The formation and evolution of a wide class of astrophysical objects are governed by turbulent, magnetized accretion disks. Understanding their secular dynamics is of primary importance. Apart from enabling mass accretion via the transport of angular momentum, the turbulence affects the long-term evolution of the embedded magnetic flux, which in turn regulates the efficiency of the transport. In this paper, we take a comprehensive next step toward?an effective mean-field model for turbulent astrophysical disks by systematically studying the key properties of magnetorotational turbulence in vertically stratified, isothermal shearing boxes. This allows us to infer emergent properties of the ensuing chaotic flow as a function of the shear parameter, as well as the amount of net?vertical flux. Using the test-field method, we furthermore characterize the mean-field dynamo coefficients that describe the long-term evolution of large-scale fields. We simultaneously infer the vertical shape and the spectral scale dependence of these closure coefficients, with the latter describing nonlocal contributions to the turbulent electromotive force. Based on this, we infer a scale-separation ratio of about 10 for the large-scale dynamo. We finally determine scaling properties of the mean-field dynamo coefficients. The relevant component of the dynamo α effect is found to scale linearly with the shear rate, as does the corresponding turbulent diffusion, η. Together, these scalings allow us to predict, in a quantitative manner, the cycle period of the well-known butterfly diagram. This lends new support to the importance of the mechanism in determining the evolution of large-scale magnetic fields in turbulent accretion disks.
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