Vortex Retention Mediated Turbulent Transitions in Self-Gravitating Bosonic and Axionic Condensates

Abstract

We investigate turbulent spin-down dynamics in self-gravitating Bose-Einstein condensates, comparing purely bosonic and axionic (higher-order interacting) systems. Through simulations of the Gross-Pitaevskii-Poisson system, we study condensates pinned to a crust potential undergoing rapid rotation slowdown. We find that axionic condensates exhibit more uniform density profiles and smaller sizes compared to their bosonic counterparts for similar interaction strengths, which facilitates earlier vortex entry. The sudden spin-down triggers vortex depinning and a turbulent cascade. For comparable sizes, both systems exhibit a short-lived Kolmogorov energy cascade ($k^{-5/3}$ scaling) followed by a transition to Vinen turbulence ($k^{-1}$ scaling). Crucially, their responses diverge with increasing interaction strength (and thus condensate size): the axionic system increasingly deviates from Kolmogorov scaling because of enhanced vortex retention, a trend quantitatively confirmed by analyzing the vortex fraction and its dependence on the final rotation frequency. Spectral analysis reveals that the growth of incompressible energy is primarily driven by quantum pressure during vortex detachment, rather than by compressible flows. The compressible spectrum shows thermalization ($k$ scaling). Our results demonstrate how distinct nonlinearities govern vortex dynamics and turbulent dissipation in self-gravitating quantum fluids.

Figures (11)

• Figure 1: (a) One-dimensional density profiles of the bosonic and axionic condensates for different interaction strengths, illustrating the enhanced spatial localization induced by higher-order axionic nonlinearity. (b) Critical rotation frequency $\Omega_c$ as a function of nonlinearity strength for bosonic and axionic condensates, showing that vortices nucleate more readily in the axionic case than in the bosonic system.
• Figure 2: Snapshots of the log-normalized condensate density in the $x-y$ plane for (a)-(e) bosonic case ($g_{3D} = 200$) and (f)-(j) axionic case ($g_{3D_2} = 200$) at various times during the spin-down process. In both systems, vortices and compressible density excitations are expelled toward the condensate periphery as spin-down proceeds. The color bars indicate the density $|\psi|^2$.
• Figure 3: Three-dimensional density isosurfaces of the axionic condensate with $g_{3D_2} = 200$ undergoing spin-down in the presence of a crust potential at times (a) $t = 1$, (b) $t = 2$, (c) $t = 5$, and (d) $t = 10$. Quantized vortices appear as thin tubular density depletion.
• Figure 4: Incompressible kinetic energy spectra for the (a,b) axionic and (c,d) bosonic condensates with $g_{3D_2}/g_{3D} = 200$. Spectra are averaged over two time intervals: (a,c) from $t = 2.2$ to $t = 3.2$, and (b,d) from $t = 3.2$ to $t = 5$. Both systems exhibit a Kolmogorov cascade ($k^{-5/3}$) shortly after spin-down, which later transitions to a Vinen turbulence scaling ($k^{-1}$). An enstrophy cascade ($k^{-3}$) is also visible.
• Figure 5: Compressible kinetic energy spectra for (a) the axionic condensate with $g_{3D_2} = 200$ and (b) the bosonic condensate with $g_{3D} = 200$, time-averaged over the interval $t=2.2$ to $t=3.2$. Both spectra exhibit a thermalized $k$ scaling within the inertial range [cf. similar spectra in rotating Bose-Einstein condensates Estrada2022].