Inefficiency of chiral dynamos in protoneutron stars and the early universe

Abstract

The chiral plasma instability (CPI) has been invoked as a possible mechanism for generating primordial magnetic fields in the universe and ultrastrong fields in neutron stars. We investigate chiral dynamos where the chirality imbalance is pumped by a source on a timescale $t_0$ and show that the CPI rate $γ$ is limited to $γ_0/(1+{\cal Q}^2)$, where ${\cal Q}= (γ_0 t_0)^{1/3}$ and $γ_0$ corresponds to models with instantaneously created chirality imbalance $(t_0=0)$. We then find that chiral flipping with rate $Γ_{\mathrm f}$ hinders the chiral dynamo if $Γ_{\mathrm f} >γ_0/(1+{\cal Q}^2)$ and completely suppresses it if $Γ_{\mathrm f} >γ_0/(1+{\cal Q}^{3/2})$. Realistic $t_0$ typically give ${\cal Q}\gg 1$, which makes the dynamo greatly vulnerable to the suppression by chiral flipping. The suppression is strong in protoneutron stars and may be (barely) avoided near the electroweak transition in the early universe.

Figures (9)

• Figure 1: Chirality/helicity flow in a system where a source $S$ pumps the chirality imbalance $\mu$ by an amount $\mu_0$ over a timescale $t_0$. The accumulated $\mu$ has two sinks: conversion into magnetic helicity by the CPI at rate $\lambda \dot H$ and destruction by chiral flipping at rate $\Gamma_{\mathrm{f}}\mu$. The amount of generated magnetic helicity $H$ is determined by the competition between the CPI and chiral flipping.
• Figure 2: Results from a fiducial simulation with $\mathcal{Q}=15$ and $\Gamma=0$. Top: evolution of the volume-averaged chirality imbalance $\langle\mu\rangle$, magnetic helicity $H$, and total helicity $\cal H$. The source builds up $\langle\mu\rangle\propto t$ until $t\approx 4t_{\mathcal{Q}}$ when its linear growth is quenched by the saturation of the CPI. Afterwards, $\langle\mu\rangle$ relaxes to $\sim\mu_{\mathcal{Q}}$ and the CPI generates $\lambda H$ from $\langle\mu\rangle$ with constant rate $\lambda\dot H\approx S$ while the source $S$ sustains $\langle\mu\rangle\approx0.3\mu_{\mathcal{Q}}=const$ (until it shuts off at $t=15t_{\mathcal{Q}}$). Bottom: evolution of the root-mean-square magnetic field $B_{\mathrm{rms}}$ and velocity field $u_{\mathrm{rms}}$. The horizontal dashed line indicates $B_{\mathrm{rms}}/B_{\mathcal{Q}}=u_{\mathrm{rms}}/u_{\mathcal{Q}}=1$, where $u_{\cal Q}=B_{\mathcal{Q}}/\sqrt{4\pi\rho}$.
• Figure 3: The magnetic and kinetic energy spectra, $E_{\tilde{B}}(k)$ (solid lines) and $E_{\tilde{u}}(k)$ (dashed lines), at different times (color-coded) from the simulation shown in Figure \ref{['fig:SingleRun_Q20']}.
• Figure 4: Visualization of the chirality imbalance $\mu$ (top row) and vertical component of the magnetic field $B_z$ (bottom row) for the fiducial simulation with $\mathcal{Q}=15$ analyzed in Figure \ref{['fig:SingleRun_Q20']}. The fields are shown right before CPI saturation (left column), right after the saturation (middle column), and at the end of the driving phase (right column).
• Figure 5: A set of simulations varying the chiral flipping parameter $\Gamma$ (color-coded) with fixed $\mathcal{Q}=15$. The $\Gamma=0$ case is the same simulation as analyzed in Figures \ref{['fig:SingleRun_Q20']} and \ref{['fig:EnergySpectrum']}. Top: evolution of the volume-averaged chirality imbalance $\langle\mu\rangle$ (solid lines) and the magnetic helicity $H$ (dashed lines). Magnetic helicity generation by the CPI is suppressed by flipping once $\Gamma$ becomes larger than ${\cal O}(1)$. Bottom: same quantities as in Figure \ref{['fig:SingleRun_Q20']}.