Small-Scale Dynamo Action in Primordial Halos

TL;DR

This paper uses the Kazantsev theory to analyze magnetic field amplification via the small-scale dynamo during primordial halo collapse, predicting rapid magnetic field growth reaching equipartition on small timescales.

Contribution

It provides a detailed analytical and numerical study of magnetic field amplification in primordial halos, incorporating chemical evolution and turbulence types, to predict magnetic field evolution during first galaxy formation.

Findings

Growth rate scales as Re^(1/2) for incompressible turbulence

Growth rate scales as Re^(1/3) for compressible turbulence

Magnetic fields reach equipartition with kinetic energy quickly during collapse

Abstract

The first galaxies form due to gravitational collapse of primordial halos. During this collapse, weak magnetic seed fields get amplified exponentially by the small-scale dynamo - a process converting kinetic energy from turbulence into magnetic energy. We use the Kazantsev theory, which describes the small-scale dynamo analytically, to study magnetic field amplification for different turbulent velocity correlation functions. For incompressible turbulence (Kolmogorov turbulence), we find that the growth rate is proportional to the square root of the hydrodynamic Reynolds number, Re^(1/2). In the case of highly compressible turbulence (Burgers turbulence) the growth rate increases proportional to Re^(1/3). With a detailed chemical network we are able to follow the chemical evolution and determine the kinetic and magnetic viscosities (due to Ohmic and ambipolar diffusion) during the collapse of the halo. This way, we can calculate the growth rate of the small-scale dynamo quantitatively and predict the evolution of the small-scale magnetic field. As the magnetic energy is transported to larger scales on the local eddy-timescale, we obtain an estimate for the magnetic field on the Jeans scale. Even there, we find that equipartition with the kinetic energy is reached on small timescales. Dynamically relevant field structures can thus be expected already during the formation of the first objects in the Universe.