How is angular momentum stored in the superfluid component of pulsars?

Question

I am trying to understand current theories about why pulsars glitch. I have come across two explanations that I'm assuming are complementary, but which I am having trouble reconciling.

1. The inner super-fluid component is spinning faster than the crust. Occasionally, the two briefly bind, during which angular momentum is transferred.

This is based off of the wikepedia entry for "glitch". Intuitively, I picture this as two aligned globes, with one spinning inside the other.

2. The inner super-fluid component contains "currents", which rotate around vortex lines. Normally, these vortex lines are pinned to the crust. However, when a large number of them unpin at once, they transfer some of the angular momentum of the currents to the crust, resulting in a glitch.

This is coming from the vortex creep model (summary in section 2). It is hard to describe in words how I picture this, so I include a picture below. I imagine these spikes are vortex lines... And that's about as far as I can get.

Are these vortex lines rotating with the crust, so that a given "packet" of super-fluid both has a global rotation about the star's axis of rotation, as well as a local rotation around the vortex line? If so, is this global rotation what is referenced in explanation 1)?

Additionally, 1) seems to be reliant on the crust and super-fluid component being unbound from each-other (except during a glitch), but 2) seems to imply that the components are bound to each other (except during a glitch). This seems to imply a fundamental misinterpretation of something on my part, but I'm not sure exactly what.

Answer 1

The second explanation is the currently accepted model of pulsar glitches. The first one is a little bit backward.

The superfluid interior of a neutron star rotates by creating a number of vortices, which carry the interior's angular momentum. The only way this part of the star can spin down is if the vortices move outwards and are removed; the outer crust does spin down, because of the emission of electromagnetic radiation. However, the vortices are "pinned" by the crust, and so the interior does not lose angular momentum and does not spin down.

The exact mechanism for how the angular momentum is eventually released, in a glitch, has long been debated. Originally, crust quakes were the suggested source of the force needed to unpin the vortices, but calculations showed that the quakes could not trigger the large glitches observed in certain pulsars, and the predictions of future glitches were largely incorrect. There is not necessarily a pattern or regularity to groups of glitches, but crust quakes seemed to predict there was. Thus, the crust quake model was overturned in favor of one taking into account superfluidity.

The snowplow model holds that vortices deep in the neutron star can unpin if the maximum pinning force is exceeded. This can happen if the vortex density is too great, which happens at a certain critical lag between the rotation of the crust and the "rotation" of the interior; the hydrodynamical Magnus force plays a strong role here. Through unpinning and repinning, the vortices eventually reach the radius $r_{\text{max}}$ of peak pinning force, where the critical lag $\Omega$ is the largest. They then reach the crust and transfer large amounts of angular momentum, leading to a glitch.

The amount of transferred angular momentum depends on the number of vortices, $N_v$ in the sheet just before this critical radius, given by $$N_v=\frac{2\pi}{\kappa}r^2_{\text{max}}\Omega_{\text{max}}$$ where $\kappa$ is a constant defined as $\kappa\equiv \pi\hbar/m_N$, where $m_N$ is the mass of a neutron. Additionally, the angular momentum transferred in the glitch, $\Delta L_{gl}$, is directly proportional to $N_v$.

Further reading

• Haskell and Melatos (2015)
• Seveso et al. (2012)

Answer 2

Note: the understanding and modelling of pulsar glitches is based on some speculative ideas. The robust points and the (many) simplifications and assumptions of some popular classes of models are discussed in the review linked below.

Your points (1) and (2) are not in contradiction, but your description of point (2) is not very precise.

1 - Yes, the superfluid tends to spin faster than the normal component.

2 - Point 1 is possible because of "vortex pinning", that is realized when quantized vortices in the neutron superfluid are blocked to impurities. Since vortices are blocked, they can not be expelled from the superfluid region, meaning that the superfluid can not spin down together with the normal component. This gives rise to a velocity difference between the two components (hence point 1).

The above picture, the details of vortex creep and vortex pinning and their associated effect on the dynamics of a pulsar are discussed in the review Insights into the physics of neutron star interiors from pulsar glitches (2022). You can find an extended list of references to other older reviews and original papers therein, including a critical revision of many glitch models.

As a final note, the "hairy ball" picture in your question does not depict the quantum vortices in a neutron star: they can be twisted and tangled but they are (on average) parallel to the rotation axis of the pulsar. According to the review, most models of glitches assume parallel vortices along the rotation axis as a working assumption, in order to simplify the problem.