add very basic discussion

Physics_Thesis_Template/bib-refs.bib

@@ -1,3 +1,17 @@
+@ARTICLE{solar_like_superflares,
+       author = {{Maehara}, Hiroyuki and {Shibayama}, Takuya and {Notsu}, Shota and {Notsu}, Yuta and {Nagao}, Takashi and {Kusaba}, Satoshi and {Honda}, Satoshi and {Nogami}, Daisaku and {Shibata}, Kazunari},
+        title = "{Superflares on solar-type stars}",
+      journal = {\nat},
+         year = 2012,
+        month = may,
+       volume = {485},
+       number = {7399},
+        pages = {478-481},
+          doi = {10.1038/nature11063},
+       adsurl = {https://ui.adsabs.harvard.edu/abs/2012Natur.485..478M},
+      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
+}
+
 @ARTICLE{connection_starspots_flares_ms_kepler,
        author = {{Roettenbacher}, Rachael M. and {Vida}, Kriszti{\'a}n},
         title = "{The Connection between Starspots and Flares on Main-sequence Kepler Stars}",

Physics_Thesis_Template/content/chapter-discussion.tex

@@ -1,3 +1,40 @@
 \chapter{Discussion \label{sec:discussion}}
 
+M dwarfs, all data, no significant dependency of flare appearance on phase using 10 bins.
+30 bins -> either 2 dips during the transition minima <-> maxima or increase of flare occurance during minima and maxima.
+Looking at stronger flares only (min 1.25/1.5 flare peak) peaks during minima, stronger peak during phase maxima, in both 10 and 30 bin histograms.
+Limiting to max 1.01, makes dip (compared to all data) clearer. Generally more flares during maxima than minima. 
+Limit to max 1.05, nearly identical histograms to all data. (different result to \cite{connection_starspots_flares_ms_kepler})
+\\\\
+
+K dwarfs, all data, siginificant peak at phase minimum, peak dominated by V471 Tau (discussed later). Slightly more flares from maximum to minimum than minimum to maximum in 10 bins. 30 bins larger dips but also larger peaks in second half of phase compared to first half.
+limiting to min 1.05 -> three peaks, dip after maximum and on at phase 1 $\pi$. gradual decrease after minimum. V471 Taus peaks at right before and right after phase minimum.
+limiting to <1.01 and 1.05, makes histogram look more and more like with all data, similarly to \cite{connection_starspots_flares_ms_kepler} peak in center (compared to their M/K plot), but additionally also peak at phase maximum.
+max 1.05 already most flares, very similar to with all data.
+
+G dwarfs, significant results, increase of flare appearance during phase minimum. Most flares are <1.05 (flares on solar like stars that increase brightness by 0.1\% to 1\% already superflares, \cite{solar_like_superflares}) -> most/all detected flares superflares. Overall dependency on phase/spot appearance.
+Limiting to flares >1.05 -> flares during minima and transitions between minima <-> maxima, increasing bins -> more data would be required.
+
+For F dwarfs, overall too little data, but the not siginificant amount detected all during phase minimum, could be similar to G dwarfs?
+
+All data combined, peak at phase minimum dominated by G/K dwarfs, dip in transition maxima -> minima dominated by dip from M dwarf results.
+
+Individual star results (subset taken):
+BD-08 995 (G type): shows a strong flare/spot dependence for amount, flare peaks not dependent on phase
+
+TYC 1360-957-1 (K type): no clear dependence on spots for flare count (1 peak around maximum, 1 during transition, another at minimum), less siginificant with more bins
+Shows strongest flares right before phase minimum though.
+
+TYC 4595-107-1 (G type): similar to BD-08 995, increase of flares right before minimum, slight (less significant) increase at maximum. (appending folded lightcurves in appendix)
+
+V471 Tau: binary with white dwarf, most flares around white dwarf transit -> magnetic interactions likely (ref. to V471 Tau specific papers)
+Strongest flares also around that
+
+HK Aqr (M dwarf): not fully trusted results, half period was detected for 2/4 lightcurves (original folding had 2 fit maxima too far away from edges, caused it to check for if half period signal was detected and use that)
+only full period results show overall less flares during the maxima
+
+KOI-256 (M dwarf): similar issue as HK Aqr, in 2/7 Kepler, 2/3 TESS lightcurves, like V471 Tau binary with white dwarf, shows siginficant dependency on spots in with period folded results. (appending folded lightcurves in appendix)
+Largest flares, when period folded only, also at around 0.8 $\pi$ (same flare shifted to 2 $\pi$ in spot modulated fold), otherwise flare energies well spread.
+
+
 

Physics_Thesis_Template/content/chapter-results.tex

@@ -71,6 +71,11 @@ Increasing the bin count to 30 (see figure \ref{fig:M-Flarecount-30_Bins_1.5_pea
     \label{fig:M-Flarecount-peaks_1.5_peak}
 \end{figure}
 
+Doing the opposite and only plotting the histograms for flares with normalized peaks of less than 1.01 can be seed in figure \ref{fig:M-Flarecount-peaks_1.01_maxpeak}.
+Figure \ref{fig:M-Flarecount-10_Bins_1.01_maxpeak} shows a similar picture to the histogram with no limits on flare peaks (see figure \ref{fig:M-Flarecount-10_Bins}). The difference here though is that there are less flares in the area of the minima around phase $0.5 \pi$ to $1.5 \pi$. Increasing the bins to 30 (figure \ref{fig:M-Flarecount-30_Bins_1.01_maxpeak}) shows overall a similar pattern, even though the differences between bins, especially in the center druing the phase minima can be larger than twice the error.\\
+Limiting the normalized flare peaks to <1.05 (figure \ref{fig:M-Flarecount-peaks_1.05_maxpeak}) shows again similar pattern to the histograms with all data. In figure \ref{fig:M-Flarecount-10_Bins_1.05_maxpeak} the major difference is that there is a peak around normalized phase $1.1 \pi$, which would be during the folded lightcurve minima.
+The difference becomes less obvious when increasing the bin size 30 (figure \ref{fig:M-Flarecount-30_Bins_1.05_maxpeak}). While overall the same are visible, there appears a new dip around phase $0.25 \pi$ which is right after the maximum. Also the shape of the peak consisting of multiple bins around phase $1.1 \pi$ changed slightly compared to the one in figure \ref{fig:M-Flarecount-30_Bins}.
+
 \begin{figure}[pt!]
     \centering
     \begin{subfigure}[b]{.49\textwidth}
@@ -132,6 +137,10 @@ Looking at the same dataset with 30 bins for the histogram (figure \ref{fig:K-Fl
     \label{fig:K-Flarecount}
 \end{figure}
 
+The histograms with limited normalized flare peaks to >1.05 is shown in figure \ref{fig:K-Flarecount-peaks_1.5_peak}. In \ref{fig:K-Flarecount-10_Bins_1.05_peak} the histogram with 10 bins is shown, while figure \ref{fig:K-Flarecount-30_Bins_1.05_peak} shows the histogram with 30 bins.
+There are multiple clear peaks visible in figure \ref{fig:K-Flarecount-10_Bins_1.05_peak}. The two highest being at phases $0.7 \pi$ as well as $1.1 \pi$, with the latter being wider having a decline till the phase maximum is reached. These two peaks are seperated by a bin at phase $0.9 \pi$ which is significantly lower (roughly twice the errorbar size). Additionally there appears a peak just slightly smaller than the other two in the first bin (at phase maximum).\\
+A similar picture forms when increasing the bin count to 30 (figure \ref{fig:K-Flarecount-30_Bins_1.05_peak}). The main differences to 10 bins is though that the heights of the afformentioned peaks is now the same, and that the errorbars started to overlap with the surrounding bins. Additionally a new peak in the last bin, during the phase maximum, appeared having the same height as the other three.
+
 \begin{figure}[pt!]
     \centering
     \begin{subfigure}[b]{.49\textwidth}
@@ -150,6 +159,11 @@ Looking at the same dataset with 30 bins for the histogram (figure \ref{fig:K-Fl
     \label{fig:K-Flarecount-peaks_1.5_peak}
 \end{figure}
 
+Similarly to what has been done to the histograms in section \ref{sec:results:m_dwarfs}, figures \ref{fig:K-Flarecount-peaks_1.01_maxpeak} and \ref{fig:K-Flarecount-peaks_1.01_maxpeak} limit the data used to plot the histograms to flares with a normalized peak of less than 1.01 and 1.05 respectively.
+In figure \ref{fig:K-Flarecount-10_Bins_1.01_maxpeak}, which limited the flare peaks to a maximum of 1.01, there appears a siginificantly large peak at around phase $1.2 \pi$ which is at the phase minimum. Another, slightly smaller peak appears at the phase maximum at $1.9 \pi$. Both of these peaks are, including error, higher than the average flare count. Checking for more specific phases for the peaks, by increasing the bin count to 30, shows an overall decrease win flares at the phase maximum at around phase $0/2 \pi$, but shows siginificant peaks at phases $1.6 \pi$ and $1.9 \pi$. These two bins are now larger than the one(s) at around phase $1 \pi$ to $1.2 \pi$.\\
+Increasing the allowed flare peaks to 1.05 in figure \ref{fig:K-Flarecount-peaks_1.05_maxpeak} shows a similar pattern to what happened in figure \ref{fig:M-Flarecount-peaks_1.05_maxpeak} with the data for M dwarfs. The resulting histogram look very similar to the ones using all available flare data for K dwarfs (figure \ref{fig:K-Flarecount}). The differences of figure \ref{fig:K-Flarecount-10_Bins_1.05_maxpeak}, which shows the histogram with 10 bins with flare peaks limited to <1.05, and \ref{fig:K-Flarecount-10_Bins}, which shows the histogram with 10 bins for all detected flares of K dwarfs, is that that the two bins at around phase $1.3 \pi$ to $1.5 \pi$ are now more prominant, even though still not outside of the error of their surrounding bins. Similarly the last bin at around phase $1.9 \pi$ is more prominant.\\
+Increasing the bins to 30 (figure \ref{fig:K-Flarecount-30_Bins_1.05_maxpeak}) shows a very similar figure to as figure \ref{fig:K-Flarecount-30_Bins} with 30 bins without any limits to flare peaks. There only very slight differences in the relative bin height.
+
 \begin{figure}[pt!]
     \centering
     \begin{subfigure}[b]{.49\textwidth}
@@ -168,6 +182,8 @@ Looking at the same dataset with 30 bins for the histogram (figure \ref{fig:K-Fl
     \label{fig:K-Flarecount-peaks_1.01_maxpeak}
 \end{figure}
 
+
+
 \begin{figure}[pt!]
     \centering
     \begin{subfigure}[b]{.49\textwidth}
@@ -191,7 +207,8 @@ Looking at the same dataset with 30 bins for the histogram (figure \ref{fig:K-Fl
 
 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.\\
 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.
+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.
 
 \begin{figure}[pt!]
     \centering
@@ -211,23 +228,8 @@ Due to the lower number of detected flares on G type stars, the error bars in fi
     \label{fig:G-Flarecount}
 \end{figure}
 
-\begin{figure}[pt!]
-    \centering
-    \begin{subfigure}[b]{.49\textwidth}
-        \centering
-        \includegraphics[width=\linewidth]{plots/sine/G/G_minFlarePeak_1.05-Flarecount-10_Bins.png}
-        \caption{10 bins}
-        \label{fig:G-Flarecount-10_Bins_1.05_peak}
-    \end{subfigure}
-    \begin{subfigure}[b]{.49\textwidth}
-        \centering
-        \includegraphics[width=\linewidth]{plots/sine/G/G_minFlarePeak_1.05-Flarecount-30_Bins.png}
-        \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 $1 \pi$.}
-    \label{fig:G-Flarecount-peaks_1.5_peak}
-\end{figure}
+Looking only at flares >1.05 on the other side significantly changes how the histograms looks like. Figure \ref{fig:G-Flarecount-10_Bins_1.05_peak} shows the histogram with 10 bins, while figure \ref{fig:G-Flarecount-30_Bins_1.05_peak} shows the one with 30 bins. The histogram with 10 bins shows 3 significant peaks. The first at around phase $0.5 \pi$ with a width of 3 bins, the second at around $1.1 \pi$ and the last at around $1.7 \pi$. All of these peaks are well above their surrounding bins including errors.\\
+Increasing the bins to 30, which is seen in figure \ref{fig:G-Flarecount-30_Bins_1.05_peak}, does not give such a clear picture. Due to the overall lower total number of flares due to the limit, and the increased bin count, all errorbars are overlapping. Even though there are still singular bins at $0.4 \pi$, $1.1 \pi$ and $1.7 \pi$ which are higher than their surroundings, but not outside the error range anymore.
 
 \begin{figure}[pt!]
     \centering
@@ -247,6 +249,24 @@ Due to the lower number of detected flares on G type stars, the error bars in fi
     \label{fig:G-Flarecount-peaks_1.05_maxpeak}
 \end{figure}
 
+\begin{figure}[pt!]
+    \centering
+    \begin{subfigure}[b]{.49\textwidth}
+        \centering
+        \includegraphics[width=\linewidth]{plots/sine/G/G_minFlarePeak_1.05-Flarecount-10_Bins.png}
+        \caption{10 bins}
+        \label{fig:G-Flarecount-10_Bins_1.05_peak}
+    \end{subfigure}
+    \begin{subfigure}[b]{.49\textwidth}
+        \centering
+        \includegraphics[width=\linewidth]{plots/sine/G/G_minFlarePeak_1.05-Flarecount-30_Bins.png}
+        \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 $1 \pi$.}
+    \label{fig:G-Flarecount-peaks_1.5_peak}
+\end{figure}
+
 \FloatBarrier
 \section{F dwarfs \label{sec:results:f_dwarfs}}
 
@@ -440,6 +460,14 @@ 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.
+
+\begin{figure}[pt!]
+    \includegraphics[width=.95\textwidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1-Flarepeaks_maxY-1.2782052782832685.png}
+    \caption{Distribution of flare peaks in relation to the normalized phase at which they occured for TYC 1360-957-1. 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:TYC_4595-107-1-flarepeaks_1.27}
+\end{figure}
+
 \FloatBarrier
 \subsection{V* V471 Tau}
 

Physics_Thesis_Template/main.tex

@@ -66,6 +66,7 @@
 \newcommand{\prd}{Physical Review D}
 \newcommand{\aj}{The Astronomical Journal}
 \newcommand{\aaps}{Astronomy and Astrophysics Supplement Series}
+\newcommand{\nat}{Nature}
 
 \usepackage{xspace}
 \newcommand{\Figure}[1]{Figure\,\ref{#1}\xspace}