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 ∝ (nL − nR). 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 BrmsξM, where ξM 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 vλ = μ50/λ1/2 and vμ = μ50η, where λ characterises the depletion of μ5 and η is the magnetic diffusivity. So vλ characterises the depletion of chiral asymmetry and vμ characterises the generation of magnetic field. We therefore say that η k1 < vμ < vλ is in regime I, and η k1 < vλ < vμ 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 λ1/2 by about 2 orders of magnitude each. We have found that the GW energy goes as ΩGWsat ∝ vλ5 vμ. 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.