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  • Letter
  • Open Access

Decay law of magnetic turbulence with helicity balanced by chiral fermions

Axel Brandenburg1,2,3,4, Kohei Kamada5, and Jennifer Schober6

  • 1Nordita, KTH Royal Institute of Technology and Stockholm University, 10691 Stockholm, Sweden
  • 2The Oskar Klein Centre, Department of Astronomy, Stockholm University, AlbaNova, 10691 Stockholm, Sweden
  • 3School of Natural Sciences and Medicine, Ilia State University, 0194 Tbilisi, Georgia
  • 4McWilliams Center for Cosmology and Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
  • 5Research Center for the Early Universe (RESCEU), Graduate School of Science, The University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
  • 6Institute of Physics, Laboratory of Astrophysics, École Polytechnique Fédérale de Lausanne (EPFL), 1290 Sauverny, Switzerland

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Phys. Rev. Research 5, L022028 – Published 11 May, 2023

DOI: https://doi.org/10.1103/PhysRevResearch.5.L022028

Abstract

In plasmas composed of massless electrically charged fermions, chirality can be interchanged with magnetic helicity while preserving the total chirality through the quantum chiral anomaly. The decay of turbulent energy in plasmas such as those in the early Universe and compact stars is usually controlled by certain conservation laws. In the case of zero total chirality, when the magnetic helicity density balances with the appropriately scaled chiral chemical potential to zero, the total chirality no longer determines the decay. We propose that in such a case, an adaptation to the Hosking integral, which is conserved in nonhelical magnetically dominated turbulence, controls the decay in turbulence with helicity balanced by chiral fermions. We show, using a high resolution numerical simulation, that this is indeed the case. The magnetic energy density decays and the correlation length increases with time just like in nonhelical turbulence with vanishing chiral chemical potential. But here, the magnetic helicity density is nearly maximum and shows a scaling with time t proportional to t−2/3. This is unrelated to the t−2/3 decay of magnetic energy in fully helical magnetic turbulence. The modulus of the chiral chemical potential decays in the same fashion. This is much slower than the exponential decay previously expected in theories of asymmetric baryon production from the hypermagnetic helicity decay after axion inflation.

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Phys. Rev. Research 5, L022028– Published 11 May, 2023
  • Received 1 February 2023
  • Accepted 4 April 2023
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