Vortex Dynamics in the Neutron Star Inner Crust

TL;DR

This work resolves the long-standing question of how superfluid vortices in the neutron-star inner crust interact with a dynamically evolving nuclear lattice in three dimensions. By coupling a continuum vortex equation of motion to a molecular-dynamics lattice, the authors quantify pinning and unpinning under varying composition, temperature, and lattice orientation, and reveal how lattice vibrations, grain boundaries, and shear can trigger widespread unpinning and potentially glitch-like avalanches. Key findings include the dependence of the unpinning threshold on the sign of the vortex–lattice interaction, strong hysteresis in pinning/unpinning, and the significant weakening of pinning at grain boundaries and under thermal or mechanical perturbations. The results have important implications for understanding pulsar glitches and the conditions under which vortex avalanches might propagate through the crust, motivating larger-scale simulations to capture macroscopic collective behavior. The study also provides a first-principles estimate of the vortex–vortex interaction drag and demonstrates the crucial role of lattice dynamics in neutron-star glitch phenomenology.

Abstract

We study the superfluid vortex motion in the neutron star inner crust through direct three-dimensional simulations of the coupled dynamics of the vortex and the nuclear lattice. We demonstrate the pinning of an initially moving vortex to the lattice through excitation of lattice vibrations, and show that the efficiency of this process is higher for attractive than for repulsive nucleus-vortex interactions. We explore the unpinning of a vortex under the action of the applied Magnus force, and find that it is influenced by multiple parameters, including the sign of the pinning force, the lattice orientation, composition, temperature, and the energy of pinning to individual nucleus. In lattices with multiple grains, the unpinning transition is triggered inside the grains with weaker pinning, propagates along the vortex (mediated by the excited Kelvin waves) and crosses into grains with stronger pinning. This is likely to effectively decrease the critical force at which vortices unpin and to produce extended regions of unpinned vorticity. Shearing of the crust lattice (e.g., by a starquake) initiates the unpinning of the vortices that are crossing the slip plane. A close encounter of an unpinned vortex with a pinned vortex would cause the latter to unpin, perhaps initiating an unpinning avalanche of many vortices.

Figures (15)

• Figure 1: One sample snapshot in the relaxation simulation to illustrate the 3-D vortex-lattice system. We show different views of the box, including the $xy$-plane (Top-left), $xz$-plane (Top-right), and the $yz$-plane (Bottom-left). We also show a zoom-in 3D box in the simulation region (Bottom-right). The line is the vortex, and the dots are nuclei.
• Figure 2: The line energy density $\epsilon_{\mathrm{le}}$, potential energy density $\epsilon_{\mathrm{pe}}$ and total energy density $\epsilon_{v}$ of the vortex vs. time in relaxation for attractive (left) and repulsive (right) interaction. The vortex undergo an energy dissipation and reach equilibrium gradually. The vortex relaxes much faster in attractive interaction compared to repulsive interaction. We fit the energy damping with a bi-exponential model $E_v = E_1e^{-\gamma_1t} + E_2e^{-\gamma_2t} + C$. We find out that on average $\gamma_1\sim 0.1$ for attractive interaction and $\gamma_1\sim0.01$ for repulsive interaction.
• Figure 3: Two selected baseline model simulations showing the vortex velocity in x direction $|v_{vx}|$, in y direction $|v_{vy}|$, and absolute value $|v_v|$ vs. the background superfluid velocity $v_b$. The solid lines show the vortex velocity when increasing $v_b$, and the dashed lines show the vortex velocity when decreasing $v_b$. These two models have different orientations, which can affect the unpinning velocity significantly. The vortex velocity shows hysteresis, where the superfluid velocity at unpinning is larger than that at repinning. The results are qualitatively similar to those in Link_2022.
• Figure 4: Damping coefficient $\gamma$ vs. vortex velocity $v_v$ for two selected simulations in attractive interaction. We assume $\gamma \propto v_v^\beta$ and find $\beta \sim -1$.
• Figure 5: Lattice displacement in different lattice spacing and vortex pinning energy $E_p$. The displacement is measured by finding the balance between the pinning force and Coulomb force. Left: lattice with nuclear charge $Z=10$; Right: $Z=40$. Dashed lines indicate our choice of the baseline model. Two horizontals solid lines show the lattice spacing with different nucleus density computed in Negele_1973. Two vertical solid lines show the $|E_p|$ for two models computed in Avogadro_2008. A displacement $> 0.1$ indicates possible non-harmonic deformation and restoration. If the Coulomb force is weak compared to the vortex interaction, we observe large lattice deformation where a fully coupled MD simulation is required; otherwise, the lattice can be well-approximated as stationary.