Simulated Synoptic Magnetograms

In order to convert the instant day maps into the form of simulated synoptic magnetograms, the relevant data from each of the instant day maps must be identified and extracted. To do this, initially a latitudinal strip with a width of 13.5◦ longitude is taken from the rightmost edge of the first instant day map. This portion of the instant day map is defined to be the portion that is initially lying at central meridian. This information is then stored as the rightmost strip of the first simulated synoptic magnetogram. A second latitudinal strip, of the same width, is then taken from the left edge of where the previous strip ended, but from the next instant day map, representing the fact that this would be the next strip to lie at central meridian. This is then stored as the next section of the simulated synoptic magnetogram. This method is then continued over 27 days of the instant day maps, making up a single simulated synoptic magnetogram covering one carrington rotation. This process is then repeated with each successive 27 instant day simulations, producing one subsequent simulated synoptic magnetogram per 27 days. Once constructed the simulated synoptic magnetograms are then

Figure 4.4: Image showing (a) a typical instant day map and (b) a simulated synoptic magnetogram. The 27 day period covered by the simulated synoptic magnetogram is the same 27 day rotation period the instant day example is taken from. The area within the vertical black lines corresponds to the portion of the instant day map that lies at central meridian and is extracted and inserted into the simulated synoptic magnetogram. Several key features have been marked on both the instant day map and the simulated synoptic magnetogram.

corrected for flux balance, which usually involves only a small correction. This involves merely totaling up the flux imbalance within the synoptic map and then adding flux of opposite sign to every pixel which has strength equal to the imbalance averaged out over the entire map in order that the surface field is now in balance. This is usually a very small correction.

Figure 4.4 shows a comparison between one of the simulated synoptic magnetograms (Figure 4.4(b)) and one of the instant day maps that was used to create it (Figure 4.4(a)). It can be seen that the method for creating simulated synoptic magnetograms produces a good average representation over a rotation. Comparing several of the features between the two images in Figure 4.4 gives a good understanding of what information and data are lost or missed when creating simulated synoptic

slightly weaker, and more longitudinally sheared than in the simulated synoptic magnetogram. This is due to its extraction at an earlier time than the time of the current instant day map. Feature 5 shows bipolar regions, within the instant day map that have yet to be extracted for the simulated synoptic magnetogram. These bipolar regions appear less sheared and stronger in the instant day simulation than the corresponding regions in the simulated synoptic magnetogram. Therefore this shows the opposite effect to that of feature 2, where the large scale solar flows and diffusion have not had as much of an affect upon it, as they will have by the time the field information is extracted. Feature 4 shows a bipole that is yet to emerge in the instant day map, but is picked up for the simulated synoptic magnetogram. Conversely, features 1 and 3 show two bipolar regions that have been missed by the conversion into simulated synoptic magnetogram form. This is a key point, as information may be missed when converting into synoptic form thereby artificially impacting the complexity of the field distribution.

After converting the instant day maps into simulated synoptic magnetograms the same flux measure- ments are taken as before, shown in Figure 4.5. The simulated synoptic magnetograms show a better match than the instant day maps. The peaks of flux at solar maximum occur at approximately the same time and magnitude. The minima give a better match between the two data sets than before. This is because the simulated synoptic magnetograms lose some information compared to the instant day simulations (in the same way that the Kitt Peak magnetograms lose information). By comparing the simulated synoptic magnetograms to the Kitt Peak Synoptic magnetogram, data produced by a similar technique are compared. From this we have confirmation that our low latitude field distribu- tions are realistic, at least in terms of absolute flux values, and subsequently will produce consistent high latitude fields.

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Figure 4.5: Graphs showing the surface flux from our simulated synoptic magnetogram conversion data. Graph (a) shows the total surface flux while (b) shows the flux at 40◦latitude. In each case the solid lines denote the flux values deduced from the Kitt Peak synoptic magnetograms where the dashed curve denotes the results of the simulations. The double ended arrows in each graph denote a 2-year time period around cycle maximum determined from the peaks in bipole emergence rate.

synoptic data are a slightly better match to the observed levels of flux within the Kitt Peak synoptic magnetograms than the instant day simulation. Graph (a) shows a plot where the solid line represents the difference in flux between the Kitt peak magnetograms and the simulated synoptic magnetograms, whilst the dashed line represents the difference in flux between the Kitt peak magnetograms and the instant day simulation. This graph allows us to see that, in general, the simulated synoptic magne-

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Figure 4.6: Graph (a) shows the difference between the amount of magnetic flux within the Kitt Peak magnetograms and the instant day simulation (dashed line) and the difference between the amount of magnetic flux in the Kitt Peak magnetograms and the simulated synoptic magnetograms (solid line). Graph (b) is a plot of the difference between these two properties, where the range of y has been limited to positive values only. This second graph highlights the points throughout the solar cycle where the flux values within the simulated synoptic maps give a better match to the flux values within the Kitt Peak magnetograms than those within the instant day simulation.

tograms provide a better match to the flux levels of the Kitt Peak magnetograms than the instant day simulation, due mostly to the fact that they are both created in the same way and will miss the same information (see Figure 4.4 for full details on this). Graph (b) shows a plot of the difference between the errors in the flux values of the two sets of data. The y axis has been limited between zero and the

maximum value of this in order to highlight the points during the solar cycle where the flux values of the simulated synoptic data better match the Kitt Peak magnetograms i.e. any point on this graph where positive values are plotted indicates a better match between the simulated synoptic data. This graph shows that, in general, the simulated synoptic data provides a slightly better match to the Kitt Peak data than the instant day simulation. The differences in flux levels, especially around solar max- imum, can be seen to provide a closer estimation to the Kitt Peak data. This means that it is prudent to determine the behaviour of coronal null points using both sets of data as a base boundary condition for potential coronal field extrapolation.