The existence of large-scale dynamos in rigidly rotating turbulent convection without shear is studied using three-dimensional numerical simulations of penetrative rotating compressible convection. We demonstrate that rotating convection in a Cartesian domain can drive a large-scale dynamo even in the absence of shear. The large-scale field contains a significant fraction of the total field in the saturated state. The simulation results are compared with one-dimensional mean-field dynamo models where turbulent transport coefficients, as determined using the test field method, are used. The reason for the absence of large-scale dynamo action in earlier studies is shown to be due to the rotation being too slow: whereas the alpha-effect can change sign, its magnitude stays approximately constant as a function of rotation, and the turbulent diffusivity decreases monotonically with increasing rotation. Only when rotation is rapid enough a large-scale dynamo can be excited. The one-dimensional mean-field model with dynamo coefficients from the test field results predicts reasonably well the dynamo excitation in the direct simulations. This result further validates the test field procedure and reinforces the interpretation that the observed dynamo is driven by a turbulent alpha-effect. This result demonstrates the existence of an alpha-effect and an alpha^2-dynamo with natural forcing.
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