Basal magnetic flux and the local solar dynamo
The average unsigned magnetic flux density in magnetograms of the quiet Sun is generally dominated by instrumental noise. Due to the entirely different scaling behavior of the noise and the solar magnetic pattern it has been possible to determine the standard deviation of the Gaussian noise distribution and remove the noise contribution from the average unsigned flux density for the whole 15-yr SOHO/MDI data set and for a selection of SDO/HMI magnetograms. There is a very close correlation between the MDI disk-averaged unsigned vertical flux density and the sunspot number, and regression analysis gives a residual level of 2.7 G when the sunspot number is zero. The selected set of HMI magnetograms, which spans the most quiet phase of solar activity, has a lower limit of 3.0 G to the noise-corrected average flux density. These apparently cycle-independent levels may be identified as a basal flux density, which represents an upper limit to the possible flux contribution from a local dynamo, but not evidence for its existence. The 3.0 G HMI level, when scaled to the Hinode spatial resolution, translates to 3.5 G, which means that the much higher average flux densities always found by Hinode in quiet regions do not originate from a local dynamo. The contributions to the average unsigned flux density come almost exclusively from the extended wings of the probability density function (PDF), also in the case of HMI magnetograms with only basal-level magnetic flux. These wings represent intermittent magnetic flux. While the global dynamo appears to dominate the magnetic energy spectrum at all the resolved spatial scales, there are indications from the observed Hanle depolarization in atomic lines that the local dynamo may dominate the spectrum at scales of order 1-10 km and below.