Anomalous Energy Injection in the Gross-Pitaevskii Framework for Turbulence in Neutron Star Glitches

Abstract

Neutron star glitches -- sudden increases in rotational frequency -- are thought to result from angular momentum transfer via quantized vortices in the superfluid core. To investigate the underlying superfluid dynamics, we employ a two-dimensional rotating atomic Bose-Einstein condensate described by a damped Gross-Pitaevskii equation with an imposed pinning potential that serves as a simplified analogue of a crust. Within this minimal framework, we examine the emergence and evolution of turbulent vortex motion following impulsive perturbations reminiscent of glitch-like forcing. Our simulations reveal a transient Kolmogorov-like turbulent cascade ($k^{-5/3}$) that transitions to a Vinen-like scaling ($k^{-1}$). We identify an anomalous secondary injection mechanism driven primarily by quantum pressure, which can sustain turbulent fluctuations in such a system. By tuning the damping coefficient $γ$, we determine an optimal regime for energy transfer. While idealized, these findings illustrate how quantum turbulence with multiple scaling regimes can arise in pinned, rotating superfluids, and they suggest possible qualitative connections to vortex-mediated dynamics in neutron stars and other astrophysical superfluid systems.

Figures (6)

• Figure 1: Snapshots of condensate density during real-time spin-down at $t_s = 10$ with the crust potential. As the condensate spins down, the initially dominant centrifugal confinement [(a)] is overtaken by the circular box trap [(b)--(d)]. Concurrently, turbulent flow induces the depinning of vortices.
• Figure 2: Incompressible kinetic energy spectra exhibiting the Kolmogorov cascade for spin-down time $t_s = 10$ (a), averaged over $t = 10$ to $t = 30$; (b) averaged over $t = 30$ to $t = 50$, and spin-down time $t_s = 20$ (c) averaged over $t = 20$ to $t = 50$; and (d) averaged over $t = 50$ to $t = 60$. The spectra initially [(a) and (c)] and later durations [(b) and (d)] exhibit $k^{-5/3}$ and $k^{-1}$ scalings, respectively alongside a $k^{-3}$ scaling.
• Figure 3: Variation of vortex density (per unit area) with respect to time on a logarithmic scale for spin-down times (a) $t_s = 10$, (b) $t_s = 20$, (c) $t_s = 30$, and (d) $t_s = 40$. The vortex decay in the Kolmogorov and Vinen turbulence regimes exhibits $t^{-3/2}$ and $t^{-1}$ scaling behaviors, respectively.
• Figure 4: Temporal profiles of the total kinetic energy exchange between its components for spin-down times(marked by dark-grey vertical lines) (a) $t_s = 10$, (b) $t_s = 20$, (c) $t_s = 30$, and (d) $t_s = 40$. The red dashed line represents energy transfer from the incompressible to the compressible component ($E_{\mathrm{ex}}^{ic}$), the green dash-dotted line represents energy transfer between the incompressible and quantum pressure components ($E_{\mathrm{ex}}^{iq}$), and the blue line with circles represents energy transfer between the compressible and quantum pressure components ($E_{\mathrm{ex}}^{cq}$). A negative exchange energy indicates a transfer from the first component $\alpha\in\{i,c,q\}$ in the superscript to the second $\beta \in\{i,c,q\}$, while a positive value indicates the reverse.
• Figure 5: Variation of (a) incompressible kinetic energy spectra and (b) compressible kinetic energy spectra for different values of the damping coefficient $\gamma$. Both spectra are calculated for the case $t_s = 10$ and averaged over the time range $t = 10$ to $t = 30$. The spectra exhibit a better fit to turbulent scaling for smaller $\gamma$ values.