Galactic dynamo action in presence of stochastic alpha and shear

Using a one-dimensional $\alpha\omega$-dynamo model appropriate to galaxies, we study the possibility of dynamo action driven by a stochastic alpha effect and shear. To determine the field evolution, one needs to examine a large number of different realizations of the stochastic component of $\alpha$. The net growth or decay of the field depends not only on the dynamo parameters but also on the particular realization, the correlation time of the stochastic $\alpha$ compared to turbulent diffusion timescale and the time over which the system is evolved. For dynamos where both a coherent and fluctuating $\alpha$ are present, the stochasticity of $\alpha$ can help alleviate catastrophic dynamo quenching, even in the absence of helicity fluxes. One can obtain final field strengths up to a fraction $\sim 0.01$ of the equipartition field $ B_{eq}$ for dynamo numbers $| D| \sim 40$, while fields comparable to $ B_{eq}$ require much larger degree of $\alpha$ fluctuations or shear. This type of dynamo may be particularly useful for amplifying fields in the central regions of disk galaxies.