[Paper Review] Dark matter transport properties and rapidly rotating neutron stars

C. J. Horowitz|arXiv (Cornell University)|May 16, 2012

Pulsars and Gravitational Waves Research3 citations

TL;DR

This paper proposes that weakly interacting massive particles (WIMPs) in neutron stars can significantly enhance shear viscosity due to their long mean free paths, potentially stabilizing r-mode oscillations and enabling rapidly rotating neutron stars—such as millisecond pulsars—to spin faster than current models predict. The stabilization requires WIMP-nucleon cross sections near current experimental limits and sufficient WIMP density in the star's core or crust.

ABSTRACT

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.

Motivation & Objective

• To investigate whether WIMPs in neutron stars can significantly alter transport properties like shear viscosity and thermal conductivity.
• To determine if enhanced WIMP-induced shear viscosity could stabilize r-mode oscillations in rapidly rotating neutron stars.
• To assess the required WIMP-nucleon cross sections and densities for observable effects on neutron star dynamics.
• To explore the role of WIMP transport in crust cooling and thermal evolution, especially in magnetized neutron stars.
• To link observable neutron star spin rates to constraints on dark matter properties via indirect astrophysical signatures.

Proposed method

• Modeling WIMP mean free path λW using σWn and nucleon density nn, assuming λW ≈ 10 km for relevant transport effects.
• Using the kinetic theory of transport, deriving WIMP contribution to shear viscosity ηW ∝ λW²nW, with strong enhancement due to long λW.
• Evaluating coherent WIMP-nucleus scattering in the neutron star inner crust using effective cross sections σ₀⟨A⟩, including form factors F(q) and static structure factors SA(q).
• Estimating optical depth τ ≈ Δr σ₀⟨A⟩⟨n⟩⟨A̅⟩ to assess WIMP trapping and scattering probability in the crust.
• Applying the relaxation time approximation to model frequency-dependent viscosity effects in r-mode oscillations.
• Speculating on WIMP contributions to thermal conductivity in the crust, especially in magnetized environments where heat transport is otherwise suppressed.

Experimental results

Research questions

• RQ1 Can WIMPs in neutron stars significantly increase shear viscosity due to their long mean free paths?
• RQ2 Is WIMP-induced shear viscosity sufficient to stabilize r-mode oscillations in rapidly rotating neutron stars?
• RQ3 What WIMP-nucleon cross section is required to achieve observable viscosity enhancement, and is it consistent with current experimental limits?
• RQ4 How do coherent WIMP-nucleus scattering and screening effects in the inner crust influence WIMP transport and trapping?
• RQ5 Can WIMP contributions to thermal conductivity explain rapid crust cooling or affect surface temperature anisotropy in magnetized neutron stars?

Key findings

• A WIMP mean free path of ~10 km requires a WIMP-nucleon cross section of σWn ≈ 3×10⁻⁴⁵ cm², near current experimental limits from CDMS and XENON 100.
• WIMPs can enhance shear viscosity by orders of magnitude due to long mean free paths, potentially stabilizing r-mode oscillations in rapidly rotating neutron stars.
• Coherent WIMP-nucleus scattering in the inner crust can produce effective cross sections σ₀⟨A⟩, with ⟨A⟩ ≈ A/2 if momentum transfer includes q* ≈ 0.3 fm⁻¹.
• The optical depth τ ≈ Δr σ₀⟨A⟩⟨n⟩⟨A̅⟩ suggests WIMPs can be trapped in the inner crust if σ₀⟨A⟩ is sufficiently large and density is ~0.05 fm⁻³.
• WIMP contributions to thermal conductivity may influence crust cooling and reduce surface temperature anisotropy in magnetized neutron stars.
• Observational evidence—such as the 716 Hz pulsar in the galactic center—may support the hypothesis that old or high-dark-matter-density-region neutron stars have stabilized r-modes via WIMP viscosity.