Sustaining the Quiet Photospheric Network: The Balance of Flux Emergence, Fragmentation, Merging, and Cancellation

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Abstract
The magnetic field in the solar photosphere evolves as flux concentrations fragment in response to sheared flows, merge when they collide with others of equal polarity, or (partially) cancel against concentrations of opposite polarity. Newly emerging flux replaces the canceled flux. We present a quantitative statistical model that is consistent with the histogram of fluxes contained in concentrations of magnetic flux in the quiet network for fluxes exceeding ≈ 2 × 1018 Mx, as well as with estimated collision frequencies and fragmentation rates. This model holds for any region with weak gradients in the magnetic flux density at scales of more than a few supergranules. We discuss the role of this dynamic flux balance (i) in the dispersal of flux in the photosphere, (ii) in sustaining the network-like pattern and mixed-polarity character of the network, (iii) in the formation of unipolar areas covering the polar caps, and (iv) on the potential formation of large numbers of very small concentrations by incomplete cancellation. Based on the model, we estimate that as much flux is cancelled as is present in quiet-network elements with fluxes exceeding ≈ 2 × 1018 Mx in 1.5 to 3 days, which is compatible with earlier observational estimates. This timescale is close to the timescale for flux replacement by emergence in ephemeral regions, so that this appears to be the most important source of flux for the quiet-Sun network; based on the model, we cannot put significant constraints on the amount of flux that is injected on scales that are substantially smaller than that of the ephemeral regions. We establish that ephemeral regions originate in the convection zone and are not merely the result of the reemergence of previously cancelled network flux. We also point out that the quiet, mixed-polarity network is generated locally and that only any relatively small polarity excess is the result of flux dispersal from active regions.