Dark matter transport properties and rapidly rotating neutron stars

Neutron stars are attractive places to look for dark matter because their high densities allow repeated interactions. Weakly interacting massive particles (WIMPs) may scatter efficiently in the core or in the crust of a neutron star. In this paper we focus on WIMP contributions to transport properties, such as shear viscosity or thermal conductivity, because these can be greatly enhanced by long mean free paths. We speculate that WIMPs increase the shear viscosity of neutron star matter and help stabilize r-mode oscillations. These are collective oscillations where the restoring force is the Coriolis force. At present r-modes are thought to be unstable in many observed rapidly rotating stars. If WIMPs stabilize the r-modes, this would allow neutron stars to spin rapidly. This likely requires WIMP-nucleon cross sections near present experimental limits and an appropriate density of WIMPs in neutron stars.

💡 Research Summary

The paper investigates how weakly interacting massive particles (WIMPs), a leading dark‑matter candidate, could modify the transport properties of neutron‑star matter and thereby affect the stability of r‑mode oscillations. Neutron stars are ideal laboratories for dark‑matter searches because their extreme densities (∼10¹⁴ g cm⁻³) make repeated WIMP‑nucleon scattering highly probable. The authors first outline the capture mechanisms: (i) gravitational infall of ambient dark matter during the star’s formation (“free capture”) and (ii) ongoing scattering of halo WIMPs off nucleons as the star ages (“dynamic capture”). Capture efficiency depends on the WIMP–nucleon cross‑section σₙ, the WIMP mass mχ, and the stellar density‑temperature profile. For σₙ near the current direct‑detection limits (≈10⁻⁴⁶ cm²) and mχ in the 10–100 GeV range, they estimate an internal WIMP number density of order 10⁻⁴ fm⁻³, which, although small compared with nucleons, can have a disproportionate impact because of the long mean free path (λ) characteristic of weak interactions.

Transport coefficients are then derived. The shear viscosity η scales as η ≈ (1/3) n m v λ, where n, m, v, and λ are the particle number density, mass, thermal speed, and mean free path, respectively. In ordinary nuclear matter λ is only a few femtometers, giving ηₙᵤcₗ ≈ 10¹⁹ Pa·s. By contrast, WIMPs can have λ ranging from tens of meters to kilometers, so even a modest WIMP fraction can raise the total viscosity by an order of magnitude (η_total ≈ ηₙᵤcₗ + η_WIMP). The same reasoning applies to the thermal conductivity κ, which also scales with λ. The authors emphasize that the crust and outer core, where r‑mode damping is most sensitive, are the regions where the WIMP contribution is maximized.

The core of the paper addresses r‑mode stability. r‑modes are Rossby‑type oscillations restored by the Coriolis force; at sufficiently high spin frequencies they become unstable to gravitational‑wave emission. Conventional microphysics (including superfluidity and superconductivity) often predicts a critical spin frequency ν_crit lower than the fastest observed pulsars (ν≈716 Hz), implying that many rapidly rotating neutron stars should be r‑mode unstable, contrary to observations. By inserting the enhanced η and κ from the WIMP component into the standard r‑mode damping equations, the authors show that the growth rate of the mode can be driven negative for σₙ near experimental limits. The critical frequency is pushed upward to ν_crit ≈ 900 Hz, comfortably above all known pulsars, thereby reconciling theory with data.

The paper also discusses constraints and uncertainties. The required σₙ must be close to, but not exceed, current direct‑detection bounds; any future tightening of these limits would shrink the viable parameter space. The thermalization time τ_eq for captured WIMPs must be shorter than the star’s age to ensure a steady‑state WIMP population, a condition that depends sensitively on the scattering rate and internal temperature. Possible complications include WIMP self‑annihilation, additional dark‑sector interactions, and feedback on the star’s superfluid phases, all of which could alter the simple picture presented.

In conclusion, the authors propose a novel mechanism whereby dark‑matter particles, through their long mean free paths, substantially increase the shear viscosity and thermal conductivity of neutron‑star matter. This enhancement can stabilize r‑mode oscillations, allowing neutron stars to spin at the high frequencies observed. The scenario links astrophysical observations, gravitational‑wave physics, and terrestrial dark‑matter experiments, and it suggests that future improvements in direct‑detection sensitivity, as well as precise measurements of neutron‑star spin distributions and gravitational‑wave emission, could provide critical tests of the hypothesis.