<commit_before>\graphicspath{{Chapter6/Figs/}}

\chapter{Conclusion}
\label{chapter6}
    
    \vspace*{\fill}\par
    \pagebreak

\section{Overview of the thesis}
    
	In this Thesis, the results of two-dimensional image analysis of sunspots and magnetic pores in the lower solar atmosphere is detailed.
    These results are compared to theoretically derived results and indicate the ubiquitous presence of slow MHD sausage waves in magnetic structures that inhabit the solar surface.
    In Chapter 2, the method used to measure the cross-sectional area and total intensity of the magnetic structures is analysed.
    This is in order to understand what effect this method has on the results of the signal analysis, which is important to reduce bias.
    In Chapter 3, this method is applied to several magnetic structures.
    The results indicate the presence of slow MHD sausage waves.
    This comes from the phase relations found using the signal analysis methods covered in Chapter 2.
    In Chapter 4, the previous method is applied further, on two magnetic pores.
    The method was extended by extracting the amplitude of the observed oscillations.
    This allowed the usage of magneto-seismology in order to calculate several properties of the waves as well as information on the background properties of these magnetic flux tubes.
    In Chapter 5, the focus shifted from analysing the cross-sectional to the analysis of a Running Penumbral Wave event in a magnetic pore.
    RPWs are typically observed in sunspot penumbras, however it was observed emanating from an magnetic pore.
    This analysis showed that RPWs are most likely an upwardly propagating wave.
    These events are able to deliver a small amount of energy into the local corona.
       
\section{Summary of results}
    
    In Chapter 2, after the summary of signal analysis methods, there was an investigation on the principle method that is used to contour magnetic structures.
    This was undertaken in order to understand if the method adds a bias to the results. 
    To do this, high quality ground-based data was used from the Dunn Solar Telescope (DST), using two instruments that are installed, the \textit{Rapid Oscillations in the Solar Atmosphere} (ROSA) and the \textit{Interferometric Bidimensional Spectrometer} (IBIS).
    There are two datasets, one for each instrument, with the telescope pointed at a magnetic pore and a sunspot for ROSA and IBIS respectively (see Figure \ref{fig:data_overview}).
    Since both sunspots and magnetic pores are analysed within this thesis, it was important to study the method on both types of magnetic structures.
    To start, both structures were contoured using a range of sigma multipliers, 3, 3.5, 4 and 4.5 and 2, 2.5, 3, 3.5 for the sunspot and magnetic pore respectively.
    The standard deviation values used came from a background box of quiet Sun, i.e., a region of the photosphere that contains no magnetic features.
    The reason for this difference in sigma multipliers is due to the lack of a good quiet Sun region within the IBIS dataset.
    Figure \ref{fig:method_overview} shows this clearly with the histograms shown on the right column.
    This had the result of increasing the sigma multipliers.
    Analysing the cross-sectional area signals using the wavelet transform revealed the range of periods within these magnetic structures.
    The range of periods found did not vary with the sigma value used, but what did vary was the strength of the detected periods (see Figure \ref{fig:sunspot_wavelet} and Figure \ref{fig:pore_wavelet}).
    Thus, it is important to contour the magnetic structures by taking into account the structures's intensity distribution, as this makes choosing a sigma multiplier an easier and more robust choice than choosing a random percentage of the background intensity. 
    Further, this implies that for the current range of ground-based solar telescopes, that the limiting factor for cross-sectional area oscillations is the resolution.
    This resolution has been fixed for the past couple of years and until Daniel K. Inouye Solar Telescope (DKIST) data becomes available, the range of sigma multipliers can vary without fear of biasing the results. 
    Finally, since the phase relations are used to identified waves modes using Table \ref{tab:phase}.
    The wavelet transform offers a good insight into the phase difference between two signals.
    This was also checked with regards to the different sigma multipliers.
    It was found that there was no major effect as one varies sigma as it would be expected.
    There were small regions that were different due to the cross-sectional signals varying but nothing that changed the results.
    
    In Chapter 3, the method detailed previously in Chapter 2 is applied to three magnetic structures.
    These are two sunspots and one magnetic pore (seen in Figure \ref{images}).
    The data used here came from the Dutch Open Telescope (DOT) and the Swedish Vacuum Solar Telescope (SVST). 
    These were detailed in Chapter 2 and also within Chapter 3.
    While these telescopes are quite old and now out of service, they offer good quality data.
    By contouring these magnetic structures, using a sigma multiplier of 2.5, a range of periods were observed.   <commit_msg>Updated first part of the conclusion.<commit_after>\graphicspath{{Chapter6/Figs/}}

\chapter{Conclusion}
\label{chapter6}
    
    \vspace*{\fill}\par
    \pagebreak

\section{Overview of the thesis}
    
	In this thesis, the results of two-dimensional image analysis of sunspots and magnetic pores in the lower solar atmosphere is detailed.
    These results are directly compared to theoretically derived results and indicate the ubiquitous presence of slow MHD sausage waves in the larger magnetic structures that inhabit the solar surface.
    In Chapter 2, first the telescopes and instruments that supplied the data analysed in this thesis are described.
    Second, the signal analysis methods used to determine the periods and phase difference were detailed.
    Finally, the method used to measure the cross-sectional area and total intensity of the magnetic structures is examined.
    The reason for this is to understand what the effects of varying the sigma multiplier has on the results of the signal analysis, which is important in order to reduce bias.
    In Chapter 3, the cross-sectional area and total intensity is measured on several magnetic structures.
    The overall results indicate the presence of slow MHD sausage waves.
    This conclusion is reached by comparing the phase difference between the cross-sectional area and total intensity which was in phase.
    In Chapter 4, the cross-sectional area and total intensity is once again measured for two new magnetic pore data sets.
    The phase difference indicated strongly that the oscillations are slow MHD sausage waves.
    The extension within this chapter was calculating the amplitudes of the cross-sectional area perturbations.
    The amplitude of these perturbations allows the usage of magneto-seismology equations.
    These equations calculate several properties of the detected waves, as well as information on the background properties of the observed magnetic flux tubes.
    In Chapter 5, the focus shifted from analysing the cross-sectional of magnetic structures to the analysis of a Running Penumbral waves (RPWs) in a magnetic pore.
    RPWs have only observed in sunspot penumbras; however, this analysis details the presence of events that have the identical signature of RPWs emanating from an magnetic pore.
    This fact has confirmed that RPWs are a visual effect of MHD sausage waves following the curvature of magnetic field lines of sunspots and magnetic pores.
    These have been previously termed Upwardly Propagating Waves (UPWs).
    This creates a delay of the appearance of the wave at higher levels, causing this patten of outwardly propagating waves.
    These events are able to deliver a small amount of energy into the local corona, but not enough to heat the active corona.
       
\section{Summary of results}
    
    In Chapter 2, after the summary of signal analysis methods, there was an investigation on the principle method that is used to contour magnetic structures.
    This was undertaken in order to understand if the method adds a bias to the results. 
    To do this, high quality ground-based data was used from the Dunn Solar Telescope (DST), using two instruments that are installed, the \textit{Rapid Oscillations in the Solar Atmosphere} (ROSA) and the \textit{Interferometric Bidimensional Spectrometer} (IBIS).
    There are two datasets, one for each instrument, with the telescope pointed at a magnetic pore and a sunspot for ROSA and IBIS respectively (see Figure \ref{fig:data_overview}).
    Since both sunspots and magnetic pores are analysed within this thesis, it was important to study the method on both types of magnetic structures.
    To start, both structures were contoured using a range of sigma multipliers, 3, 3.5, 4 and 4.5 and 2, 2.5, 3, 3.5 for the sunspot and magnetic pore respectively.
    The standard deviation values used came from a background box of quiet Sun, i.e., a region of the photosphere that contains no magnetic features.
    The reason for this difference in sigma multipliers is due to the lack of a good quiet Sun region within the IBIS dataset.
    Figure \ref{fig:method_overview} shows this clearly with the histograms shown on the right column.
    This had the result of increasing the sigma multipliers.
    Analysing the cross-sectional area signals using the wavelet transform revealed the range of periods within these magnetic structures.
    The range of periods found did not vary with the sigma value used, but what did vary was the strength of the detected periods (see Figure \ref{fig:sunspot_wavelet} and Figure \ref{fig:pore_wavelet}).
    Thus, it is important to contour the magnetic structures by taking into account the structures's intensity distribution, as this makes choosing a sigma multiplier an easier and more robust choice than choosing a random percentage of the background intensity. 
    Further, this implies that for the current range of ground-based solar telescopes, that the limiting factor for cross-sectional area oscillations is the resolution.
    This resolution has been fixed for the past couple of years and until Daniel K. Inouye Solar Telescope (DKIST) data becomes available, the range of sigma multipliers can vary without fear of biasing the results. 
    Finally, since the phase relations are used to identified waves modes using Table \ref{tab:phase}.
    The wavelet transform offers a good insight into the phase difference between two signals.
    This was also checked with regards to the different sigma multipliers.
    It was found that there was no major effect as one varies sigma as it would be expected.
    There were small regions that were different due to the cross-sectional signals varying but nothing that changed the results.
    
    In Chapter 3, the method detailed previously in Chapter 2 is applied to three magnetic structures.
    These are two sunspots and one magnetic pore (seen in Figure \ref{images}).
    The data used here came from the Dutch Open Telescope (DOT) and the Swedish Vacuum Solar Telescope (SVST). 
    These were detailed in Chapter 2 and also within Chapter 3.
    While these telescopes are quite old and now out of service, they offer good quality data.
    By contouring these magnetic structures, using a sigma multiplier of 2.5, a range of periods were observed.   
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