Primordial Magnetic Fields from Cosmological First Order Phase Transitions

TL;DR

The paper addresses the origin of cosmological magnetic fields by examining primordial seed-field generation during first-order phase transitions, focusing on bubble-wall charge separation, hydrodynamic instabilities, and viscous damping. It develops a two-stage mechanism: first, instability-driven currents at phase boundaries create seed fields with a finite wavelength range; second, MHD turbulence amplifies these seeds toward equipartition with the fluid, concentrating energy at large scales. Applying the framework to the electroweak and QCD transitions, it yields present-day large-scale field estimates of order $B \sim 10^{-29}$ G for the EW case and $B \sim 10^{-20}$ G for the QCD case on 10 Mpc scales, with spectra shaped by the turbulent cascade. The results suggest that early-universe turbulence could plausibly seed and grow magnetic fields that contribute to galactic and extragalactic magnetism, potentially enhanced by later hydromagnetic processes.

Abstract

We give an improved estimate of primordial magnetic fields generated during cosmological first order phase transitions. We examine the charge distribution at the nucleated bubble wall and its dynamics. We consider instabilities on the bubble walls developing during the phase transition. It is found that damping of these instabilities due to viscosity and heat conductivity caused by particle diffusion can be important in the QCD phase transition, but is probably negligible in the electroweak transition. We show how such instabilities together with the surface charge densities on bubble walls excite magnetic fields within a certain range of wavelengths. We discuss how these magnetic seed fields may be amplified by MHD effects in the turbulent fluid. The strength and spectrum of the primordial magnetic field at the present time for the cases where this mechanism was operative during the electroweak or the QCD phase transition are estimated. On a 10 Mpc comoving scale, field strengths of the order 10**(-29) G for electroweak and 10**(-20) G for QCD, could be attained for reasonable phase transition parameters.