Large Scale Dynamo in a Primordial Accretion Flow -- An Interpretation
  from Hydrodynamic Simulation
  Without an existing large scale coherent magnetic field in the early
Universe, Population III (PopIII) stars would likely rotate at or near break-up
speed. In this work, focusing on the accretion phase of PopIII stars, we
investigate the possibility of generating a coherent magnetic field through
large scale dynamo processes, as well as the corresponding field saturation
level. Using results from hydrodynamic simulations, we demonstrate that
primordial accretion disks are turbulent with a Shakura-Sunyaev disk parameter
$\alpha_{ss} \gtrsim 10^{-3}$, and evidence helical turbulence with a dynamo
number $\vert D_{\alpha \Omega} \vert \gg 10$. The presence of helical
turbulence at these levels allows large scale dynamo modes to grow, and the
saturation level is determined by the amount of net helicity remaining in the
dynamo-active regions (a.k.a. the quenching problem). %We demonstrate that the
magnetic field can reach approximate equipartition, with $B/B_{\rm eq} \sim 3$,
indicating that the dynamo quenching problem could be alleviated through an
accretion flow. We demonstrate that, if the accretion could successfully
alleviate the quenching problem, the magnetic field can reach approximate
equipartition with $B/B_{\rm eq} \sim 3$.
