454 lines
31 KiB
TeX
454 lines
31 KiB
TeX
\chapter{Results \label{sec:results}}
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This chapter includes the main results of this study. The data for the plots were generated using the "New FC" Button from the main GUI described in section \ref{sec:gui:data_processing}.
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The results contain plots for the different spectral types M, K, G, and F as well as combined results of every possible combination. Additionally for all these possible combinations, plots with data limits, e.g. only stars with a rotational period of less than 2 days or minimal/maximal normalized flare peak limits, were also generated. Additionally plots for stars with a more detailed spectral type like M0 or G5 were created. Furthermore there is a selection of individual star results. For every plot group a CSV file is generated, which contains information about every star and flare used to generate the plot.
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The results also only contain the data of folded lightcurves which could be fitted with a sine function and less than 30 iterations of the fold optimization. The data which uses polynomial fits or both sine and polynomial fits as well as all plots and the accompanying CSV files are available at \href{https://drive.google.com/drive/folders/1L_F21W3WwZicVZg9052B12B2hJNuJBwK?usp=drive_link}{google drive}.
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\section{M dwarfs \label{sec:results:m_dwarfs}}
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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}.\\
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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.\\
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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.\\
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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.
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\begin{figure}[pt!]
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\centering
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/M/M-Flarecount-10_Bins.png}
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\caption{10 bins}
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\label{fig:M-Flarecount-10_Bins}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/M/M-Flarecount-30_Bins.png}
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\caption{30 bins}
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\label{fig:M-Flarecount-30_Bins}
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\end{subfigure}
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\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 $1 \pi$.}
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\label{fig:M-Flarecount}
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\end{figure}
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Filtering the data by the minimal flare peak (see figures \ref{fig:M-Flarecount-10_Bins_1.25_peak} to \ref{fig:M-Flarecount-30_Bins_1.5_peak}), makes the trend of figure \ref{fig:M-Flarecount-30_Bins} clearer. There are increasinly more flares in the minima at phase $1 \pi$ (more/bigger star spots) and maxima at phase $0$ and $2 \pi$ (less/smaller star spots) compared to the transitions.
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Taking a closer look at figure \ref{fig:M-Flarecount-10_Bins_1.25_peak}, which accounts only for normalized flare peaks greater than 1.25 with 10 bins, the same dips (around phases $0.5 \pi$ and $1.5 \pi$) as in the previous figure (figure \ref{fig:M-Flarecount-30_Bins}) are visible. Comparing to the dip visible in figure \ref{fig:M-Flarecount-10_Bins}, it widened by 1 bin.
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At phase \textasciitilde$1.7 \pi$ to $2 \pi$ there is a major peak. While the last bin overlaps slightly with the one at phase $0.9 \pi$ with accounting for error, the second to last does not.\\
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The same data, just with 30 bins can be seen in figure \ref{fig:M-Flarecount-30_Bins_1.25_peak}. There are no continuous peaks like in the previous figure, but at the same phases there are bins with an increased number of flares. Additionally, at around phase $0.6 \pi$, there is a larger amount of flares compared to the bins next to it.\\
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Increasing the normalized minimal flare peak further to 1.5 decreases the total amount of flares further, which results in a comparatively large error. This makes the error half the size or even larger than some of the bins in figure \ref{fig:M-Flarecount-10_Bins_1.5_peak}. Nontheless its visible that the largest flares seem to appear more often around phase $1 \pi$ and phase $0 \pi$/$2 \pi$. Including the error, those peaks are still higher than the flare count of the in previous figures mentioned dips.\\
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Increasing the bin count to 30 (see figure \ref{fig:M-Flarecount-30_Bins_1.5_peak}) decreases the individual bin heights so far, that the errorbars start to explode in size, which causes all of them to overlap and not give any proper results.
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\begin{figure}[pt!]
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\centering
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\begin{subfigure}[b]{.49\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/M/M_minFlarePeak_1.25-Flarecount-10_Bins.png}
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\caption{Minimum flare peak 1.25, 10 bins}
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\label{fig:M-Flarecount-10_Bins_1.25_peak}
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\end{subfigure}
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\hfill
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\begin{subfigure}[b]{.49\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/M/M_minFlarePeak_1.25-Flarecount-30_Bins.png}
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\caption{Minimum flare peak 1.25, 30 bins}
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\label{fig:M-Flarecount-30_Bins_1.25_peak}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[b]{.49\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/M/M_minFlarePeak_1.5-Flarecount-10_Bins.png}
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\caption{Minimum flare peak 1.5, 10 bins}
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\label{fig:M-Flarecount-10_Bins_1.5_peak}
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\end{subfigure}
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\hfill
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\begin{subfigure}[b]{.49\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/M/M_minFlarePeak_1.5-Flarecount-30_Bins.png}
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\caption{Minimum flare peak 1.5, 30 bins}
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\label{fig:M-Flarecount-30_Bins_1.5_peak}
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\end{subfigure}
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\caption{Histograms showing the amount of flares with a normalized peak of greater than 1.25 (\subref{fig:M-Flarecount-10_Bins_1.25_peak} and \subref{fig:M-Flarecount-30_Bins_1.25_peak})/1.5 (\subref{fig:M-Flarecount-10_Bins_1.5_peak} and \subref{fig:M-Flarecount-30_Bins_1.5_peak}) 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} and \subref{fig:M-Flarecount-10_Bins_1.5_peak})/30 (\subref{fig:M-Flarecount-30_Bins_1.25_peak} and \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 $1 \pi$.}
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\label{fig:M-Flarecount-peaks}
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\end{figure}
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\FloatBarrier
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\section{K dwarfs \label{sec:results:k_dwarfs}}
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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}.\\
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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}.\\
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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.
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\begin{figure}[pt!]
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\centering
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/K/K-Flarecount-10_Bins.png}
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\caption{10 bins}
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\label{fig:K-Flarecount-10_Bins}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/K/K-Flarecount-30_Bins.png}
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\caption{30 bins}
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\label{fig:K-Flarecount-30_Bins}
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\end{subfigure}
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\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 $1 \pi$.}
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\label{fig:K-Flarecount}
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\end{figure}
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\FloatBarrier
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\section{G dwarfs \label{sec:results:g_dwarfs}}
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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.\\
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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 $1.1 \pi$.\\
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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.
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\begin{figure}[pt!]
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\centering
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/G/G-Flarecount-10_Bins.png}
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\caption{10 bins}
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\label{fig:G-Flarecount-10_Bins}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/G/G-Flarecount-30_Bins.png}
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\caption{30 bins}
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\label{fig:G-Flarecount-30_Bins}
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\end{subfigure}
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\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 $1 \pi$.}
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\label{fig:G-Flarecount}
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\end{figure}
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\FloatBarrier
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\section{F dwarfs \label{sec:results:f_dwarfs}}
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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}.\\
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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.
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\begin{figure}[pt!]
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\centering
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/F/F-Flarecount-10_Bins.png}
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\caption{10 bins}
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\label{fig:F-Flarecount-10_Bins}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/F/F-Flarecount-30_Bins.png}
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\caption{30 bins}
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\label{fig:F-Flarecount-30_Bins}
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\end{subfigure}
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\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 $1 \pi$.}
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\label{fig:F-Flarecount}
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\end{figure}
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\FloatBarrier
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\section{Combined results \label{sec:results:combined}}
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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.\\
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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.\\
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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 $1.5 \pi$.
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\begin{figure}[pt!]
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\centering
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/MKGF-Flarecount-10_Bins.png}
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\caption{10 bins}
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\label{fig:MKGF-Flarecount-10_Bins}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/MKGF-Flarecount-30_Bins.png}
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\caption{30 bins}
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\label{fig:MKGF-Flarecount-30_Bins}
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\end{subfigure}
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\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 $1 \pi$.}
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\label{fig:MKGF-Flarecount}
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\end{figure}
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\FloatBarrier
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\section{Individual stars \label{sec:results:individual}}
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This section contains a selection of results for individual stars. The results for this section were selected because either they match what this study was looking for or because the opposite is the case or were in some other way interesting.
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\subsection{BD-08 995}
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\begin{figure}[pt!]
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\centering
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/BD-08_995/BD-08\space\space\space995-Flarecount-10_Bins.png}
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\caption{10 bins}
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\label{fig:BD-08_995-Flarecount-10_Bins}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/BD-08_995/BD-08\space\space\space995-Flarecount-30_Bins.png}
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\caption{30 bins}
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\label{fig:BD-08_995-Flarecount-30_Bins}
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\end{subfigure}
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\caption{Histograms of BD-08 995 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 $0 \pi$/$2 \pi$.}
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\label{fig:BD-08_995-Flarecount}
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\end{figure}
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\begin{figure}[pt!]
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\centering
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/BD-08_995/BD-08\space\space\space995_TESS-5-foldedLC-marked_fit_flares.png}
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\caption{TESS Sector 5}
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\label{fig:BD-08_995-TESS5_foldedLC}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/BD-08_995/BD-08\space\space\space995_TESS-32-foldedLC-marked_fit_flares.png}
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\caption{TESS Sector 32}
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\label{fig:BD-08_995-TESS32_foldedLC}
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\end{subfigure}
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\caption{Folded lightcurves for BD-08 995. The blue lines shows the sine fits calculated. The red crosses indicate the detected flare peaks.}
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\label{fig:BD-08_995-TESS_foldedLCs}
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\end{figure}
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\FloatBarrier
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\subsection{TYC 1360-957-1}
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\begin{figure}[pt!]
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\centering
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/TYC_1360-957-1/TYC 1360-957-1-Flarecount-10_Bins.png}
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\caption{10 bins}
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\label{fig:TYC_1360-957-1-Flarecount-10_Bins}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/TYC_1360-957-1/TYC 1360-957-1-Flarecount-30_Bins.png}
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\caption{30 bins}
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\label{fig:TYC_1360-957-1-Flarecount-30_Bins}
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\end{subfigure}
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\caption{Histograms of TYC 1360-957-1 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 $0 \pi$/$2 \pi$.}
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\label{fig:TYC_1360-957-1-Flarecount}
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\end{figure}
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\begin{figure}[pt!]
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\centering
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/TYC_1360-957-1/TYC 1360-957-1_TESS-44-foldedLC-marked_fit_flares.png}
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\caption{TESS Sector 44}
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\label{fig:TYC_1360-957-1-TESS44_foldedLC}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/TYC_1360-957-1/TYC 1360-957-1_TESS-45-foldedLC-marked_fit_flares.png}
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\caption{TESS Sector 45}
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\label{fig:TYC_1360-957-1-TESS45_foldedLC}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/TYC_1360-957-1/TYC 1360-957-1_TESS-46-foldedLC-marked_fit_flares.png}
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\caption{TESS Sector 46}
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\label{fig:TYC_1360-957-1-TESS46_foldedLC}
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\end{subfigure}
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\caption{Folded lightcurves for TYC 1360-957-1. The blue lines shows the sine fits calculated. The red crosses indicate the detected flare peaks.}
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\label{fig:TYC_1360-957-1-TESS_foldedLCs}
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\end{figure}
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\FloatBarrier
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\subsection{TYC 4595-107-1}
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\begin{figure}[pt!]
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\centering
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1-Flarecount-10_Bins.png}
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\caption{10 bins}
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\label{fig:TYC_4595-107-1-Flarecount-10_Bins}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[b]{.95\textwidth}
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\centering
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\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1-Flarecount-30_Bins.png}
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\caption{30 bins}
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\label{fig:TYC_4595-107-1-Flarecount-30_Bins}
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\end{subfigure}
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\caption{Histograms of TYC 4595-107-1 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 $0 \pi$/$2 \pi$.}
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\label{fig:TYC_4595-107-1-Flarecount}
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\end{figure}
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\FloatBarrier
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\subsection{V* V471 Tau}
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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}).
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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.
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The blue lines show the used fits for the individual folded lightcurves.
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In the first figure, there appear two different peaks. The first being at phase $0.5 \pi$, and the second one at phase $1.1 \pi$. These bins are significantly higher than the surrounding bins with 13/15 flares respectively compared to 1 to 8 on the other bins.\\
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As seen in figures \ref{fig:V471Tau-TESS42_foldedLC}, \ref{fig:V471Tau-TESS43_foldedLC} and \ref{fig:V471Tau-TESS44_foldedLC} the transit of the white dwarf occurs at around phase 0 (in these figures) which translates to phase $1 \pi$ in the normalized phase.\\
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Increasing the bins to 30 (figure \ref{fig:V471Tau-Flarecount-30_Bins}) does not change the result much. Due to the individual flare count being lower per bin compared to the previous figure, the errorbars increase in size comparatively. There are still peaks at around $0.5 \pi$ and $1 \pi$.
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\begin{figure}[pt!]
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|
\centering
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|
\begin{subfigure}[b]{.95\textwidth}
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|
\centering
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|
\includegraphics[width=\linewidth]{plots/sine/V471Tau/V_star_ V471 Tau-Flarecount-10_Bins.png}
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\caption{10 bins}
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\label{fig:V471Tau-Flarecount-10_Bins}
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\end{subfigure}
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\vspace{1em}
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\begin{subfigure}[b]{.95\textwidth}
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|
\centering
|
|
\includegraphics[width=\linewidth]{plots/sine/V471Tau/V_star_ V471 Tau-Flarecount-30_Bins.png}
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\caption{30 bins}
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\label{fig:V471Tau-Flarecount-30_Bins}
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\end{subfigure}
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\caption{Histograms of V471 Tau 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 $0 \pi$/$2 \pi$.}
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\label{fig:V471Tau-Flarecount}
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\end{figure}
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Looking at the folded lightcurves for this star (see figures \ref{fig:V471Tau-TESS42_foldedLC}, \ref{fig:V471Tau-TESS43_foldedLC} and \ref{fig:V471Tau-TESS44_foldedLC}), the transit of the white dwarf (sudden dip in the folded lightcurve) is clearly visible, and always happens around phase 0.
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|
\begin{figure}[pt!]
|
|
\centering
|
|
\begin{subfigure}[b]{.95\textwidth}
|
|
\centering
|
|
\includegraphics[width=\linewidth]{plots/sine/V471Tau/V_star_ V471 Tau_TESS-42-foldedLC-marked_fit_flares.png}
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\caption{TESS Sector 42}
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\label{fig:V471Tau-TESS42_foldedLC}
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\end{subfigure}
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\vspace{1em}
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|
\begin{subfigure}[b]{.95\textwidth}
|
|
\centering
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|
\includegraphics[width=\linewidth]{plots/sine/V471Tau/V_star_ V471 Tau_TESS-43-foldedLC-marked_fit_flares.png}
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|
\caption{TESS Sector 43}
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\label{fig:V471Tau-TESS43_foldedLC}
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\end{subfigure}
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|
\vspace{1em}
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|
\begin{subfigure}[b]{.95\textwidth}
|
|
\centering
|
|
\includegraphics[width=\linewidth]{plots/sine/V471Tau/V_star_ V471 Tau_TESS-44-foldedLC-marked_fit_flares.png}
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|
\caption{TESS Sector 44}
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\label{fig:V471Tau-TESS44_foldedLC}
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\end{subfigure}
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\caption{Folded lightcurves for V* V471 Tau. The blue lines shows the sine fits calculated. The red crosses indicate the detected flare peaks.}
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\label{fig:V471Tau-TESS_foldedLCs}
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|
\end{figure}
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|
Figure \ref{fig:V471Tau-flarepeaks_1.053} shows the normalized phase and peak of each flare in the data during which part of the phase it happened. It shows that the largest flares happened at around phase $0.5 \pi$, $1 \pi$ and $1.5 \pi$. The phase in which the white dwarf transit happens is at around phase $1 \pi$.
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|
\begin{figure}[pt!]
|
|
\includegraphics[width=.95\textwidth]{plots/sine/V471Tau/V_star_ V471 Tau-Flarepeaks_maxY-1.0539907609848342.png}
|
|
\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.}
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|
\label{fig:V471Tau-flarepeaks_1.053}
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\end{figure}
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\FloatBarrier
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|
\subsection{V* HK Aqr}
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|
|
|
\begin{figure}[pt!]
|
|
\centering
|
|
\begin{subfigure}[b]{.95\textwidth}
|
|
\centering
|
|
\includegraphics[width=\linewidth]{plots/sine/HKAqr/V_star_ HK Aqr-Flarecount-10_Bins.png}
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|
\caption{10 bins}
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\label{fig:HKAqr-Flarecount-10_Bins}
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|
\end{subfigure}
|
|
\vspace{1em}
|
|
\begin{subfigure}[b]{.95\textwidth}
|
|
\centering
|
|
\includegraphics[width=\linewidth]{plots/sine/HKAqr/V_star_ HK Aqr-Flarecount-30_Bins.png}
|
|
\caption{30 bins}
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|
\label{fig:HKAqr-Flarecount-30_Bins}
|
|
\end{subfigure}
|
|
\caption{Histograms of V* HK Aqr 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:HKAqr-Flarecount}
|
|
\end{figure}
|
|
|
|
\begin{figure}[pt!]
|
|
\centering
|
|
\begin{subfigure}[b]{.95\textwidth}
|
|
\centering
|
|
\includegraphics[width=\linewidth]{plots/sine/HKAqr/V_star_ HK Aqr_TESS-2-foldedLC-marked_fit_flares.png}
|
|
\caption{TESS Sector 2}
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|
\label{fig:HKAqr-TESS2_foldedLC}
|
|
\end{subfigure}
|
|
\vspace{1em}
|
|
\begin{subfigure}[b]{.95\textwidth}
|
|
\centering
|
|
\includegraphics[width=\linewidth]{plots/sine/HKAqr/V_star_ HK Aqr_TESS-29-foldedLC-marked_fit_flares.png}
|
|
\caption{TESS Sector 29}
|
|
\label{fig:HKAqr-TESS29_foldedLC}
|
|
\end{subfigure}
|
|
\vspace{1em}
|
|
\begin{subfigure}[b]{.95\textwidth}
|
|
\centering
|
|
\includegraphics[width=\linewidth]{plots/sine/HKAqr/V_star_ HK Aqr_TESS-42-foldedLC-marked_fit_flares.png}
|
|
\caption{TESS Sector 42}
|
|
\label{fig:HKAqr-TESS42_foldedLC}
|
|
\end{subfigure}
|
|
\begin{subfigure}[b]{.95\textwidth}
|
|
\centering
|
|
\includegraphics[width=\linewidth]{plots/sine/HKAqr/V_star_ HK Aqr_TESS-69-foldedLC-marked_fit_flares.png}
|
|
\caption{TESS Sector 69}
|
|
\label{fig:HKAqr-TESS69_foldedLC}
|
|
\end{subfigure}
|
|
\caption{Folded lightcurves for V* HK Aqr. The blue lines shows the sine fits calculated. The red crosses indicate the detected flare peaks.}
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|
\label{fig:HKAqr-TESS_foldedLCs}
|
|
\end{figure}
|
|
|
|
\begin{figure}[pt!]
|
|
\centering
|
|
\begin{subfigure}[b]{.95\textwidth}
|
|
\centering
|
|
\includegraphics[width=\linewidth]{plots/sine/HKAqr/V_star_ HK Aqr-Flarecount-10_Bins_Period.png}
|
|
\caption{10 bins}
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|
\label{fig:HKAqr-Flarecount-10_Bins_Period}
|
|
\end{subfigure}
|
|
\vspace{1em}
|
|
\begin{subfigure}[b]{.95\textwidth}
|
|
\centering
|
|
\includegraphics[width=\linewidth]{plots/sine/HKAqr/V_star_ HK Aqr-Flarecount-30_Bins_Period.png}
|
|
\caption{30 bins}
|
|
\label{fig:HKAqr-Flarecount-30_Bins_Period}
|
|
\end{subfigure}
|
|
\caption{Histograms of V* HK Aqr 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:HKAqr-Flarecount_Period}
|
|
\end{figure}
|
|
|
|
\begin{figure}[pt!]
|
|
\centering
|
|
\begin{subfigure}[b]{.95\textwidth}
|
|
\centering
|
|
\includegraphics[width=\linewidth]{plots/sine/HKAqr/V_star_ HK Aqr_TESS-29-periodFoldedLC-marked_fit_flares.png}
|
|
\caption{TESS Sector 29}
|
|
\label{fig:HKAqr-TESS29_foldedLC_Period}
|
|
\end{subfigure}
|
|
\vspace{1em}
|
|
\begin{subfigure}[b]{.95\textwidth}
|
|
\centering
|
|
\includegraphics[width=\linewidth]{plots/sine/HKAqr/V_star_ HK Aqr_TESS-42-periodFoldedLC-marked_fit_flares.png}
|
|
\caption{TESS Sector 42}
|
|
\label{fig:HKAqr-TESS42_foldedLC_Period}
|
|
\end{subfigure}
|
|
\caption{Folded lightcurves for V* HK Aqr. The blue lines shows the sine fits calculated. The red crosses indicate the detected flare peaks.}
|
|
\label{fig:HKAqr-TESS_foldedLCs_Period}
|
|
\end{figure}
|
|
|
|
\FloatBarrier
|
|
\subsection{KOI-256}
|
|
|
|
detect twice a strong faster periodicity, ~1.38, ~0.69 days, Kepler 37, 38, 53, 80
|
|
|