The Spin‐down Rate of a Pinned Superfluid

The spinning down (up) of a superfluid is associated with a radial motion ofits quantized vortices. In the presence of pinning barriers against the motionof the vortices, a spin-down may be still realized through ``random unpinning''and ``vortex motion,'' as two physically separate processes, as suggestedrecently. The spin-down rate of a pinned superfluid is calculated, in thisframework, by directly solving the equation of motion applicable to only theunpinned moving vortices, at any given time. The results indicate that thepinned superfluid in the crust of a neutron star may as well spin down at thesame steady-state rate as the rest of the star, through random unpinningevents, while pinning conditions prevail and the superfluid rotational lag issmaller than the critical lag value.Comment: to appear in ApJ (vol. 649 ?