Weibel Instability-Driven Seed Magnetic Fields during Reionization

Abstract

Cosmological reionization was a highly out-of-equilibrium event that affected every parcel of the intergalactic medium, making it a candidate for astrophysical generation of intergalactic magnetic fields. During reionization, the first stars and galaxies ionized the surrounding, largely neutral, medium in ever-expanding envelopes. Photoionization from sources on one side of the front, combined with the quadrupolar angular dependence of the photoionization cross section, leads to an anisotropic electron velocity distribution. We investigate instabilities in these reionization fronts as a mechanism to generate seed magnetic fields. The Weibel instability has the potential to create a magnetic field from these anisotropies. We calculate the magnitude of the isotropic and anisotropic distribution within a simulated reionization front. We find that the fractional anisotropy can grow to $6\times 10^{-3}$ toward the middle of the ionization front. We show that the linear growth timescale of the Weibel instability is fast compared to the crossing time of the ionization front ($\sim 2\times 10^5$ seconds). We briefly speculate on the possible non-linear evolution of the instability and the implications for cosmological magnetogenesis.

Figures (9)

• Figure 1: The evolution of the neutral fraction of H and He in the reionization front model. The neutral fraction is plotted on a logit scale on the vertical axis. The horizontal axis is the distance from the ionizing source. As illustrated by the banner, the left side is closest to the ionizing source. Moving right along the horizontal axis is further into the neutral region of the ionization front.
• Figure 2: The flowchart for the calculation of $G^{\rm iso}$ and $G^{\rm ani}$. It illustrates the development of both $G^{\rm iso}$ and $G^{\rm ani}$ in terms of the relevant forces and laws, including both positive feedback ("$+$" loop: current perturbations create a magnetic field that deflects particles to add to the perturbation) and negative feedback ("$-$" loop: growing currents create a growing magnetic field, which induces an electric field that opposes the current perturbation). The table below the flowchart lists the equations of $G^{\rm ani}$ and $G^{\rm iso}$ in both the free streaming and collisional limits. See Appendix \ref{['sec:calc_sigma']} for derivations.
• Figure 3: The change in the imaginary $G^{\rm iso}/u$ term across wave number (k) slabs (Eq. \ref{['eq:Giso-sol']}). The vertical axis is the isotropic distribution value and the horizontal axis is the distance through the reionization front. The increasing k slabs are inversely proportional to different length scales at which we can examine the perturbation. We calculated the sum of $G^{\rm iso}/u$ over 142 velocity bins for this simulation. At the largest distances from the source, the isotropic part of the distribution reaches a maximum for all scales. However, close to the source only small scales (large $k$) are largely isotropic which indicates that the large scales have a significant anisotropic component.
• Figure 4: The change in the source term across 142 velocity slabs for the last wavenumber ($k = 10^{-6} ~ \rm{m}^{-1}$) slab (Eq. \ref{['eq:S_2,0']}). The vertical axis is the value of the source term. The horizontal axis is the velocity of electrons at which we are calculating the source term. Specific reionization front slabs chosen in Figure \ref{['fig:im_w_2d']} are used to illustrate the change in $S_{2,0}$ through the reionization front. Vertical lines mark the electron velocity at 11.0 eV (the maximum photoelectron velocity from a photon that can ionize H but not He i) and at 29.8 eV (the maximum photoelectron velocity from a photon that can ionize He i but not He ii).
• Figure 5: The change in the magnitude of the multipole moment across 142 velocity slabs for the last wavenumber, $k = 10^{-6}\,{\rm m}^{-1}$ (Eq. \ref{['eq: partial_a_lm']}). The vertical axis is the value of the multipole moment. The horizontal axis is the velocity of electrons at which we are calculating the source term. The change in $a_{2,0}$ is illustrated at the specific reionization front slabs chosen in Figure \ref{['fig:im_w_2d']}. Vertical lines mark the electron velocity at 11.0 eV (the maximum photoelectron velocity from a photon that can ionize H but not He i) and at 29.8 eV (the maximum photoelectron velocity from a photon that can ionize He i but not He ii).