Dome-Tunnels

In Section 3.5.2, we considered a separatrix dome created from the separatrix surfaces of two null points stitched together along the spine lines of a third null. The separatrix surface from the third null point formed an open separatrix curtain. In the example shown in Figure 3.9, the separatrix dome occurred in a region of open field, however, these double-null domes can also occur in regions of closed field. In a closed-field region the separatrix surface that forms the open separatrix curtain folds back down to the photosphere creating a tunnel structure. Figure 5.12 shows the footprint of such a structure on the photosphere.

Similarly to the double cave configuration the dome-tunnel configuration can form from extended chains of nulls with the proviso that there are an odd number of nulls in the chain and that none of the spines of these nulls are open. If there are open spines then a dome and open separatrix curtain structure will form such as that seen in Section 3.5.2.

Figure 5.13 shows the 12 Carrington rotation running mean of the number of these dome-tunnel structures over the solar cycle. These structures are not as common as the double-cave structures with fewer than one occurring per Carrington Rotation. There does not seem to be a clear cyclic variation of the numbers of dome-tunnels, but considering the very low numbers of these this is not particularly surprising.

Figure 5.13: Number of dome tunnels with time (12CR running mean). Sunspot number is plotted to indicate the solar cycles (red line).

5.4

Discussion

In the recent extended solar minimum we have seen very different behaviour in the magnetic skeleton to that seen in previous solar minima. In all solar minima there are more isolated separatrix domes than at solar maxima. These domes can form over small magnetic features in the quiet sun and can often be nested within one another or nested under a larger more complex separatrix structure. In the recent extended solar minimum there are many more isolated dome structures than the previous two solar minima where the global dipole was stronger. There is also an increase in the number of nulls that have separator connections to the HCS in the weak dipole solar minimum compared to the strong dipole solar minima. This means that, during the cycle 23/24 minimum, most null points are likely to be either isolated domes or part of the separator network that connects to the HCS null line.

A large network of null points connected to the HCS null line via separator con- nections could mean that reconnection around any of these null points or separators could have global consequences in terms of allowing closed field under the HCS curtain to become open field leading to a change in the tilt of the HCS.

The network of nulls connected to the HCS contains a large proportion of the total number of nulls that are present for each rotation at both solar maximum and during the recent weak solar minimum. This is due to the warping of the HCS because of the weakening of the global solar dipole field allowing separatrix curtains that are connected to the HCS to form. These will have one connection to the HCS if they are open and two connections to the HCS if they are closed.

The double separatrix cave structure is one example of a structure that we can easily identify simply by considering the separator network. Such structures are most prevalent during solar minima where the global dipole is strong and hence there is much low-level magnetic structure that is enclosed under, and does not interact with, the HCS curtains.

Data Comparison

In this thesis, several different data sets comprising magnetograms taken from both ground-based and satellite observatories are considered. These magnetograms can vary both in their sensitivity and resolution. In this Chapter, two data sets of PFSS models with different resolutions but which are extrapolated from magnetograms from the same instrument are compared in order to understand the effect that varying resolution can have on the magnetic topology both at local scales, as well as globally.

6.1

Magnetogram data

This section will consider data from the SOLIS telescope at the low resolution de- scribed in Chapter 4 and also at a higher resolution. These data sets begin at CR2007 (starting August 30th 2003) and continue to the present. This gives us nearly 11 years worth of data. The low resolution maps have a resolution of 360 by 180 pixels in lon- gitude and sine latitude. The PFSS models from these low-resolution data have a maximum number of harmonics lmax = 81. This gives an extrapolation resolution of

329 grid points in longitude, 165 in latitude and 48 exponentially spaced in the radial direction. The high-resolution maps have a resolution of 1800 pixels in equal steps of longitude and 900 pixels in equal steps of sine latitude. We can perform the PFSS extrapolation on this data using 301 harmonics. This gives us a resolution of 1209 grid-points in equal steps of longitude, 605 grid-points in equal steps of latitude and 177 grid-points exponentially spaced between 1.00R and 2.5R.