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Physics_Thesis_Template/content/chapter-results.tex
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@@ -6,7 +6,7 @@ The results also only contain the data of folded lightcurves which could be fitt
\section{M dwarfs \label{sec:results:m_dwarfs}}
This section shows the results for all 144 M dwarfs in this study. The list of stars can be found in table \ref{apA:list_of_m_stars}.\\
This section shows the results for 49 M dwarfs for which flares could be detected. The list of stars can be found in table \ref{apA:list_of_m_stars}.\\
Figures \ref{fig:M-Flarecount-10_Bins} and \ref{fig:M-Flarecount-30_Bins} show histograms, with 10 and 30 bins respectively, of the amount of flares during the normalized phase.\\
Looking at figure \ref{fig:M-Flarecount-10_Bins} there is an even distribution within error of flares across the normalized phase, with the excepion of the bin at phase $0.5 \pi$. The bin at phase $0.5 \pi$ shows a significant dip of roughly twice the error below the surrounding bins.\\
Looking at the same data, just with 30 instead of 10 bins (figure \ref{fig:M-Flarecount-30_Bins}), the same dip is visible. In this figure the dip spans 3 bins. Additionally there are additional dips at around phase $0.7 \pi$, $1.3 \pi$ and $1.4 \pi$. Including the error, the major dip (which was already visible in figure \ref{fig:M-Flarecount-10_Bins}) is still below the average. Similar for the dips at phases $0.7 \pi$ and $1.3 \pi$. The dip at phase $1.4 \pi$ on the other hand overlaps with its error with the errorbars of the bins at phase \textasciitilde$1.7 \pi$ and and onward, which are good assumption for an average value. Due to the dips surrounding the center, it may look like there is an increased number of flares in the center. If we look at the errorbars, it is clear that only the bin at phase \textasciitilde$1.25 \pi$ is above the average.
@@ -25,7 +25,7 @@ Looking at the same data, just with 30 instead of 10 bins (figure \ref{fig:M-Fla
\caption{30 bins}
\label{fig:M-Flarecount-30_Bins}
\end{subfigure}
\caption{Histogram showing the amount of flares per phase for all 144 M dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 bins (\subref{fig:M-Flarecount-10_Bins})/30 bins (\subref{fig:M-Flarecount-30_Bins}) of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histogram showing the amount of flares per phase of 49 M dwarfs for which flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 bins (\subref{fig:M-Flarecount-10_Bins})/30 bins (\subref{fig:M-Flarecount-30_Bins}) of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:M-Flarecount}
\end{figure}
@@ -50,7 +50,7 @@ Increasing the bin count to 30 (see figure \ref{fig:M-Flarecount-30_Bins_1.5_pea
\caption{30 bins}
\label{fig:M-Flarecount-30_Bins_1.25_peak}
\end{subfigure}
\caption{Histograms showing the amount of flares with a normalized peak of greater than 1.25 per phase for all 144 M dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:M-Flarecount-10_Bins_1.25_peak}) /30 (\subref{fig:M-Flarecount-30_Bins_1.25_peak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histograms showing the amount of flares with a normalized peak of greater than 1.25 per phase of 27 M dwarfs for which such flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:M-Flarecount-10_Bins_1.25_peak}) /30 (\subref{fig:M-Flarecount-30_Bins_1.25_peak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:M-Flarecount-peaks_1.25_peak}
\end{figure}
\begin{figure}[pt!]
@@ -67,7 +67,7 @@ Increasing the bin count to 30 (see figure \ref{fig:M-Flarecount-30_Bins_1.5_pea
\caption{30 bins}
\label{fig:M-Flarecount-30_Bins_1.5_peak}
\end{subfigure}
\caption{Histograms showing the amount of flares with a normalized peak of greater than 1.5 per phase for all 144 M dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:M-Flarecount-10_Bins_1.5_peak})/30 (\subref{fig:M-Flarecount-30_Bins_1.5_peak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histograms showing the amount of flares with a normalized peak of greater than 1.5 per phase for 20 M dwarfs for which such flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:M-Flarecount-10_Bins_1.5_peak})/30 (\subref{fig:M-Flarecount-30_Bins_1.5_peak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:M-Flarecount-peaks_1.5_peak}
\end{figure}
@@ -90,7 +90,7 @@ The difference becomes less obvious when increasing the bin size 30 (figure \ref
\caption{30 bins}
\label{fig:M-Flarecount-30_Bins_1.01_maxpeak}
\end{subfigure}
\caption{Histograms showing the amount of flares with a normalized peak of less than 1.01 per phase for all 144 M dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:M-Flarecount-10_Bins_1.01_maxpeak})/30 (\subref{fig:M-Flarecount-30_Bins_1.01_maxpeak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histograms showing the amount of flares with a normalized peak of less than 1.01 per phase of 17 M dwarfs for which such flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:M-Flarecount-10_Bins_1.01_maxpeak})/30 (\subref{fig:M-Flarecount-30_Bins_1.01_maxpeak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:M-Flarecount-peaks_1.01_maxpeak}
\end{figure}
@@ -108,14 +108,14 @@ The difference becomes less obvious when increasing the bin size 30 (figure \ref
\caption{30 bins}
\label{fig:M-Flarecount-30_Bins_1.05_maxpeak}
\end{subfigure}
\caption{Histograms showing the amount of flares with a normalized peak of less than 1.05 per phase for all 144 M dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:M-Flarecount-10_Bins_1.05_maxpeak})/30 (\subref{fig:M-Flarecount-30_Bins_1.05_maxpeak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histograms showing the amount of flares with a normalized peak of less than 1.05 per phase of 32 M dwarfs for which such flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:M-Flarecount-10_Bins_1.05_maxpeak})/30 (\subref{fig:M-Flarecount-30_Bins_1.05_maxpeak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:M-Flarecount-peaks_1.05_maxpeak}
\end{figure}
\FloatBarrier
\section{K dwarfs \label{sec:results:k_dwarfs}}
This section shows the results for all 37 K dwarfs in this study. A full list of the stars used can be found in table \ref{apA:list_of_k_stars}.\\
This section shows the results for 37 K dwarfs for which flares could be detected. A full list of the stars used can be found in table \ref{apA:list_of_k_stars}.\\
Figure \ref{fig:K-Flarecount-10_Bins} shows the amount of flares per phase with 10 bins of 37 K type dwarfs in used in this study. Overall the distribution is even within error, with a slight increase in flares when going from the maximum to the minimum of the lightcurve at phase $0.5 \pi$, and a slight decrease when going from minimum to maximum at phase $1.5 \pi$. There is also a peak at around $1 \pi$ with around 95 flares compared to the 60-80 flares per bin in the rest of the histogram. This peak is dominated by $V*~V471~Tau$. The individual results for this star are visible in section \ref{sec:results:individual}.\\
Looking at the same dataset with 30 bins for the histogram (figure \ref{fig:K-Flarecount-30_Bins}), the peak in the phase minimum at $1 \pi$ is still visible. Additionally there appear more peaks at phase $>1.3 \pi$ ($1.3,~1.6,~1.9 \pi$), while the amount of flares between phase $0 \pi$ and $1 \pi$ shows a slight trend to more flares with dips inbetween and a larger dip right before and after the big peak at phase $1 \pi$ which was also visible in figure \ref{fig:K-Flarecount-10_Bins} with 10 bins. The major dips at phase $0.7 \pi$, $1.3 \pi$, $1.6 \pi$ and $1.9 \pi$ are all well outside the errorbars of the surrounding peak bins, while the smaller ones between phase $0 \pi$ and $1 \pi$ overlap with their errorbars with their surrounding bins.
@@ -133,7 +133,7 @@ Looking at the same dataset with 30 bins for the histogram (figure \ref{fig:K-Fl
\caption{30 bins}
\label{fig:K-Flarecount-30_Bins}
\end{subfigure}
\caption{Histogram showing the amount of flares per phase for all 37 K dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 bins (\subref{fig:K-Flarecount-10_Bins})/30 bins (\subref{fig:K-Flarecount-30_Bins}) of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histogram showing the amount of flares per phase of 37 K dwarfs for which flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 bins (\subref{fig:K-Flarecount-10_Bins})/30 bins (\subref{fig:K-Flarecount-30_Bins}) of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:K-Flarecount}
\end{figure}
@@ -155,7 +155,7 @@ A similar picture forms when increasing the bin count to 30 (figure \ref{fig:K-F
\caption{30 bins}
\label{fig:K-Flarecount-30_Bins_1.05_peak}
\end{subfigure}
\caption{Histograms showing the amount of flares with a normalized peak of greater than 1.05 per phase for all 37 K dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:K-Flarecount-10_Bins_1.05_peak})/30 (\subref{fig:K-Flarecount-30_Bins_1.05_peak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histograms showing the amount of flares with a normalized peak of greater than 1.05 per phase of 13 K dwarfs for which such flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:K-Flarecount-10_Bins_1.05_peak})/30 (\subref{fig:K-Flarecount-30_Bins_1.05_peak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:K-Flarecount-peaks_1.5_peak}
\end{figure}
@@ -178,7 +178,7 @@ Increasing the bins to 30 (figure \ref{fig:K-Flarecount-30_Bins_1.05_maxpeak}) s
\caption{30 bins}
\label{fig:K-Flarecount-30_Bins_1.01_maxpeak}
\end{subfigure}
\caption{Histograms showing the amount of flares with a normalized peak of less than 1.01 per phase for all 37 K dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:K-Flarecount-10_Bins_1.01_maxpeak})/30 (\subref{fig:K-Flarecount-30_Bins_1.01_maxpeak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histograms showing the amount of flares with a normalized peak of less than 1.01 per phase of 20 K dwarfs for which such flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:K-Flarecount-10_Bins_1.01_maxpeak})/30 (\subref{fig:K-Flarecount-30_Bins_1.01_maxpeak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:K-Flarecount-peaks_1.01_maxpeak}
\end{figure}
@@ -198,14 +198,14 @@ Increasing the bins to 30 (figure \ref{fig:K-Flarecount-30_Bins_1.05_maxpeak}) s
\caption{30 bins}
\label{fig:K-Flarecount-30_Bins_1.05_maxpeak}
\end{subfigure}
\caption{Histograms showing the amount of flares with a normalized peak of less than 1.05 per phase for all 37 K dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:K-Flarecount-10_Bins_1.05_maxpeak})/30 (\subref{fig:K-Flarecount-30_Bins_1.05_maxpeak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histograms showing the amount of flares with a normalized peak of less than 1.05 per phase of 20 K dwarfs for which such flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:K-Flarecount-10_Bins_1.05_maxpeak})/30 (\subref{fig:K-Flarecount-30_Bins_1.05_maxpeak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:K-Flarecount-peaks_1.05_maxpeak}
\end{figure}
\FloatBarrier
\section{G dwarfs \label{sec:results:g_dwarfs}}
This section shows the results for 71 G dwarfs in this study. Table \ref{apA:list_of_g_stars} contains a list of all G type stars used.\\
This section shows the results for 21 G dwarfs for which flares could be detected. Table \ref{apA:list_of_g_stars} contains a list of all G type stars used.\\
The first histogram over all data of G type dwarfs with 10 bins in figure \ref{fig:G-Flarecount-10_Bins} shows a significant increase of occuring flares well outside the errorbar range in the lightcurve minima at around phase $1 \pi$ compared to the maxima at phase $0 \pi$/$2 \pi$. The rise in flare occurances from maxima to minima (phase $0 \pi$ to $1 \pi$) seems to be gradual, while there is a steep fall off after the sixth bin at phase $1.1 \pi$.\\
Due to the lower number of detected flares on G type stars, the error bars in figure \ref{fig:G-Flarecount-30_Bins} are rather large. The increase of flares in the minima of the folded lightcurve from the previous figure is now splint into two peaks at phase $0.6 \pi$ and $1 \pi$. An additional peak bin appears at around phase $0.25 \pi$ in this figure. This peaks errorbar does not overlap with its surrounding bins errorbars. Right before this peak is a significant dip visible at phase $0.2 \pi$. On the other half of the phase after the peak at phase $1 \pi$, the near even distribution of figure \ref{fig:G-Flarecount-10_Bins} becomes more noisy, even though its still well within error.\\
Limiting the flare peaks to <1.05 (figure \ref{fig:G-Flarecount-peaks_1.05_maxpeak}) does not change the resulting histograms much. There are only miniscule differences, mainly the bin at phase $1.1 \pi$ is now slightly smaller relative to the two prior bins in figure \ref{fig:G-Flarecount-10_Bins_1.05_maxpeak} compared to figure \ref{fig:G-Flarecount-10_Bins} with all flares.
@@ -224,7 +224,7 @@ Limiting the flare peaks to <1.05 (figure \ref{fig:G-Flarecount-peaks_1.05_maxpe
\caption{30 bins}
\label{fig:G-Flarecount-30_Bins}
\end{subfigure}
\caption{Histogram showing the amount of flares per phase for all 71 G dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 bins (\subref{fig:G-Flarecount-10_Bins})/30 bins (\subref{fig:G-Flarecount-30_Bins}) of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histogram showing the amount of flares per phase of 21 G dwarfs for which flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 bins (\subref{fig:G-Flarecount-10_Bins})/30 bins (\subref{fig:G-Flarecount-30_Bins}) of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:G-Flarecount}
\end{figure}
@@ -245,7 +245,7 @@ Increasing the bins to 30, which is seen in figure \ref{fig:G-Flarecount-30_Bins
\caption{30 bins}
\label{fig:G-Flarecount-30_Bins_1.05_maxpeak}
\end{subfigure}
\caption{Histograms showing the amount of flares with a normalized peak of less than 1.05 per phase for all 37 K dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:G-Flarecount-10_Bins_1.05_maxpeak})/30 (\subref{fig:G-Flarecount-30_Bins_1.05_maxpeak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histograms showing the amount of flares with a normalized peak of less than 1.05 per phase of 16 G dwarfs for which such flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:G-Flarecount-10_Bins_1.05_maxpeak})/30 (\subref{fig:G-Flarecount-30_Bins_1.05_maxpeak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:G-Flarecount-peaks_1.05_maxpeak}
\end{figure}
@@ -263,14 +263,14 @@ Increasing the bins to 30, which is seen in figure \ref{fig:G-Flarecount-30_Bins
\caption{30 bins}
\label{fig:G-Flarecount-30_Bins_1.05_peak}
\end{subfigure}
\caption{Histograms showing the amount of flares with a normalized peak of greater than 1.05 per phase for all 71 G dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:G-Flarecount-10_Bins_1.05_peak})/30 (\subref{fig:G-Flarecount-30_Bins_1.05_peak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histograms showing the amount of flares with a normalized peak of greater than 1.05 per phase of 13 G dwarfs for which such flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 (\subref{fig:G-Flarecount-10_Bins_1.05_peak})/30 (\subref{fig:G-Flarecount-30_Bins_1.05_peak}) bins of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:G-Flarecount-peaks_1.5_peak}
\end{figure}
\FloatBarrier
\section{F dwarfs \label{sec:results:f_dwarfs}}
This section shows the results for all 13 F dwarfs in this study. The list of F type stars can be found in table \ref{apA:list_of_f_stars}.\\
This section shows the results for 4 F dwarfs for which flares could be detected. The list of F type stars can be found in table \ref{apA:list_of_f_stars}.\\
Due to the low number of F type stars in this study, and the difficulty to detect flares on them, the detected number of flares in figures \ref{fig:F-Flarecount-10_Bins} and \ref{fig:F-Flarecount-30_Bins} is very low which causes the errorbars of the histogram to grow very large. Nontheless all detected flares were around the minimum of the lightcurves.
\begin{figure}[pt!]
@@ -287,14 +287,14 @@ Due to the low number of F type stars in this study, and the difficulty to detec
\caption{30 bins}
\label{fig:F-Flarecount-30_Bins}
\end{subfigure}
\caption{Histogram showing the amount of flares per phase for all 13 F dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 bins (\subref{fig:F-Flarecount-10_Bins})/30 bins (\subref{fig:F-Flarecount-30_Bins}) of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histogram showing the amount of flares per phase of 4 F dwarfs for which flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 bins (\subref{fig:F-Flarecount-10_Bins})/30 bins (\subref{fig:F-Flarecount-30_Bins}) of the phase, showing the number of flares per bin. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:F-Flarecount}
\end{figure}
\FloatBarrier
\section{Combined results \label{sec:results:combined}}
The results for all 265 stars in the study are shown in this chapter. This includes the stars from tables \ref{apA:list_of_m_stars} to \ref{apA:list_of_f_stars}. The histograms in figure \ref{fig:MKGF-Flarecount-10_Bins} and \ref{fig:MKGF-Flarecount-30_Bins} are stacked histograms. The flare amount of the individual stars are per bin are stacked on top of each other resulting in the final value.\\
The results for all 95 stars in the study for which flares could be detected. This includes the stars from tables \ref{apA:list_of_m_stars} to \ref{apA:list_of_f_stars}. The histograms in figure \ref{fig:MKGF-Flarecount-10_Bins} and \ref{fig:MKGF-Flarecount-30_Bins} are stacked histograms. The flare amount of the individual stars are per bin are stacked on top of each other resulting in the final value.\\
The dip at phase $0.5 \pi$ which was present in the histogram for the M type stars (see figure \ref{fig:M-Flarecount-10_Bins} in section \ref{sec:results:m_dwarfs}) propagates and casues the dip to be also visible in figure \ref{fig:MKGF-Flarecount-10_Bins}. The peak at phase $1 \pi$ is also a result of propagation, but from the K and G type star data. Due to the large number of overall flares, the errorbars are small and the errorbars of the peak in the center at phase $1 \pi$ does not overlap with the other errorbars.\\
Looking at the same data with 30 bins over the phase in figure \ref{fig:MKGF-Flarecount-30_Bins}, the propagation of the variation in the data of the M type stars is clearly visible with the dip around phase $0.5 \pi$ and $1.4 \pi$. Additionally the peaks from the data of K (figure \ref{fig:K-Flarecount-30_Bins}) and G (figure \ref{fig:G-Flarecount-30_Bins}) type stars cause a wider peak at around phase $1 \pi$. Additionally there are also smaller, especially less wide peaks at around phases $0.4 \pi$, $0.7 \pi$ and $1.5 \pi$.
@@ -312,7 +312,7 @@ Looking at the same data with 30 bins over the phase in figure \ref{fig:MKGF-Fla
\caption{30 bins}
\label{fig:MKGF-Flarecount-30_Bins}
\end{subfigure}
\caption{Histograms showing the amount of flares per phase for all 265 dwarfs used in this study. The x-axis represents the normalized phase of the folded lightcurves. There are 10 bins (\subref{fig:MKGF-Flarecount-10_Bins})/30 bins (\subref{fig:MKGF-Flarecount-30_Bins}) of the phase, showing the number of flares per bin. The colors show the individual amount for each spectral type with the amount being stacked ontop of each other. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\caption{Histograms showing the amount of flares per phase for all 95 dwarfs for which flares could be detected. The x-axis represents the normalized phase of the folded lightcurves. There are 10 bins (\subref{fig:MKGF-Flarecount-10_Bins})/30 bins (\subref{fig:MKGF-Flarecount-30_Bins}) of the phase, showing the number of flares per bin. The colors show the individual amount for each spectral type with the amount being stacked ontop of each other. The error bar shows the standard deviation for the histogram. The blue line indicates an idialized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
\label{fig:MKGF-Flarecount}
\end{figure}
@@ -323,7 +323,7 @@ This section contains a selection of results for individual stars. The results f
\subsection{BD-08 995}
BD-08 995, also known by TIC 43472154, is a G type star with a surface temperature of 5231.2 K, which is \textasciitilde87 pc away. It is a very active solar like star, producing over 200 superflares per year (\cite{tess_1st_year_superflares}). It has a rotational period of 2.8 days (\cite{tess_1st_year_superflares}). There are two TESS lightcurves available, sectors 5 and 32.\\
BD-08 995, also known by TIC 43472154, is a G type star with a surface temperature of 5316 K (\cite{revised_tess_input_catalogue}), which is \textasciitilde87 pc away (\cite{simbad}). It is a very active solar like star, producing over 200 superflares per year (\cite{tess_1st_year_superflares}). It has a rotational period of 2.8 days (\cite{tess_1st_year_superflares}). There are two TESS lightcurves available, sectors 5 and 32.\\
Looking at figure \ref{fig:BD-08_995-Flarecount-10_Bins}, which shows the flare distribution across the normalized phase of the folded lightcurves with 10 bins, it shows a clear peak of flares appearance in the lightcurve minima at phase $1 \pi$. The errorbars of this wide peak only overlap with the first bin of the plot at phase $0 \pi$.
This bin belong to the phase maxima which also shows slight increase in flare activity at phase $0/2 \pi$ compared to the transition regions at around phase $0.5 \pi$ (maxima to minima) and $1.5 \pi$ (minima to maxima). Considering errors for this, the errorbars of the bins at the phase maxima overlap with those of the transition regions.\\
Figure \ref{fig:BD-08_995-Flarecount-30_Bins} shows the same data just with 30 bins instead of 10. Ignoring the errorbars, it shows a similar picture as the previous figure. But due to the low number of total detected flares, and a the relatively large bin count, the errorbars become large compared to the individual bins. Due to this, the errorbars of most bins overlap with each other, with the exceptions of the the first bin at phase $0 \pi$ and the bin at phase \textasciitilde$1.1 \pi$, whichs erorbars only overlap with other higher bins like the ones at phase \textasciitilde$0.9 \pi$ and \textasciitilde$1.4 \pi$.
@@ -460,7 +460,8 @@ The histogram with 30 bins (figure \ref{fig:TYC_4595-107-1-Flarecount-30_Bins})
\label{fig:TYC_4595-107-1-Flarecount}
\end{figure}
The flare peak at normalized phase distribution can be seen in figure \ref{fig:TYC_4595-107-1-flarepeaks_1.27}. The strongest flare was detected at normalized phase \textasciitilde$0.8 \pi$. Two sligthly higher flare peaks have been detected at phases $0.5 \pi$ and $2 \pi$ respectively, but otherwise there does not seem to be any pattern.
The flare peak at normalized phase distribution can be seen in figure \ref{fig:TYC_4595-107-1-flarepeaks_1.27}. The strongest flare was detected at normalized phase \textasciitilde$0.8 \pi$. Two sligthly higher flare peaks have been detected at phases $0.5 \pi$ and $2 \pi$ respectively, but otherwise there does not seem to be any pattern.\\
All of the folded lightcurves of TYC 4595-107-1 can be found in appendix \ref{apB:TYC_4595-107-1}, figures \ref{apB:fig:TYC_4595-107-1-TESS_foldedLC1} and \ref{apB:fig:TYC_4595-107-1-TESS_foldedLC2}.
\begin{figure}[pt!]
\includegraphics[width=.95\textwidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1-Flarepeaks_maxY-1.2782052782832685.png}
@@ -470,6 +471,7 @@ The flare peak at normalized phase distribution can be seen in figure \ref{fig:T
\FloatBarrier
\subsection{V* V471 Tau}
\label{results:v471_tau}
V471 Tau is a post-common envelope binary system consiting of a K2 type dwarf and a white dwarf (\cite{v471tau_revised}). The K2 dwarf has a always present dominant spot, which faces the white dwarf (\cite{V471tau_magnetic_activity}).
Figures \ref{fig:V471Tau-Flarecount-10_Bins} and \ref{fig:V471Tau-Flarecount-30_Bins} show the histograms of 5 TESS folded lightcurves for V471 Tau with 10 and 30 bins respectively. The TESS lightcurves used are of sectors 42, 43, 44, 70 and 71. The lightcurve of K2 target table ID 80 was rejected by the algorithm. Due to the lightcurve spanning 90 days, and the variability in spots, the folding and fitting algorithm could not produce a reliable output.
@@ -533,6 +535,7 @@ Figure \ref{fig:V471Tau-flarepeaks_1.053} shows the normalized phase and peak of
\FloatBarrier
\subsection{V* HK Aqr}
\label{results:hk_aqr}
HK Aqr is a M dwarf with a mass of 0.57 $M_\odot$, a radius of 0.53 $R_\odot$ and is around 22.3 pc away from our solar system. Its effective temperature is aroun 3800 K (\cite{conch_shell_m_dwarfs}). It was observed in four TESS sectors.
HK Aqr is mentioned here, as it is a star, for which the optimize fold algorithm partially broke. This happened for its lightcurves for the sectors 29 and 42. The algorithm found for both periodograms a second signal for a possible period. This resulted in the folded lightcurves seen in figures \ref{fig:HKAqr-TESS29_foldedLC} and \ref{fig:HKAqr-TESS42_foldedLC}. Figures \ref{fig:HKAqr-Flarecount-10_Bins} and \ref{fig:HKAqr-Flarecount-30_Bins} were created with this dataset.\\
@@ -632,6 +635,7 @@ The flare count in figure \ref{fig:HKAqr-Flarecount-30_Bins_Period} is very low.
\FloatBarrier
\subsection{KOI-256}
\label{results:koi_256}
KOI-256 is, similarly to V471 Tau, a binary system consisting of a M dwarf and a white dwarf (\cite{eclipsing_binaries_koi_256}, \cite{koi_256_effects_of_magnetic}). It has a mass of 0.51 M$_\odot$, a radius of 0.540 R$_\odot$ and an effective temperature of 3450 K (\cite{eclipsing_binaries_koi_256}). Similarly to HK Aqr, a second periodicity was detected, which was the used to fold for spot modulation. This happened for Kepler target table ids 37, 38, 53 and TESS sector 80.\\
Figure \ref{fig:KOI-256-Flarecount-10_Bins} shows the histogram with 10 bins for KOI-256 with all detected spot modulations, including the mentioned ones that were wrongfully detected. This figure shows a increase in flare count around phase $1 \pi$, which peaks at phases $0.7 \pi$ and around $1.4 \pi$. Additionally there appears a peak at phase $1.7 \pi$.
@@ -656,7 +660,7 @@ Increasing the bins to 30 (figure \ref{fig:KOI-256-Flarecount-30_Bins}) shows cl
\label{fig:KOI-256-Flarecount}
\end{figure}
Figures \ref{fig:KOI-256-Flarecount-10_Bins_Period} and \ref{fig:KOI-256-Flarecount-30_Bins_Period} show the histograms based on the, by the optimized fold algorithm determined, period folded lightcurves. Therefor only the period folded lightcurves from Kepler target table id 37, 38, 53 and TESS sector 80 were used.
Figures \ref{fig:KOI-256-Flarecount-10_Bins_Period} and \ref{fig:KOI-256-Flarecount-30_Bins_Period} show the histograms based on the, by the optimized fold algorithm determined, period folded lightcurves. Therefor only the period folded lightcurves from Kepler target table id 37, 38, 53 and TESS sector 80 were used. The folded lightcurves can be found in appendix \ref{apB:koi-256}, figures \ref{apB:fig:KOI-256-Kepler_foldedLC} and \ref{apB:fig:KOI-256-TESS_foldedLC}.
In figure \ref{fig:KOI-256-Flarecount-10_Bins_Period}, which shows a histogram with 10 bins for the flare distribution across the normalized phase, there is a clear increase of flares seen around the minima at phase $1 \pi$. The distribution nearly reminds one of a normal distribution, with the exception that the last two bins around phase $1.8 \pi$ to $2 \pi$ do not fall off as much as the first bin at phase $0 \pi$ does compared to the bins in the center.\\
Looking at figure \ref{fig:KOI-256-Flarecount-30_Bins_Period} which shows the same data, just with 30 bins, the peak at the phase minimum at $1 \pi$ is still present. Additionally there are three more peaks visible at around phases $0.3 \pi$, $1.4 \pi$ and $2 \pi$. These three peaks are only 1 bin wide and stand out far from their surrounding by around 1.5 times the errorbar. The peak in the center on the otherhand has gradual increases/descreases before and after, with the exception of the dip in the bin right before at around phase $0.9 \pi$.
@@ -678,7 +682,7 @@ Looking at figure \ref{fig:KOI-256-Flarecount-30_Bins_Period} which shows the sa
\label{fig:KOI-256-Flarecount_Period}
\end{figure}
Comparing the results of the flare peak distributions across the normalized phases of the two datasets in figure \ref{fig:KOI-256-flarepeaks} shows that the highest normalized flare peaks of up to 1.7 were detected in the lightcurves with proper period detection. Comparing flare peaks which exist in both data sample, one can see that the highest peak of \subref{fig:KOI-256-flarepeaks_1.3_period} at around phase $0.8 \pi$ and a normalized peak of \textasciitilde1.3 was moved to around phase $0.4 \pi$ in figure \subref{fig:KOI-256-flarepeaks_1.7_spot} due to the additional found periodicity.
Comparing the results of the flare peak distributions across the normalized phases of the two datasets in figure \ref{fig:KOI-256-flarepeaks} shows that the highest normalized flare peaks of up to 1.7 were detected in the lightcurves with proper period detection (folded lightcurves in appendix \ref{apB:koi-256}, figures \ref{apB:fig:KOI-256-Kepler_periodfoldedLC} and \ref{apB:fig:KOI-256-TESS_periodfoldedLC}). Comparing flare peaks which exist in both data sample, one can see that the highest peak of \subref{fig:KOI-256-flarepeaks_1.3_period} at around phase $0.8 \pi$ and a normalized peak of \textasciitilde1.3 was moved to around phase $0.4 \pi$ in figure \subref{fig:KOI-256-flarepeaks_1.7_spot} due to the additional found periodicity.
\begin{figure}[pt!]
\centering
@@ -694,6 +698,54 @@ Comparing the results of the flare peak distributions across the normalized phas
\caption{Period folded}
\label{fig:KOI-256-flarepeaks_1.3_period}
\end{subfigure}
\caption{Distribution of flare peaks in relation to the normalized phase at which they occured. Y-Axis shows the flare peak and is limited to the value of the highest peak detected. The x-axis shows the normalized phase.}
\caption{Distribution of flare peaks for KOI-256 in relation to the normalized phase at which they occured. Y-Axis shows the flare peak and is limited to the value of the highest peak detected. The x-axis shows the normalized phase.}
\label{fig:KOI-256-flarepeaks}
\end{figure}
\FloatBarrier
\subsection{2MASS J19230963+3739397}
\label{results:2MASS_J19230963p3739397}
2MASS J19230963+3739397, also known as KIC 2300039 or TIC 122672447, is a M dwarf around 213 pc away from our solar system (\cite{simbad}). It was observed in 3 Kepler target table IDs as well as 4 TESS sectors. The results for its flare distributions can be seen in figure \ref{fig:2MASS_J19230963p3739397-Flarecount}. It was selected as an example as it shows quite the opposite of what was expected. As seen in the histogram with 10 bins (figure \ref{fig:2MASS_J19230963p3739397-Flarecount-10_Bins}) it shows an increased flare occurance during the transition between phase minimum and maximum and during the maximum (phase $1.3 \pi$ to $2 \pi$). An additional significant peak is seen in the second bin. The flare count during the phase minimum at phase $1 \pi$ is at a minimum. Increasing the bin count to 30 (see figure \ref{fig:2MASS_J19230963p3739397-Flarecount-30_Bins}) creates a similarly shaped histogram. The errorbars increase in size relatively though, and makes the individual less accurate. The folded lightcurves for the Kepler target table IDs 47, 48 and 49 can be seen in figure \ref{fig:2MASS_J19230963p3739397-Kepler_foldedLCs}. There were no flares detected in the TESS lightcurves. As seen in the Kepler lightcurves, flare peaks as high as 1.5 have been detected, all around the phase maxima.
\begin{figure}[pt!]
\centering
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/2MASS J19230963+3739397/2MASS J19230963+3739397-Flarecount-10_Bins.png}
\caption{10 bins}
\label{fig:2MASS_J19230963p3739397-Flarecount-10_Bins}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/2MASS J19230963+3739397/2MASS J19230963+3739397-Flarecount-30_Bins.png}
\caption{30 bins}
\label{fig:2MASS_J19230963p3739397-Flarecount-30_Bins}
\end{subfigure}
\caption{Histograms of 2MASS J19230963+3739397 across the phase showing the number of flares in each bin. The error bar shows the standard deviation for the histogram. The blue lines show the various fits for the folded lightcurves used to generate the data, with the phase minimum at $1 \pi$ and phase maximum at $0 \pi$/$2 \pi$.}
\label{fig:2MASS_J19230963p3739397-Flarecount}
\end{figure}
\begin{figure}[pt!]
\centering
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/2MASS J19230963+3739397/2MASS J19230963+3739397_Kepler-47-foldedLC-marked_fit_flares.png}
\caption{Kepler target table ID 47}
\label{fig:2MASS_J19230963p3739397-Kepler47_foldedLC}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/2MASS J19230963+3739397/2MASS J19230963+3739397_Kepler-48-foldedLC-marked_fit_flares.png}
\caption{Kepler target table ID 48}
\label{fig:2MASS_J19230963p3739397-Kepler48_foldedLC}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/2MASS J19230963+3739397/2MASS J19230963+3739397_Kepler-49-foldedLC-marked_fit_flares.png}
\caption{Kepler target table ID 48}
\label{fig:2MASS_J19230963p3739397-Kepler48_foldedLC}
\end{subfigure}
\caption{Folded lightcurves for 2MASS J19230963+3739397. The blue lines shows the sine fits calculated. The red crosses indicate the detected flare peaks.}
\label{fig:2MASS_J19230963p3739397-Kepler_foldedLCs}
\end{figure}