Angular Momentum Transfer in Vela-like Pulsar Glitches

The angular momentum transfer associated to Vela-like glitches has never been calculated {\em directly} within a realistic scenario for the storage and release of superfluid vorticity; therefore, the explanation of giant glitches in terms of vortices has not yet been tested against observations. We present the first physically reasonable model, both at the microscopic and macroscopic level (spherical geometry, n=1 polytropic density profile, density-dependent pinning forces compatible with vortex rigidity), to determine where in the star the vorticity is pinned, how much of it, and for how long. For standard neutron star parameters ($M=1.4 M_{\odot}, R_s=10$ km, $\dot{\Omega}=\dot{\Omega}{\rm Vela}=-10^{-10}$ Hz s$^{-1}$), we find that maximum pinning forces of order $f_m\approx10^{15}$ dyn cm$^{-1}$ can accumulate $\Delta L{\rm gl}\approx10^{40}$ erg s of superfluid angular momentum, and release it to the crust at intervals $\Delta t_{\rm gl}\approx3$ years. This estimate of $\Delta L_{\rm gl}$ is one order of magnitude smaller than what implied indirectly by current models for post-glitch recovery, where the core and inner-crust vortices are taken as physically disconnected; yet, it successfully yields the magnitudes observed in recent Vela glitches for {\em both} jump parameters, $\Delta\Omega_{\rm gl}$ and $\Delta\dot{\Omega}_{\rm gl}$, provided one assumes that only a small fraction ($<10%$) of the total star vorticity is coupled to the crust on the short timescale of a glitch. This is reasonable in our approach, where no layer of normal matter exists between the core and the inner-crust, as indicated by existing microscopic calculation. The new scenario presented here is nonetheless compatible with current post-glitch models.

💡 Research Summary

The paper presents the first physically realistic calculation of the angular‑momentum transfer associated with Vela‑like pulsar glitches, directly linking the storage and release of superfluid vorticity to observable glitch parameters. The authors abandon the traditional cylindrical, uniform‑density approximations and adopt a spherical neutron‑star model with an n = 1 polytropic equation of state (P ∝ ρ²). The stellar density profile is given by ρ(r) = λ sin(π r/Rₛ)/(π r/Rₛ), where λ = π M/(4 Rₛ³) and Rₛ ≈ 10 km for a 1.4 M⊙ star. The core–crust boundary is set at a density ρ_c = 0.6 ρ₀ (ρ₀ = 2.8 × 10¹⁴ g cm⁻³), and the inner crust occupies the outer region (ξ > x_c).

A key ingredient is the density‑dependent pinning force per unit length, f_pin(ρ), which the authors model on the basis of microscopic calculations (Donati & Pizzochero 2003‑2006). The force peaks at f_m ≈ 10¹⁵ dyn cm⁻¹ around ρ ≈ 0.2 ρ₀, vanishes at the core–crust transition (ρ_c) and at neutron drip (ρ_d ≈ 0.0015 ρ₀). Integrating the Magnus force and the pinning force along a vortex line yields a critical lag ω_cr(x) that depends only on the cylindrical radius x = R/Rₛ. In the inner‑crust region ω_cr(x) shows a sharp maximum ω_max near x_m ≈ 0.8 (the location of the pinning peak), while in the core ω_cr is roughly constant at a much lower value ω_min ≈ 10⁻² ω_max.

The model distinguishes two dynamical regimes. In the crust, pinning is continuous; as the star spins down, the lag ω grows until it reaches ω_max, at which point a large number of vortices simultaneously unpin, transferring a superfluid angular momentum ΔL_gl ≈ 10⁴⁰ erg s to the normal component. In the core, vortices are only pinned at their ends (the weak‑drag limit) and therefore experience rapid depinning/re‑pinning cycles on a timescale τ_c ≈ 10⁰–10¹ s, effectively keeping the average lag at |Ω̇| τ_c. This “creep” ensures that, on long timescales, the core and crust are effectively coupled, reproducing the corotation picture used in earlier phenomenological models.

A thin vortex sheet accumulates excess vorticity at a radius x(t) that moves outward as the lag increases (ω = |Ω̇_∞| t). When the sheet reaches the pinning peak (x = x_m) the stored vorticity is released in a single avalanche, producing a glitch. The calculated angular‑momentum budget ΔL_gl ≈ 10⁴⁰ erg s corresponds to a change in angular velocity ΔΩ_gl ≈ 10⁻⁶ Ω and a change in spin‑down rate ΔΩ̇_gl ≈ 10⁻² Ω̇, matching the observed Vela glitches, provided that only a small fraction (<10 %) of the total stellar vorticity participates in the short‑timescale transfer. This fraction is justified because the model assumes no normal‑matter layer separating core and inner‑crust superfluids, consistent with recent microscopic studies that predict continuous vortex lines throughout the star.

The authors also discuss the implications for post‑glitch recovery. Traditional two‑component models treat the core and crust superfluids as disconnected, leading to an angular‑momentum transfer of order 10⁴¹ erg s—an order of magnitude larger than the energy budget inferred from observations of the Vela wind nebula (≈10⁴² erg). By limiting the coupled vorticity to <10 % and using realistic pinning forces, the present model yields a transfer compatible with both the glitch magnitude and the observed energy constraints. Moreover, the model remains compatible with both weak‑drag (type‑I) and strong‑drag (type‑II) superconductivity scenarios for protons in the core, as the core contribution to the glitch is modest.

In summary, the paper delivers a self‑consistent, analytically tractable framework that links microscopic vortex‑pinning physics to macroscopic glitch observables. It reproduces the ∼3‑year recurrence time, the size of the angular‑velocity jumps, and the characteristic changes in spin‑down rate, while respecting energetic limits. By incorporating spherical geometry, realistic density profiles, and density‑dependent pinning forces, it resolves longstanding discrepancies in earlier simplified models and provides a solid foundation for future numerical simulations and observational tests of neutron‑star interior physics.