Resistively controlled primordial magnetic turbulence decay

¹ Nordita, KTH Royal Institute of Technology and Stockholm University, Hannes Alfvéns väg 12, 10691 Stockholm, Sweden
e-mail: brandenb@nordita.org
² The Oskar Klein Centre, Department of Astronomy, Stockholm University, AlbaNova, 10691 Stockholm, Sweden
³ McWilliams Center for Cosmology & Department of Physics, Carnegie Mellon University, 5000 Forbes Ave, Pittsburgh, PA 15213, USA
⁴ School of Natural Sciences and Medicine, Ilia State University, 3-5 Cholokashvili Avenue, 0194 Tbilisi, Georgia
⁵ Department of Astrophysics, American Museum of Natural History, 200 Central Park West, New York, NY 10024, USA
⁶ Astroparticules et Cosmologie, Université Paris Cité, CNRS, Astroparticule et Cosmologie, 75006 Paris, France
⁷ Laboratory of Astrophysics, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
⁸ Dipartimento di Fisica e Astronomia, Università di Bologna, Via Gobetti 93/2, 40129 Bologna, Italy
⁹ INAF Istituto di Radioastronomia, Via P. Gobetti 101, 40129 Bologna, Italy
¹⁰ Hamburger Sternwarte, Universität Hamburg, Gojenbergsweg 112, 41029 Hamburg, Germany

Received: 18 January 2024
Accepted: 17 March 2024

Abstract

Context. Magnetic fields generated in the early Universe undergo turbulent decay during the radiation-dominated era. The decay is governed by a decay exponent and a decay time. It has been argued that the latter is prolonged by magnetic reconnection, which depends on the microphysical resistivity and viscosity. Turbulence, on the other hand, is not usually expected to be sensitive to microphysical dissipation, which affects only very small scales.

Aims. We want to test and quantify the reconnection hypothesis in decaying hydromagnetic turbulence.

Methods. We performed high-resolution numerical simulations with zero net magnetic helicity using the PENCIL CODE with up to 2048³ mesh points and relate the decay time to the Alfvén time for different resistivities and viscosities.

Results. The decay time is found to be longer than the Alfvén time by a factor that increases with increasing Lundquist number to the 1/4 power. The decay exponent is as expected from the conservation of the Hosking integral, but a timescale dependence on resistivity is unusual for developed turbulence and not found for hydrodynamic turbulence. In two dimensions, the Lundquist number dependence is shown to be leveling off above values of ≈25 000, independently of the value of the viscosity.

Conclusions. Our numerical results suggest that resistivity effects have been overestimated in earlier work. Instead of reconnection, it may be the magnetic helicity density in smaller patches that is responsible for the resistively slow decay. The leveling off at large Lundquist number cannot currently be confirmed in three dimensions.