Primordial magnetic field from chiral plasma instability with sourcing

TL;DR

This paper shows that a chirality source can enable the chiral plasma instability (CPI) to generate a primordial helical magnetic field even when chirality-erasing processes would, in standard scenarios, suppress CPI below $80\,\mathrm{TeV}$. By formulating chiMHD with a time-dependent chirality source and washout, the authors derive analytic evolution for the chiral chemical potential and magnetic helicity, and validate these results with high-resolution numerical simulations using the Pencil Code. They predict the resulting magnetic helicity $h_M$ and the characteristic CPI scales in the presence of sourcing, finding good agreement between the analytic estimate $h_M \approx \frac{\sqrt{e}\tilde{\bar{S}}_5}{\lambda t_\phi \Gamma_5^2}$ and the simulated value. The findings suggest that chirality sourcing during baryogenesis or related out-of-equilibrium processes could seed cosmological magnetic fields during the electroweak or QCD epochs, potentially impacting galactic dynamos and cosmological observables.

Abstract

In an electron-positron plasma, an imbalance in the number of right- and left-chiral particles can lead to the growth of a helical magnetic field through a phenomenon called the chiral plasma instability (CPI). In the early universe, scattering reactions that violate chirality come into thermal equilibrium when the plasma cools below a temperature of approximately $80 \, \mathrm{TeV}$. Since these reactions tend to relax any pre-existing chiral asymmetry to zero as the system approaches equilibrium, the standard lore is that primordial magnetogenesis via the CPI is not viable below $80 \, \mathrm{TeV}$. In this work, we propose that the presence of a source for chirality can allow the CPI to operate even below $80 \, \mathrm{TeV}$, we explore the implications of this scenario, and we derive predictions for the resultant magnetic field helicity using a combination of analytical methods and direct numerical simulation.

Figures (7)

• Figure 1: Evolution of the chiral source $S_5(t)$ with conformal time $t$. The maximum occurs at $t = t_\phi$ where $S_5(t_\phi) = \bar{S}_5$.
• Figure 2: Evolution of the volume averaged chiral asymmetry. We plot the comoving scaled volume averaged chiral chemical potential $\langle \tilde{\mu}_5(\hbox{\boldmath $x$}{},t) \rangle$ in units of $l_\ast^{-1}$ as a function of conformal time $t$ in units of $t_\ast$. The chemical potential is calculated numerically by solving the equations of chiMHD for the run $\textbf{A}^\ast$ (see Table \ref{['tab:runs']}). For comparison, we also plot the comoving chiral source $\tilde{S}_5(t) / \Gamma_5$, and the Chern-Simons terms $\eta \langle \tilde{\mu}_5 \rangle \langle \mathbf{B}^2 \rangle / \Gamma_5$ and $\eta \lambda \langle \hbox{\boldmath $J$} {} \cdot \hbox{\boldmath $B$} {} \rangle / \Gamma_5$, in units of $l_\ast^{-1}$. Vertical dotted lines indicate the time scales in Eq. (\ref{['eq:time_scales']}).
• Figure 3: Evolution of the root mean squared (rms) magnetic and velocity fields. We plot the comoving rms field strength $B_\mathrm{rms}(t)$ in units of $E_\ast^{1/2} l_\ast^{-3/2}$ and $u_{\mathrm{rms}}(t)$ in units of $l_{\ast} t_{\ast}^{-1}$ as functions of conformal time $t$ in units of $t_\ast$. Vertical dotted lines represent the time scales in Eq. (\ref{['eq:time_scales']}).
• Figure 4: Evolution of the magnetic helicity. We show the magnetic helicity $h_M$, the chiral chemical potential expressed in units of helicity, and the integral leading to a change in the total net helicity, $\Delta h_{\rm tot}$, where $h_{\rm tot} = h_M + \tfrac{2}{\lambda} \langle \tilde{\mu}_5 \rangle$. The horizontal dotted line corresponds to the estimate of the magnetic helicity produced by the CPI with a source given in Eq. (\ref{['eq:hel_prod_source']}). The numerical relative error $|h_{\rm tot} - \Delta h_{\rm tot}|/|h_{\rm tot}| < 10 \%$ at all times in the simulation, where $\Delta h_{\rm tot}$ corresponds to the integral over conformal time given in Eq. (\ref{['eq:hel_prod']}). Vertical dotted lines represent the time scales in Eq. (\ref{['eq:time_scales']}).
• Figure 5: Evolution of the magnetic spectra. We plot the comoving magnetic energy density ${\rm d} {} \rho_B / {\rm d} {} \ln k$ in units of $E_\ast l_\ast^{-3}$ as a function of the comoving wavenumber $k$ in units of $l_\ast^{-1}$ for several values of the conformal time $t$. Vertical dotted lines represent the inverse length scales in Eq. (\ref{['eq:wavenumbers']}).