Vortex Pinning and Dynamics in the Neutron Star Crust

The nature of the interaction between superfluid vortices and the neutron star crust, conjectured by Anderson and Itoh in 1975 to be at the heart vortex creep and the cause of glitches, has been a long-standing question in astrophysics. Using a qualitatively new approach, we follow the dynamics as superfluid vortices move in response to the presence of “nuclei” (nuclear defects in the crust). The resulting motion is perpendicular to the force, similar to the motion of a spinning top when pushed. We show that nuclei repel vortices in the neutron star crust, and characterize the force per unit length of the vortex line as a function of the vortex element to the nucleus separation.

Figure 1

Schematic figure explaining the method used for the force extraction. The force $\mathit{F}$ depends on relative distance between vortex and nucleus $R$, moving with a constant velocity ${\mathit{v}}_0$. The external force ${\mathit{F}}_{\mathrm{ext}}(t)$ is chosen to compensate exactly $\mathit{F}$.

Figure 2

Dynamics of the system for times corresponding to small vortex-nucleus separations for neutron matter density $n=0.014{\mathrm{fm}}^{-3}$ (top) and $0.031{\mathrm{fm}}^{-3}$ (bottom). Frames from left to right correspond to times $(10,12,14,16)\times 1000\mathrm{fm}/c$ (for full movies, see [16]). Blue line indicates the vortex core position extracted from the order parameter $\mathrm{\Delta }$ (see [16] for details). Red dot indicates position of the center of mass of protons. The vector attached to the red dot denotes the vortex-nucleus force $\mathit{F}(R)$. Vectors attached to the vortex indicate contributions to the force $-d\mathit{F}$ extracted from force per unit length, see Eq. (3) and inset (a) of Fig. 3. They are scaled by a factor of 3 for better visibility. Projections of the view are shown on sides of the box. Red dashed lines denote shape of nucleus (defined as a point where density of protons drops to value $0.005{\mathrm{fm}}^{-3}$). By blue triangles (on $XY$ plane), trajectory of the vortex up to given time is shown.

Figure 3

Extracted force per unit length $f(r)$ for both densities. Negative values correspond to the repulsive force. In inset (a), the schematic configuration is shown explaining the extraction procedure according to Eq. (3). Inset (b) shows the measured total force $F(R)$ as shown in Fig. 1 for both densities. The force has been decomposed into tangential and centripetal components with respect to the instantaneous vortex position.