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Magnetic Fields Produced by Phase Transition Bubbles in the Electroweak Phase Transition

Gordon Baym, Dietrich Bödeker, Larry McLerran

TL;DR

The paper investigates seed magnetic field generation during a first-order electroweak phase transition by considering bubble-induced turbulence and currents from dipole charge layers on bubble walls. It argues that turbulence from colliding bubbles can amplify seed fields to near equipartition at the bubble scale, generating substantial magnetic energy. It then shows that rotating dipole layers contribute an additional seed field, but this field is vastly weaker than equipartition, making turbulence the primary amplifier. Finally, it connects small-scale seeds to large-scale fields via a dipole-based statistical model, deriving a correlation function and predicting present-day seed field strengths on diffusion scales and galactic scales, with $B$ of order $10^{-7}$–$10^{-9}$ G on ~10 AU scales and $10^{-17}$–$10^{-20}$ G on galactic scales.

Abstract

The electroweak phase transition, if proceeding through nucleation and growth of bubbles, should generate large scale turbulent flow, which in turn generates magnetic turbulence and hence magnetic fields on the scale of turbulent flow. We discuss the seeding of this turbulent field by the motion of the dipole charge layers in the phase transition bubble walls, and estimate the strength of the produced fields.

Magnetic Fields Produced by Phase Transition Bubbles in the Electroweak Phase Transition

TL;DR

The paper investigates seed magnetic field generation during a first-order electroweak phase transition by considering bubble-induced turbulence and currents from dipole charge layers on bubble walls. It argues that turbulence from colliding bubbles can amplify seed fields to near equipartition at the bubble scale, generating substantial magnetic energy. It then shows that rotating dipole layers contribute an additional seed field, but this field is vastly weaker than equipartition, making turbulence the primary amplifier. Finally, it connects small-scale seeds to large-scale fields via a dipole-based statistical model, deriving a correlation function and predicting present-day seed field strengths on diffusion scales and galactic scales, with of order – G on ~10 AU scales and – G on galactic scales.

Abstract

The electroweak phase transition, if proceeding through nucleation and growth of bubbles, should generate large scale turbulent flow, which in turn generates magnetic turbulence and hence magnetic fields on the scale of turbulent flow. We discuss the seeding of this turbulent field by the motion of the dipole charge layers in the phase transition bubble walls, and estimate the strength of the produced fields.

Paper Structure

This paper contains 4 sections, 30 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Electroweak phase transition bubbles and turbulence
  3. Magnetic field generated by dipole charge layer in the bubble wall
  4. Large scale magnetic fields

Figures (2)

  • Figure 1: Bubble structure in (1+1) dimensions for a first-order electroweak phase transition. The energy density $\epsilon$ and the fluid rapidity $\Theta=\ln[(1+v_{\rm fluid})/(1-v_{\rm fluid})]$ are plotted versus the space-time rapidity $y=\ln[(t+x)/(t-x)]$. (a) Deflagration bubble; $\Theta_{\rm def}$ and $\Theta_{\rm sh }$ denote the rapidities of the deflagration front and the shock front, respectively. (b) Detonation bubble; here $\Theta_{\rm s}$ is the rapidity corresponding to the sound velocity and $\Theta_{\rm det }$ denotes the rapidity of the detonation front.
  • Figure 2: Fluid velocities during the collision of two bubbles. The dashed line represents the shock (detonation) front for a deflagration (detonation) bubble.