Large scale dynamo action precedes turbulence in shearing box simulations of the magnetorotational instability

We study the dynamo generation (exponential growth) of large scale (planar averaged) fields in unstratified shearing box simulations of the magnetorotational instability (MRI). In contrast to previous studies restricted to horizontal ($x$-$y$) averaging, we demonstrate the presence of large scale fields when either horizontal or vertical ($y$-$z$) averaging is employed. By computing planar averaged fields and power spectra, we find large scale dynamo action in the early MRI growth phase---a previously unidentified feature. Fast growing horizontal low modes and fiducial vertical modes over a narrow range of wave numbers amplify these planar averaged fields in the MRI growth phase, before turbulence sets in. The large scale field growth requires linear fluctuations but not nonlinear turbulence (as defined by mode-mode coupling) and grows as a direct global mode of the MRI. Only by vertical averaging, can it be shown that the growth of horizontal low wavenumber MRI modes directly feed-back to the initial vertical field providing a clue as to why the large scale vertical field sustains against turbulent diffusion in the saturation regime. We compute the terms in the planar averaged mean field equations to identify the individual contributions to large scale field growth for both vertical and horizontal averaging. The large scale fields obtained from such vertical averaging are found to compare well with global cylindrical simulations and quasilinear analytical analysis from a previous study by Ebrahimi \& Blackman. We discuss the potential implications of these new results for understanding large scale MRI dynamo saturation and turbulence.