Relic Gravitational Waves From The Chiral Magnetic Effect

A system of fermions can exhibit chiral asymmetry, which can be quantified by the chiral chemical potential μ₅, proportional to the number density difference between left- and right-handed fermions, i.e. μ₅ ∝ (n_L − n_R). If μ₅ is large enough, it can work as a dynamo effect and exponentially increase a seed magnetic field. This is known as the chiral magnetic effect (CME). While active, the CME converts the initial chiral asymmetry μ₅₀ into magnetic helicity on the order of B_rmsξ_M, where ξ_M is the magnetic correlation length. Although magnetic helicity generated by CME alone is too small compared to the constraint inferred from the non-observations of GeV-energy halos around TeV blazars, and the frequency of CME-induced gravitational waves (GWs) is too high compared to current and future detectors' sensitivity, we could still treat the CME as a proxy of other sourcing mechanisms for primordial GWs. In terms of GW production, we identify two regimes of interest, distinguished by the relative magnitude of two characteristic velocities v_λ = μ₅₀/λ^1/2 and v_μ = μ₅₀η, where λ characterises the depletion of μ₅ and η is the magnetic diffusivity. So v_λ characterises the depletion of chiral asymmetry and v_μ characterises the generation of magnetic field. We therefore say that η k₁ < v_μ < v_λ is in regime I, and η k₁ < v_λ < v_μ is in regime II, where k₁ is the smallest wavenumber in the domain and μ₅₀ > k₁ is excitation threshold for CME. In both regimes, we note that there are two evolutionary phases, where in phase 1) the magnetic field is CME-driven and reaches maximum, which determines the GW energy, and in phase 2) the magnetic length scales increase as its energy decreases, which is probably irrelevant to GW production. In this study, we performed a series of numerical simulations, where η was varied by more than 4 orders of magnitude, μ₅₀ and λ^1/2 by about 2 orders of magnitude each. We have found that the GW energy goes as Ω_GW^sat ∝ v_λ⁵ v_μ. Perhaps a counterintuitive finding is that in regime II, large GW energies can be generated. However, we note that, in general, the overall conversion from CME-induced magnetic to GW energy is less efficient than for forced and decaying turbulence due to the small length scales associated with the CME.

References: Brandenburg, A., He, Y., Kahniashvili, T., Rheinhardt, M. & Schober, J. Relic gravitational waves from the chiral magnetic effect. ApJ, in press (2021). 2101.08178.