Using 1 cm and 3 mm CARMA and 2 mm GISMO observations, we follow up the first extragalactic detection of anomalous microwave emission (AME) reported by Murphy et al. 2010 in an extranuclear region (Enuc. 4) of the nearby face-on spiral galaxy NGC 6946. We find the spectral shape and peak frequency of AME in this region to be consistent with models of spinning dust emission. However, the strength of the emission far exceeds the Galactic AME emissivity given the abundance of polycyclic aromatic hydrocarbons (PAHs) in that region. Using our galaxy-wide 1 cm map (21 resolution), we identify a total of eight 21x21 regions in NGC 6946 that harbour AME at >95% significance at levels comparable to that observed in Enuc. 4. The remainder of the galaxy has 1 cm emission consistent with or below the observed Galactic AME emissivity per PAH surface density. We probe relationships between the detected AME and dust surface density, PAH emission, and radiation field, though no environmental property emerges to delineate regions with strong versus weak or non-existent AME. On the basis of these data and other AME observations in the literature, we determine that the AME emissivity per unit dust mass is highly variable. We argue that the spinning dust hypothesis, which predicts the AME power to be approximately proportional to the PAH mass, is therefore incomplete.
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