[Paper Review] The superfluid two-stream instability and pulsar glitches

Nils Andersson, G. L. Comer+1 more|arXiv (Cornell University)|Nov 7, 2002

Solar and Space Plasma Dynamics2 references3 citations

TL;DR

This paper proposes that the superfluid two-stream instability—driven by relative flow between superfluid neutrons and superconducting protons in neutron stars—could trigger pulsar glitches by destabilizing vortex pinning. Using two-fluid hydrodynamics and dispersion analysis, it shows that entrainment enables the instability to set in at astrophysically plausible flow levels, offering a mechanism for glitch onset in mature neutron stars, particularly in the core where rotational lag builds up.

ABSTRACT

This paper provides the first study of a new dynamical instability in superfluids. This instability is similar to the two-stream instability known to operate in plasmas. It is analogous to the Kelvin-Helmholtz instability, but has the distinguishing feature that the two fluids are interpenetrating. The instability sets in once the relative flow between the two components of the system reaches a critical level. Our analysis is based on the two-fluid equations that have been used to model the dynamics of the outer core of a neutron star, where superfluid neutrons are expected to coexist with superconducting protons and relativistic electrons. These equations are analogous to the standard Landau model for superfluid Helium. We study this instability for two different model problems. First we analyze a local dispersion relation for waves in a system where one fluid is at rest while the other flows at a constant rate. This provides a proof of principle of the existence of the two-stream instability for superfluids. Our second model problem concerns two rotating fluids confined within an infinitesimally thin spherical shell. The aim of this model is to assess whether the two-stream instability may be relevant (perhaps as a trigger mechanism) for pulsar glitches. Our results for this problem show that the entrainment effect could provide a sufficiently strong coupling for the instability to set in at a relative flow small enough to be astrophysically plausible.

Motivation & Objective

• To investigate whether a new two-stream instability—known in plasma physics—can occur in superfluid systems like neutron star interiors.
• To assess whether this instability could serve as a physical trigger for pulsar glitches, which remain poorly understood despite decades of study.
• To analyze the stability of two interpenetrating superfluid components under relative flow, using the two-fluid model relevant to neutron star cores.
• To evaluate whether the entrainment effect in superfluid neutron stars is strong enough to allow the instability to set in at low relative flow speeds, making it astrophysically viable.
• To explore the implications of the instability for glitch recurrence times and its potential operation in slowly rotating or magnetar-like pulsars.

Proposed method

• Formalism based on the two-fluid equations for superfluid neutron stars, modeling superfluid neutrons and a coupled proton-electron fluid as distinct components.
• Derivation of a local dispersion relation for waves in a system with one fluid at rest and the other flowing uniformly, to prove the existence of the two-stream instability.
• Analysis of a second model: two rotating fluids confined in a thin spherical shell, mimicking the outer core of a neutron star.
• Incorporation of entrainment effects via thermodynamic conjugates (chemical potentials and the entrainment function α) in the energy density formulation.
• Use of the Euler-type equations for each fluid, including relative velocity terms and gradient forces, to derive the linear stability conditions.
• Numerical evaluation of the growth rate of unstable modes to determine the critical relative flow threshold for instability onset.

Experimental results

Research questions

• RQ1 Can a two-stream instability analogous to the plasma Farley-Buneman instability occur in superfluid systems such as neutron star cores?
• RQ2 What is the role of entrainment in enabling the two-stream instability to set in at low relative flow speeds in superfluid neutron stars?
• RQ3 Is the instability strong enough to trigger pulsar glitches under realistic astrophysical conditions, particularly in mature neutron stars?
• RQ4 How does the rotational lag between superfluid and normal components affect the onset of the instability and glitch recurrence?
• RQ5 Can the two-stream instability operate in slowly rotating or magnetar-like pulsars, given that glitches are observed in such systems?

Key findings

• The superfluid two-stream instability can exist in neutron star cores, as demonstrated by a local dispersion analysis showing unstable modes when relative flow exceeds a critical threshold.
• The entrainment effect significantly enhances coupling between the superfluid components, allowing the instability to set in at relative flow speeds that are astrophysically plausible.
• In the spherical shell model, the instability grows at a rate consistent with triggering a glitch when the rotational lag reaches a critical value, suggesting a viable physical mechanism for glitch onset.
• The critical relative flow for instability onset is estimated to be on the order of ΔΩ/Ω ≈ 5×10⁻⁴, which corresponds to interglitch timescales consistent with observations of young pulsars.
• The model predicts that glitches can occur in slowly rotating stars as long as the spindown rate is sufficient to build up the required rotational lag, explaining glitches in low-period pulsars and magnetars.
• The results suggest that the two-stream instability may serve as a trigger mechanism for core-originated glitches, particularly in scenarios where crustal vortex unpinning is too weak to explain recurrent glitches.