Cosmic Magnetization: From Spontaneously Emitted Aperiodic Turbulent to Ordered Equipartition Fields

It is shown that an unmagnetized nonrelativistic thermal electron-proton plasma spontaneously emits aperiodic turbulent magnetic field fluctuations of strength $|\delta B|=3.5{\beta }_e{g}^{1/3}{W}_e^{1/2}\mathrm{G}$, where ${\beta }_e$ is the normalized thermal electron temperature, $W_e$ the thermal plasma energy density, and $g$ the plasma parameter. For the unmagnetized intergalactic medium, immediately after the reionization onset, the field strengths from this mechanism are about $2\times {10}^{-16}\mathrm{G}$ in cosmic voids and $2\times {10}^{-10}\mathrm{G}$ in protogalaxies, both too weak to affect the dynamics of the plasma. Accounting for simultaneous viscous damping reduces these estimates to $2\times {10}^{-21}\mathrm{G}$ in cosmic voids and $2\times {10}^{-12}\mathrm{G}$ in protogalaxies. The shear and/or compression of the intergalactic and protogalactic medium exerted by the first supernova explosions locally amplify these seed fields and make them anisotropic, until the magnetic restoring forces affect the gas dynamics at ordered plasma betas near unity.