update koi 256

Physics_Thesis_Template/content/chapter-results.tex

@@ -495,5 +495,70 @@ The flare count in figure \ref{fig:HKAqr-Flarecount-30_Bins_Period} is very low.
 \FloatBarrier
 \subsection{KOI-256}
 
-detect twice a strong faster periodicity, ~1.38, ~0.69 days, Kepler 37, 38, 53, 80
+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 $1.7 \pi$. 
+Increasing the bins to 30 (figure \ref{fig:KOI-256-Flarecount-30_Bins}) shows clearer peaks at phase $0.7 \pi$ as well as $1.2 \pi$. Including errorbars, the mentioned peaks of both figures are above their surrounding bins.
 
+
+\begin{figure}[pt!]
+    \centering
+    \begin{subfigure}[b]{.95\textwidth}
+        \centering
+        \includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256-Flarecount-10_Bins.png}
+        \caption{10 bins}
+        \label{fig:KOI-256-Flarecount-10_Bins}
+    \end{subfigure}
+    \vspace{1em}
+    \begin{subfigure}[b]{.95\textwidth}
+        \centering
+        \includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256-Flarecount-30_Bins.png}
+        \caption{30 bins}
+        \label{fig:KOI-256-Flarecount-30_Bins}
+    \end{subfigure}
+    \caption{Histograms of KOI-256 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: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.
+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 $0.9 \pi$.
+
+\begin{figure}[pt!]
+    \centering
+    \begin{subfigure}[b]{.95\textwidth}
+        \centering
+        \includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256-Flarecount-10_Bins_Period.png}
+        \caption{10 bins}
+        \label{fig:KOI-256-Flarecount-10_Bins_Period}
+    \end{subfigure}
+    \vspace{1em}
+    \begin{subfigure}[b]{.95\textwidth}
+        \centering
+        \includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256-Flarecount-30_Bins_Period.png}
+        \caption{30 bins}
+        \label{fig:KOI-256-Flarecount-30_Bins_Period}
+    \end{subfigure}
+    \caption{Histograms of KOI-256 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: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.
+
+\begin{figure}[pt!]
+    \centering
+    \begin{subfigure}[b]{.95\textwidth}
+        \centering
+        \includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256-Flarepeaks_maxY-1.7092845644155863.png}
+        \caption{Spot modulation folded}
+        \label{fig:KOI-256-flarepeaks_1.7_spot}
+    \end{subfigure}
+    \vspace{1em}
+    \begin{subfigure}[b]{.95\textwidth}
+        \centering
+        \includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256-Flarepeaks_maxY-1.3100095148043271_Period.png}
+        \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.}
+    \label{fig:KOI-256-flarepeaks}
+\end{figure}