Resistive Magnetic Field Generation at Cosmic Dawn

Relativistic charged particles (CR for cosmic-rays) produced by Supernova explosion of the first generation of massive stars that are responsible for the re-ionization of the universe escape into the intergalactic medium, carrying an electric current. Charge imbalance and induction give rise to a return current, $\vec j_t$, carried by the cold thermal plasma which tends to cancel the CR current. The electric field, $\vec E=\eta \vec j_t$, required to draw the collisional return current opposes the outflow of low energy cosmic rays and ohmically heats the cold plasma. Owing to inhomogeneities in the resistivity, $\eta(T)$, caused by structure in the temperature, $T$, of the intergalactic plasma, the electric field possesses a rotational component which sustains Faraday’s induction. It is found that magnetic field is robustly generated throughout intergalactic space at rate of 10$^{-17}-10^{-16}$ Gauss/Gyr, until the temperature of the intergalactic medium is raised by cosmic reionization. The magnetic field may seed the subsequent growth of magnetic fields in the intergalactic environment.

💡 Research Summary

The paper proposes a novel mechanism for the generation of magnetic fields during the cosmic dawn, i.e., the epoch when the first generation of massive stars explode as supernovae and begin to re‑ionize the universe. Relativistic charged particles – cosmic rays (CR) – produced in these explosions escape into the intergalactic medium (IGM) and carry an electric current, ( \mathbf{j}_{\rm CR} ). Because the IGM is initially a cold, weakly ionized plasma, a return current ( \mathbf{j}_t ) is induced in the thermal electrons to maintain charge neutrality. The return current is collisional; it requires an electric field ( \mathbf{E} = \eta(T),\mathbf{j}_t ), where ( \eta ) is the Spitzer‑type resistivity that scales as ( \eta \propto T^{-3/2} ).

In the pre‑reionization IGM the temperature is only a few kelvin, but density fluctuations from early structure formation produce spatial variations in temperature, and therefore in resistivity. The gradient of resistivity, ( \nabla\eta ), combined with the return current yields a rotational component of the electric field:

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