A model of the Solar Magnetic Carpet

There are four key processes that dictate the behaviorof the magnetic flux concentrations that form the so-called `magnetic carpet' of the quiet photosphere. These processes are emergence, cancellation, coalescence, and fragmentation. Rates of emergence have been estimated from observations, but the rates of cancellation, coalescence, and fragmentation are much more difficult to determine observationally. A model is set up to simulate an area of magnetic carpet in the quiet Sun. In the model there are three imposed parameters: the rate of emergence of new flux, the distribution of emerged flux and the rate of fragmentation of flux concentrations. The rate of cancellation and the rate of coalescence are deduced from the model. From the simulations it is estimated that the average emergence rate of new flux in the quiet Sun must be between 6×10^–6 and 10^{– 5} Mx cm^–2 s^–1 to maintain an absolute flux density of between 2.5 and 3 G. For this rate of emergence a fragmentation rate of more than 12×10^–5 s^–1 is required to produce the observed exponential index for the number density of flux concentrations. This is equivalent to each fragment canceling more than once every 200 minutes. The rate of cancellation is calculated from the model and is found naturally to be equivalent to the rate of emergence. However, it is found that the frequency of cancellation is much greater than the frequency of emergence. In fact, it is likely that there are several orders of magnitude more cancellation events than emergence events. This implies that flux is injected in relatively large concentrations whereas cancellation occurs though the disappearance of many small concentrations.