Glitches in Rotating Supersolids

Glitches, spin-up events in neutron stars, are of prime interest, as they reveal properties of nuclear matter at subnuclear densities. We numerically investigate the glitch mechanism due to vortex unpinning using analogies between neutron stars and dipolar supersolids. We explore the vortex and crystal dynamics during a glitch and its dependence on the supersolid quality, providing a tool to study glitches from different radial depths of a neutron star. Benchmarking our theory against neutron-star observations, our work will open a new avenue for the quantum simulation of stellar objects from Earth.

Figure 1

Comparison between a neutron star and a dipolar supersolid. (a) Structure of a neutron star, together with the density distributions of neutrons (cyan) and protons (black) near the inner-to-outer crust, for baryonic density $n_b\simeq 5.77\times {10}^{-3}{\mathrm{fm}}^{-3}$ (a₁) and the inner crust-to-core interface, for $n_b\simeq 2.08\times {10}^{-2}{\mathrm{fm}}^{-3}$ (a₂) (adapted with permission from Elsevier from [27]). (b) Illustration of a glitch; see the text. (c),(d) Density distribution of a dipolar quantum gas, with the corresponding density $n$ cut along $y=z=0$ at (c) $a_s=88a_0$ and (d) $a_s=93a_0$, where $a_0$ is the Bohr radius. In both cases, the strength of the superfluid connection is quantified by the density contrast $C=(n_{\max }-n_{\min })/(n_{\max }+n_{\min })$.

Figure 2

Glitches in a dipolar supersolid. (a) Rotating supersolid with $\mathrm{\Omega }=0.41{\omega }_r$ and $a_s=91a_0$. Top: dipolar supersolid showing two isosurfaces at 15% (opaque) and 0.05% (translucent) of the maximum density, and vortex lines in black. Middle: column densities normalized to the peak density. Bottom: phase profile $\arg [\mathrm{\Psi }(x,y,z=0)]$. (b) Rotation frequency in time, with torque $N_{\mathrm{em}}=4.3\times {10}^{-35}\mathrm{kg}{\mathrm{m}}^2/{\mathrm{s}}^2$. Arrows indicate glitch positions. (c) Relative change in $\mathrm{\Omega }$, computed as $\mathrm{\Delta }\mathrm{\Omega }=[\mathrm{\Omega }(t)-{\mathrm{\Omega }}_{\mathrm{lin}}]/{\mathrm{\Omega }}_{\mathrm{lin}}$, where ${\mathrm{\Omega }}_{\mathrm{lin}}$ is the result of a linear fit of the curve in (b). (d) Vortex number. The gray shaded area in (b)–(d) highlights the time window in (e) and (f). (e) Column density saturated to highlight vortex positions and shape, with one vortex escaping (orange circle) and another taking its place (blue circle). (f) Crystal excitations, showing the column density differences between time steps, $n(t)-n(t-\mathrm{\Delta }t)$, with $\mathrm{\Delta }t=2.4\mathrm{ms}$.

Figure 3

Glitches originating from different radial depths. (a) Glitches as a function of the scattering length $a_s$. Note that $a_s=92a_0$ emulates the conditions close to the inner crust-to-core boundary and $a_s=86a_0$ for those in the outer crust. Inset: fraction of nonclassical rotational inertia. (b) Relative change in $\mathrm{\Omega }$, decreasing amplitude with scattering length. Some glitches dispel more than one vortex, increasing the amplitude.