is depends on detailed considerations about the strength of vortex pinning. On the other hand the opposing centrifugal buoyancy mechanism will always function whenever there is differential rotation. It will be seen in the next section that when it is fully effective the oppositely directed pinning mechanism will be strong enough to overwhelm (i.e. to more than cancel) the buoyancy mechanism, but the latter mechanism is more robust in the sense that it will always make a significant contribution.

Our tentative conclusion - which we are proposing as a subject for debate and further investigation - is that the hitherto neglected centrifugal buoyancy effect may be the dominant cause of the crustquakes that are observed as pulsar glitches, while vortex pinning crustquakes, if they occur at all, are relatively rare. This does not mean that vortex pinning is unimportant for the phenomenon, because it is likely to be what determines the magnitude of the relevant moment of inertia contribution in the estimate (14) for the ratio of to . However what it means is that the vortex pinning stresses are not what is immediately responsible for the discontinuous breakdown, and hence not what is of dominant relevance for estimating the absolute values of at which it is likely to occur.

© European Southern Observatory (ESO) 2000

Online publication: October 2, 2000