SGCMarkus/Masterthesis
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Compare commits

base: SGCMarkus/Masterthesis:538a72cb82e31eaeeec6bd5c503b86ae0e80870a
Branches Tags
SGCMarkus/Masterthesis:main
..
compare: SGCMarkus/Masterthesis:4cfffa101004746eb6bc27e7b638fbd6a75e84c3
Branches Tags
SGCMarkus/Masterthesis:main

3 Commits
538a72cb82 .. 4cfffa1010

Author SHA1 Message Date
SGCMarkus 4cfffa1010 update discussion, and more 2025-06-01 16:34:24 +02:00
SGCMarkus 67c2fc688a add more plots of various stars 2025-06-01 16:33:47 +02:00
SGCMarkus 9c8cba801e update plots to only show number of stars which found flares 2025-06-01 16:32:35 +02:00
55 changed files with 5987 additions and 366 deletions
Expand all files Collapse all files
Physics_Thesis_Template/bib-refs.bib
+19 -1
View File
@@ -1,3 +1,21 @@
@misc{koidr25,
doi = {10.26133/NEA5},
url = {https://catcopy.ipac.caltech.edu/dois/doi.php?id=10.26133/NEA19},
author = {{NASA Exoplanet Archive}},
title = {Kepler Objects of Interest DR25},
publisher = {NExScI-Caltech/IPAC},
version = {Version: YYYY-MM-DD HH:MM},
year = {YYYY}
}
@INPROCEEDINGS{flare_study_2, @INPROCEEDINGS{flare_study_2,
author = {{Maehara}, Hiroyuki and {Notsu}, Yuta and {Notsu}, Shota and {Namekata}, Kousuke and {Ikuta}, Kai and {Honda}, Satoshi and {Nogami}, Daisaku and {Shibata}, Kazunari}, author = {{Maehara}, Hiroyuki and {Notsu}, Yuta and {Notsu}, Shota and {Namekata}, Kousuke and {Ikuta}, Kai and {Honda}, Satoshi and {Nogami}, Daisaku and {Shibata}, Kazunari},
title = "{Starspots on late-type stars and their correlation with flare activity}", title = "{Starspots on late-type stars and their correlation with flare activity}",
@@ -631,7 +649,7 @@ archivePrefix = {arXiv},
} }
@MISC{vizier, @MISC{vizier,
author = { Ochsenbein F. et. al}, author = {{Ochsenbein F. et. al}},
title = "{ The VizieR database of astronomical catalogues }", title = "{ The VizieR database of astronomical catalogues }",
doi = {10.26093/cds/vizier}, doi = {10.26093/cds/vizier},
} }
Physics_Thesis_Template/content/appendixA.tex
+720 -329
View File
File diff suppressed because it is too large Load Diff
Physics_Thesis_Template/content/appendixB.tex
+228
View File
@@ -1,3 +1,231 @@
\chapter{Additional folded lightcurves \label{chap:apB}} \chapter{Additional folded lightcurves \label{chap:apB}}
\section{KOI-256 \label{apB:KOI-256}}
\section{TYC 4595-107-1 \label{apB:TYC_4595-107-1}} \section{TYC 4595-107-1 \label{apB:TYC_4595-107-1}}
\begin{figure}[pt!]
\centering
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-14-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 14}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-18-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 18}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-19-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 19}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-24-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 24}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-25-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 25}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-26-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 26}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-40-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 40}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-41-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 41}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-47-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 47}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-51-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 51}
\end{subfigure}
\caption{Folded lightcurves for TYC 4595-107-1.}
\label{apB:fig:TYC_4595-107-1-TESS_foldedLC1}
\end{figure}
\begin{figure}[pt!]
\centering
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-52-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 52}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-53-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 53}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-54-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 54}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-58-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 58}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-59-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 59}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-60-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 60}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-73-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 73}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1_TESS-74-foldedLC-marked_fit_flares.png}
\caption{TESS Sector 74}
\end{subfigure}
\caption{Folded lightcurves for TYC 4595-107-1.}
\label{apB:fig:TYC_4595-107-1-TESS_foldedLC2}
\end{figure}
\FloatBarrier
\section{V471 Tau \label{apB:V471_tau}}
\begin{figure}[pt!]
\centering
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/V471Tau/V_star_ V471 Tau_TESS-42-periodFoldedLC-marked_fit_flares.png}
\caption{TESS Sector 42}
\label{apB:fig:V471Tau-TESS42}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/V471Tau/V_star_ V471 Tau_TESS-43-periodFoldedLC-marked_fit_flares.png}
\caption{TESS Sector 43}
\label{apB:fig:V471Tau-TESS43}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/V471Tau/V_star_ V471 Tau_TESS-44-periodFoldedLC-marked_fit_flares.png}
\caption{TESS Sector 44}
\label{apB:fig:V471Tau-TESS44}
\end{subfigure}
\caption{Folded lightcurves for V* V471 Tau.}
\label{apB:fig:V471Tau-TESS_foldedLC}
\end{figure}
\FloatBarrier
\section{KOI-256 \label{apB:koi-256}}
\begin{figure}[pt!]
\centering
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_Kepler-35-foldedLC-marked_fit_flares.png}
\caption{Kepler target table ID 35}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_Kepler-36-foldedLC-marked_fit_flares.png}
\caption{Kepler target table ID 36}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_Kepler-37-foldedLC-marked_fit_flares.png}
\caption{Kepler target table ID 37}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_Kepler-38-foldedLC-marked_fit_flares.png}
\caption{Kepler target table ID 38}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_Kepler-39-foldedLC-marked_fit_flares.png}
\caption{Kepler target table ID 39}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_Kepler-40-foldedLC-marked_fit_flares.png}
\caption{Kepler target table ID 40}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_Kepler-69-foldedLC-marked_fit_flares.png}
\caption{Kepler target table ID 69}
\end{subfigure}
\caption{Folded Kepler lightcurves for KOI-256.}
\label{apB:fig:KOI-256-Kepler_foldedLC}
\end{figure}
\begin{figure}[pt!]
\centering
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_Kepler-37-periodFoldedLC-marked_fit_flares.png}
\caption{Kepler target table ID 37}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_Kepler-38-periodFoldedLC-marked_fit_flares.png}
\caption{Kepler target table ID 38}
\end{subfigure}
\caption{Folded Kepler lightcurves for KOI-256 by rotational period.}
\label{apB:fig:KOI-256-Kepler_periodfoldedLC}
\end{figure}
\begin{figure}[pt!]
\centering
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_TESS-53-foldedLC-marked_fit_flares.png}
\caption{TESS sector 53}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_TESS-75-foldedLC-marked_fit_flares.png}
\caption{TESS sector 75}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_TESS-80-foldedLC-marked_fit_flares.png}
\caption{TESS sector 80}
\end{subfigure}
\caption{Folded TESS lightcurves for KOI-256.}
\label{apB:fig:KOI-256-TESS_foldedLC}
\end{figure}
\begin{figure}[pt!]
\centering
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_TESS-53-periodFoldedLC-marked_fit_flares.png}
\caption{TESS sector 53}
\end{subfigure}
\begin{subfigure}[b]{.49\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/sine/KOI-256/KOI-256_TESS-80-periodFoldedLC-marked_fit_flares.png}
\caption{TESS sector 80}
\end{subfigure}
\caption{Folded TESS lightcurves for KOI-256 by rotational period.}
\label{apB:fig:KOI-256-TESS_periodfoldedLC}
\end{figure}
Physics_Thesis_Template/content/appendixC.tex
+57 -1
View File
@@ -1 +1,57 @@
\chapter{Appendix C} \chapter{Miscellaneous lightcurves}
\label{apC}
Appendix for miscellaneous lightcurves that can not be attributed to any of the topics, but are still noteworthy.
\begin{figure}[pt!]
\centering
\begin{subfigure}[b]{.98\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/KOI-6423/2MASS J19033576+3941263_TESS-40-lc.png}
\caption{TESS Sector 40}
\label{apC:fig:KOI-6423-TESS40}
\end{subfigure}
\begin{subfigure}[b]{.98\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/KOI-6423/2MASS J19033576+3941263_TESS-41-lc.png}
\caption{TESS Sector 41}
\label{apC:fig:KOI-6423-TESS41}
\end{subfigure}
\caption{Lightcurves for 2MASS J19033576+3941263, also known as KOI-6423.}
\label{apC:fig:KOI-6423-TESS_lightcurves1}
\end{figure}
\begin{figure}[pt!]
\centering
\begin{subfigure}[b]{.98\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/KOI-6423/2MASS J19033576+3941263_TESS-53-lc.png}
\caption{TESS Sector 53}
\label{apC:fig:KOI-6423-TESS53}
\end{subfigure}
\begin{subfigure}[b]{.98\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/KOI-6423/2MASS J19033576+3941263_TESS-54-lc.png}
\caption{TESS Sector 54}
\label{apC:fig:KOI-6423-TESS54}
\end{subfigure}
\caption{Lightcurves for 2MASS J19033576+3941263, also known as KOI-6423.}
\label{apC:fig:KOI-6423-TESS_lightcurves2}
\end{figure}
\begin{figure}[pt!]
\centering
\begin{subfigure}[b]{.98\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/V452Lyr/V_star_ V452 Lyr_Kepler-55-lc-marked_flares.png}
\caption{Kepler target table ID 55, normalized lightcurve}
\label{apC:fig:V452Lyr-Kepler55_lc}
\end{subfigure}
\begin{subfigure}[b]{.98\textwidth}
\centering
\includegraphics[width=\linewidth]{plots/V452Lyr/V_star_ V452 Lyr_Kepler-55-flattened_lc-marked_flares.png}
\caption{Kepler target table ID 55, flattened lightcurve}
\label{apC:fig:V452Lyr-Kepler55_flattenedlc}
\end{subfigure}
\caption{Lightcurves for 2MASS J19033576+3941263, also known as KOI-6423.}
\label{apC:fig:V452Lyr-Kepler_lightcurves}
\end{figure}
Physics_Thesis_Template/content/chapter-conclusion.tex
+1 -1
View File
@@ -1,3 +1,3 @@
\chapter{Conclusion and Outlook \label{sec:conclusion}} \chapter{Conclusion and Outlook \label{sec:conclusion}}
% better algorithms, handle edge cases better, analyse more stars, take kepler/k2 long cadence into consideration for more data, create plots for flare peaks between x and y
Physics_Thesis_Template/content/chapter-data.tex
+3 -1
View File
@@ -17,14 +17,16 @@ The initial dataset was taken from a list of well known flaring stars from \cite
This chapter explains the methods used in this study, split into the algorithms for flare detection and folding lightcurves. Everything, like the GUI discussed in chapter \ref{sec:gui}, was written in python 3 (\cite{10.5555/1593511}). It also makes extensive use of the python packages astropy (\cite{astropy:2018}), numpy (\cite{numpy}), scipy (\cite{scipy}), pandas (\cite{pandas}) and lightkurve (\cite{lightkurve}). The focus of this chapter lays in the description of the method used to create the final output, which is less customizable than the GUI, which exposes most parameters offered in the functions of the lightkurve API. Unless stated otherwise, the default parameters are used. Furthermore for the final output only PDCSAP\_FLUX is used, which is set as the default flux in the lightkurve $LightCurve$ objects after reading the fit file. The methods are the same for both $KeplerLightCurve$ and $TessLightCurve$ subclasses. This chapter explains the methods used in this study, split into the algorithms for flare detection and folding lightcurves. Everything, like the GUI discussed in chapter \ref{sec:gui}, was written in python 3 (\cite{10.5555/1593511}). It also makes extensive use of the python packages astropy (\cite{astropy:2018}), numpy (\cite{numpy}), scipy (\cite{scipy}), pandas (\cite{pandas}) and lightkurve (\cite{lightkurve}). The focus of this chapter lays in the description of the method used to create the final output, which is less customizable than the GUI, which exposes most parameters offered in the functions of the lightkurve API. Unless stated otherwise, the default parameters are used. Furthermore for the final output only PDCSAP\_FLUX is used, which is set as the default flux in the lightkurve $LightCurve$ objects after reading the fit file. The methods are the same for both $KeplerLightCurve$ and $TessLightCurve$ subclasses.
\subsection{Flare detection} \subsection{Flare detection}
\label{sec:data:data_reduction:flare_detection}
The first step is to normalize the lightcurve. This is done to apply the same thresholds to all files in later steps. An example of this is shown in figure \ref{fig:full_gui_normal_selection_normalize_options} in chapter \ref{sec:gui:data_display}. The normalization is done via the $normalize()$ function of the $LightCurve$ class of the lightkurve api. Afterwards the lightcurves are flattened by called $flatten()$ of the $LightCurve$ objects. The resulting object is then used as the base for the detection of flares. This removes all longterm trends like brightness changes due to spot modulation or similar, while retaining short term events like flares or transits. A similar approach was used by \cite{au_mic_flaring_spi}.\\ The first step is to normalize the lightcurve. This is done to apply the same thresholds to all files in later steps. An example of this is shown in figure \ref{fig:full_gui_normal_selection_normalize_options} in chapter \ref{sec:gui:data_display}. The normalization is done via the $normalize()$ function of the $LightCurve$ class of the lightkurve api. Afterwards the lightcurves are flattened by called $flatten()$ of the $LightCurve$ objects. The resulting object is then used as the base for the detection of flares. This removes all longterm trends like brightness changes due to spot modulation or similar, while retaining short term events like flares or transits. A similar approach was used by \cite{au_mic_flaring_spi}.\\
The next step is then to call $calculateFlareFitsForLightcurve()$ with the flattened lightcurve as well as the normalized lightcurve as parameters. It returns two lists of dictionaries with the data for the flare peak as well as a fit which is described in the following paragraphs. The next step is then to call $calculateFlareFitsForLightcurve()$ with the flattened lightcurve as well as the normalized lightcurve as parameters. It returns two lists of dictionaries with the data for the flare peak as well as a fit which is described in the following paragraphs.
It parses the flattened lightcurve with the scipy $find_peaks$ function. This function returns local maxima, which can be further filtered by their minimum height as well as the minimum distance of datapoints they need to be apart. The minimum distance between points is set to 1 with no minimum required height. Afterwards the found peaks are sorted by height, and the highest 100 are returned. This was found to be a good amount as the most flares per fits file found in this study were around 70 for CD-56 1032A and B.\\ It parses the flattened lightcurve with the scipy $find\_peaks$ function. This function returns local maxima, which can be further filtered by their minimum height as well as the minimum distance of datapoints they need to be apart. The minimum distance between points is set to 1 with no minimum required height. Afterwards the found peaks are sorted by height, and the highest 100 are returned. This was found to be a good amount as the most flares per fits file found in this study were around 70 for CD-56 1032A and B.\\
Afterwards each individual peak is checked. For this purpose every datapoint of the normalized flattened lightcurve is subtracted by 1 to move the average from 1 to 0. Additionally the star and end point of the flare are estimated. This is done by checking the datapoints before and after the peak. If it finds that the flux delta is below 0.005 for three consecutive datapoints, it stops, and assumes that the last checked point is the start/end of the flare. In the case it finds an infinite or NaN value (which can happen if there are gaps in the lightcurve data), or it reaches 100 datapoints before/after it will stop. This was found to cover most flares detected and provides enough datapoints for the following steps.\\ Afterwards each individual peak is checked. For this purpose every datapoint of the normalized flattened lightcurve is subtracted by 1 to move the average from 1 to 0. Additionally the star and end point of the flare are estimated. This is done by checking the datapoints before and after the peak. If it finds that the flux delta is below 0.005 for three consecutive datapoints, it stops, and assumes that the last checked point is the start/end of the flare. In the case it finds an infinite or NaN value (which can happen if there are gaps in the lightcurve data), or it reaches 100 datapoints before/after it will stop. This was found to cover most flares detected and provides enough datapoints for the following steps.\\
Afterwards multiple checks are done. The first checking if the 1 datapoint before the peak, and 1 after the peak are above a threshold of 0.003, or if 2 datapoint after the peak after above the same threshold (which is a similar approach to \cite{kepler_411_study}). Afterwards it is checked if the datapoint at two indices before the peak is larger than the datapoint right before the registered peak. While this eliminates the positive detection of 2 flares in they case of them appearing very shortly after another, it was by visual inspection found to eliminate more false positives. Shortly after another appearing flares are still allowed, if the criteria are met, and theres atleast one more datapoint between the peaks. Then a fit of the flare is generated. The first half of the fit, till the peak, is that of a gaussian function, with the second half being an exponential decay (similar approach to \cite{au_mic_flaring_spi} and \cite{doyle_2018}). Then the residual sum of squares (RSS) between the fit and the flux of the flare, as well as the total sum of squares (TSS) are calculated. Afterwards R-squared is calculated, and if it is below 0.8, the flare is rejected as the flare would not have the typical form. In the last step, the location of the flare in the normalized and flattened lightcurve are compared. This step has been introduced, as in some rare cases the flattening algorithm can produce a large spike (values of 10 or higher when normalized). Afterwards multiple checks are done. The first checking if the 1 datapoint before the peak, and 1 after the peak are above a threshold of 0.003, or if 2 datapoint after the peak after above the same threshold (which is a similar approach to \cite{kepler_411_study}). Afterwards it is checked if the datapoint at two indices before the peak is larger than the datapoint right before the registered peak. While this eliminates the positive detection of 2 flares in they case of them appearing very shortly after another, it was by visual inspection found to eliminate more false positives. Shortly after another appearing flares are still allowed, if the criteria are met, and theres atleast one more datapoint between the peaks. Then a fit of the flare is generated. The first half of the fit, till the peak, is that of a gaussian function, with the second half being an exponential decay (similar approach to \cite{au_mic_flaring_spi} and \cite{doyle_2018}). Then the residual sum of squares (RSS) between the fit and the flux of the flare, as well as the total sum of squares (TSS) are calculated. Afterwards R-squared is calculated, and if it is below 0.8, the flare is rejected as the flare would not have the typical form. In the last step, the location of the flare in the normalized and flattened lightcurve are compared. This step has been introduced, as in some rare cases the flattening algorithm can produce a large spike (values of 10 or higher when normalized).
\subsection{Lightcurve folding} \subsection{Lightcurve folding}
\label{sec:data:data_reduction:lightcurve_folding}
This section will mainly describe how the $getOptimizedFold()$ function works. It takes the normalized lightcurve as well as a fit type as parameters. The fit type can either be "sine" for a sine fit, "poly" for a polynomlial fit, or "linear" for a linear fit. The default value is "sine", but can be changed for each individual star in the GUI. This section will mainly describe how the $getOptimizedFold()$ function works. It takes the normalized lightcurve as well as a fit type as parameters. The fit type can either be "sine" for a sine fit, "poly" for a polynomlial fit, or "linear" for a linear fit. The default value is "sine", but can be changed for each individual star in the GUI.
The function at first generates two periodograms with the lightkurve function $to\_periodogram$. The first one uses the lombscargle algorithm, while the second one uses the boxleastsquares algorithm. Afterwards the 4 highest peaks of each are taken and converted into periods (unit in days). The function at first generates two periodograms with the lightkurve function $to\_periodogram$. The first one uses the lombscargle algorithm, while the second one uses the boxleastsquares algorithm. Afterwards the 4 highest peaks of each are taken and converted into periods (unit in days).
Physics_Thesis_Template/content/chapter-discussion.tex
+19 -3
View File
@@ -1,10 +1,14 @@
\chapter{Discussion \label{sec:discussion}} \chapter{Discussion \label{sec:discussion}}
The flare to spot correlation in this study is based on a large sample of known active stars, which were observed by the Kepler/K2 and TESS missions. To also catch shorter events, short-cadence data was used for Kepler/K2. Not all stars analysed were used though to generate the plots in the results section (see table \ref{apA:list_of_unused_stars}). This list contains stars that either did not match the spectral types which were analysed in this study (e.g. some A type stars from the list of stars by \cite{althukair_starlist}), could not produce valid fits (reached 30 tries during the fit optimization for folded lightcurves) or no consistent period was found. The full list of stars analyzed can be found in table \ref{apA:list_of_all_stars}.\\
The analysis was done with a self written python program (discussed in chapter \ref{sec:gui}). The reason a GUI was made was for ease of management of the data (e.g. easily looking up parameters of a star), as well as checking individual results in a fast and easy way during the development stage. This also allowed to quickly compare the outputs of the algorithms between different fits files of the same star as well as between different stars fits files. The algorithms are based on the approaches of \cite{kepler_411_study}, \cite{au_mic_flaring_spi} and \cite{doyle_2018}. The thresholds described in section \ref{sec:data:data_reduction:flare_detection} for the flare detection algorithm have been set by trial and visual inspection of the lightcurves of multiple stars/fits files. The last step for flare detection, which was introduced to prevent failures of the flattening algorithm to be detected as (massive) flares, was introduced due to the results for the stars 2MASS J19033576+3941263 (TESS sectors 40, 41 and 53), 2MASS J19370439+4626209 (TESS sector 54) and V* V452 Lyr (Kepler target table ID 55). 2MASS J19033576+3941263, also known by KOI-6423 or KIC 4544623 shows regular dips in its lightcurve, which could indicate one or multiple transiting planets. It has currently been marked as a false positive candidate in the NASA Exoplanet Archive (\cite{koidr25}, \href{https://exoplanetarchive.ipac.caltech.edu/overview/KOI-6423}{https://exoplanetarchive.ipac.caltech.edu/overview/KOI-6423}). The TESS lightcurves for KOI-6423 can be found in appendix \ref{apC} in figures \ref{apC:fig:KOI-6423-TESS_lightcurves1} and \ref{apC:fig:KOI-6423-TESS_lightcurves2}. While there are no noteworthy dips upon manual inspection in the lightcurve for 2MASS J19370439+4626209, flattening it still generates peaks of over 800 on a normalized lightcurve. V* V452 Lyr was observed in multiple Kepler target table IDs, with the only detected flares (4 total) in target table ID 55. The lightcurve itself is very flat (see figure \ref{apC:fig:V452Lyr-Kepler_lightcurves} in appendix \ref{apC}). Further to notice, the flare detection can only distinguish high and low flare peaks, but it does not calculate the flare energy.\\
While the folding algorithm (see section \ref{sec:data:data_reduction:lightcurve_folding}) works on most stars/fits files, it has its limitations in edge cases like V* HK Aqr or KOI-256 as described in sections \ref{results:hk_aqr} and \ref{results:koi_256}. It is set to check for an additional periodicity signal if the fit for the folded lightcurve has two peaks which are further than 10\% of the total phase from the edge. While it is expected to find two peaks when folding and fitting a sine function due to marging of error of the fitting parameters, there has to be set a limit for when to search for additional periodicity. A well working (and near perfect) example is V471 Tau. It shows additional periodicity in the TESS lightcurves 42, 32 and 44 (see figure \ref{apB:fig:V471Tau-TESS_foldedLC} in appendix \ref{chap:apB}), but not 70 and 71. Additionally the shift by the difference of the fit minimum to the (currently used) epoch for the fold is necessary to generate reliable results, as otherwise it has been found the minimum of the fit/folded lightcurve can vary by up to \textasciitilde25\% depending on which first minimum is detected in the lightcurve.\\\\
Out of a total of \textasciitilde160 M dwarfs in the list of stars to be analyzed, flares could only be detected on 49 stars. This could be due to a not sensitive enough algorithm or instruments, too noisy data or it could be that there were just no flares during the observation time. For the remaining 49 stars, a total of \textasciitilde3500 flares were detected. Using all available flares, there was no significant spot dependency detected in the histogram with 10 bins. In the third bin there were \textasciitilde50 flares less detected compared to other bins. This bin is located in the transition from the phase maxima to minima. While not being significant, the 6th bin has the most flares detected, which would be at the phase minimum. This could show a possible dependency with more available data. The data also contains the detected flares from KOI-256 and V* HK Aqr, which were not folded correctly. Manually comparing the results for V* HK Aqr (figures \ref{fig:HKAqr-Flarecount-10_Bins} and \ref{fig:HKAqr-Flarecount-10_Bins_Period}), as well as the folded lightcurves shows that for TESS sector 29 the detected minimum ($\pm$ quarter of the phase) the amount of detected flares flipped. While more flares should be counted in the minimum (see figure \ref{fig:HKAqr-TESS29_foldedLC_Period}) compared to the maximum (see figure \ref{fig:HKAqr-TESS29_foldedLC}), the opposite is the case. Similarly for TESS sector 42. Overall these changes make the spot dependence of flares on V* HK Aqr more clear, as the histogram (10 bins) with only the rotational period folded lightcurves indicates a spot dependency. There are significantly more flares counted around the minimum compared to the phase maximum. The flares with the highest peaks V* HK Aqr were also detected during the phase minimum in TESS sector 29 with a normalized peak of up to 1.8. KOI-256 shows a similar behaviour, showing a clear spot dependence when using only period folded lightcurves for the histogram, while having more spread out peaks around the phase minimum when using all spot modulation folded lightcurves.\\
2MASS J19230963+3739397 on the other hand is a star, which shows an inverted spot dependency. This could be an indication that similarly to what \cite{kepler_411_210_comparison} found, the spot area is not the only important parameter.\\
Limiting the flare by maximum flare peak height indicates a dependency of flares on spots. While no flare energies were calculated in this study, this could be parameters to look at in the future. Limiting the flare peak to 1\% above the flux shows a higher count in the phase maxima compared to he phase minima. The same dip as with all flares can be seen here already too. Increasing the flare peak limit to 5\% above the flux shows a nearly identical histogram (in form) to the one with all flares. A noteworthy difference here is the peak in the bin at the phase minimum at $1 \pi$. \cite{connection_starspots_flares_ms_kepler} found an increase of flares in M and K dwarfs at phase minimum with flares which had a flux increase at their peaks between 1\% and 5\%. The differences could be due to a different set of stars and flare detection methods.
%methods: lombscargle generally finds lower periods with higher peaks (e.g. halfs of rotational period), which boxleastsquares does not always detect within the 4 highest % 14 - 10; 10 - 14
%M dwarfs, all data, no significant dependency of flare appearance on phase using 10 bins. %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. %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. %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.
@@ -12,16 +16,28 @@
%Limit to max 1.05, nearly identical histograms to all data. (different result to \cite{connection_starspots_flares_ms_kepler}) %Limit to max 1.05, nearly identical histograms to all data. (different result to \cite{connection_starspots_flares_ms_kepler})
%\\\\ %\\\\
Out of a total of \textasciitilde40 K dwarfs in the list of stars to be analyzed, flares could only be detected on 37 stars. This could be due to a not sensitive enough algorithm or instruments, too noisy data or it could be that there were just no flares during the observation time. Overall the results for the flare distribution on K dwarfs is similar to those of M dwarfs. There is no real dependence on spots visible, with the exception of the bin (bins for the histogram with 30 bins) around the phase minimum. One of the causes for this is V* V471 Tau (see section \ref{results:v471_tau}), which is in close orbit with a white dwarf (\cite{v471tau_revised}, \cite{V471tau_magnetic_activity}). This can lead to magnetic interactions between the K dwarf and the white dwarf (\cite{V471tau_magnetic_activity}), which could lead to the increased flarecount seen.\\
Limiting the flare peaks to greater than 5\% of the flux shows two peaks around the center bin, with one higher bin being at the maximum at phase $0 \pi$. While the two peaks around the phase minimum could indicate a dependency on spots, it is not the only relevant bin found.
Limiting the flare peaks to a maximum of 1\% above the flux shows an interesting pattern. There is a larger count of flares found during the phase minimum, but also during the phase maximum, while less flares have been detected in the transition between phase miminum/maximum. Increasing the allowed flare peak to 5\% above the flux shows a similar pattern, but the gaps between peaks/dips closes and is already very similar to the histogram with all flares.
% 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. % 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 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. % 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. % max 1.05 already most flares, very similar to with all data.
Out of a total of \textasciitilde80 G dwarfs in the list of stars to be analyzed, flares could only be detected on 21 stars. This could be due to a not sensitive enough algorithm or instruments, too noisy data or it could be that there were just no flares during the observation time. Most of the flares detected had a peak below 5\% above the flux, but as \cite{solar_like_superflares} found, flares with a flux increase between 0.1 to 1\% would already be categorized as superflares. For the flares found in this study for G type stars, there appears to be a spot dependency, as the flare count peaks around the phase minimum. Unlike the other results, there is a gradual fall off to each sides till the phase maximum is reached.\\
Limiting the flare peaks to a minimum of 1.05 shows three major peaks. The highest being at the phase minimum, while the other two are in the transition between maximum and miminum and minimum and maximum. This does not indicate a pure spot dependency, and a more detailed look at the individual events is necessary.\\
BD-08 995, which seems to be a late G type star, reflects this trend well. It shows the same bell curve style histogram. Additionally though it also shows a slight increase in flares around the phase maximum. Its highest flare peak was detected around the phase maximum though. The maximum flare count for TYC 4595-107-1 on the other hand is slightly offset to before the phase minimum. It also shows a slight increase of flares around the maximum. Its highest flare peak was detected in the same bin as the highest flare count.
% 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. % 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. % Limiting to flares >1.05 -> flares during minima and transitions between minima <-> maxima, increasing bins -> more data would be required.
Out of a total of \textasciitilde13 F dwarfs in the list of stars to be analyzed, flares could only be detected on 4 stars. This could be due to a not sensitive enough algorithm or instruments, too noisy data or it could be that there were just no flares during the observation time. While all flares detected are centered around the phase minimum, the total of 5 flares detected is not a large enough sample to come to a conclusion if there exists a flare spot dependency for these stars.
% For F dwarfs, overall too little data, but the not siginificant amount detected all during phase minimum, could be similar to G dwarfs? % For F dwarfs, overall too little data, but the not siginificant amount detected all during phase minimum, could be similar to G dwarfs?
Looking at all results together, there appears to be a slight flare dependence, which is mostly influenced by the results for K and G stars. The dip in the otherwise seemingly stable histogram for the results of M dwarfs propagates for the overall results.
% All data combined, peak at phase minimum dominated by G/K dwarfs, dip in transition maxima -> minima dominated by dip from M dwarf results. % 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): % Individual star results (subset taken):
Physics_Thesis_Template/content/chapter-introduction.tex
+14 -6
View File
@@ -7,12 +7,12 @@ This chapter gives an introduction to the goals of this study. Afterwards there
\section{Goals and current knowledge \label{sec:intro:goals}} \section{Goals and current knowledge \label{sec:intro:goals}}
The goal of this study is to relate flares/superflares to the appearance of spots on the surfaces of stars of various spectral types. Flares are well studied for the sun (\cite{solar_flares_1}, \cite{solar_flares_2}, \cite{solar_flares_3}) as well as its impact on earths magnetic field (\cite{solar_flare_mag_field}). While the first stellar flares were discovered in middle of the last century (\cite{early_stellar_flares1}, \cite{early_stellar_flares2}), the topic gained a lot of traction with the launch of the likes of Kepler and the Transiting Exoplanet Survey Satellite (TESS). They allowed the survey of thousands of stars. With this, studies of flares and superflares on a large number of stars have been conducted (e.g. \cite{flare_study_1}, \cite{flare_study_2}, \cite{connection_starspots_flares_ms_kepler}, \cite{flare_occurance_periodicity}), but the origin of superflares (flares with an energy above $10^{33}$ erg) is still not clear. So far no superflare has been observed on our sun, but there have been studies focusing on the possible origin on superflares and their likelyhood to happen on our sun (\cite{superflares_on_sun}). They found that superflares on our sun would be rare events (every \textasciitilde800 years for superflares with $10^{34}$ erg).\\ The goal of this study is to relate flares/superflares to the appearance of spots on the surfaces of stars of various spectral types. Flares are well studied for the sun (\cite{solar_flares_1}, \cite{solar_flares_2}, \cite{solar_flares_3}) as well as its impact on earths magnetic field (\cite{solar_flare_mag_field}). While the first stellar flares were discovered in middle of the last century (\cite{early_stellar_flares1}, \cite{early_stellar_flares2}), the topic gained a lot of traction with the launch of the likes of Kepler and the Transiting Exoplanet Survey Satellite (TESS). They allowed the survey of thousands of stars. With this, studies of flares and superflares on a large number of stars have been conducted (e.g. \cite{flare_study_1}, \cite{flare_study_2}, \cite{connection_starspots_flares_ms_kepler}, \cite{flare_occurance_periodicity}), but the origin of superflares (flares with an energy above $10^{33}$ erg) is still not clear. So far no superflare has been observed on our sun, but there have been studies focusing on the possible origin on superflares and their likelyhood to happen on our sun (\cite{superflares_on_sun}). They found that superflares on our sun would be rare events (every \textasciitilde800 years for superflares with $10^{34}$ erg).\\
A few proposed caused could be star-planet interaction (SPI) (\cite{au_mic_flaring_spi}, \cite{SPI_1}, \cite{SPI_2}), or just being scaled up version of normal flares which we see from our sun coming from large spots (\cite{superflares_1}, \cite{superflares_2}).\\ A few proposed causes could be star-planet interaction (SPI) (\cite{au_mic_flaring_spi}, \cite{SPI_1}, \cite{SPI_2}), or just being scaled up version of normal flares which we see from our sun coming from large spots (\cite{superflares_1}, \cite{superflares_2}).\\
\cite{kepler_411_study} focused on Kepler-411 by investigating the relation between superflares and star spots on that star. They found a positive correlation between the energy of flares and the area of star spots (\cite{kepler_411_study}) on Kepler-411. They then compared their results for Kepler-411, which produced multiple superflares, with Kepler-210, which did not produce superflares while having the same number of spots (\cite{kepler_411_210_comparison}). They found the spots on Kepler-210 to be larger, warmer and therefor being magnetically weaker/less complex compared to Kepler-411 and concluded that the area of starspots is not the only relevant parameter for superflare occurance (\cite{kepler_411_210_comparison}).\\ \cite{doyle_2018} studied 34 M dwarfs from the K2 mission, using short cadence observational data. They confirmed that the stars in their dataset with a rotational period of less than 10 days showed more flares, which was already shown previously (\cite{faster_rot_stars_more_flares1}, \cite{faster_rot_stars_more_flares2}). Furthermore they found no star with a preference for when flares occured during the rotational phase (\cite{doyle_2018}). A similar study using TESS 2 minute cadence data has been conducted by \cite{doyle_2019}. In this study they used data of 167 M dwarfs and found a total of 1834 flares. Similar to the study on K2 data, they found no preference for roational phase (\cite{doyle_2019}).\\
\cite{doyle_2018} studied 34 M dwarfs from the K2 mission, using short cadence observational data. They confirmed that stars with a rotational period of less than 10 days showed more flares, which was already shown previously (\cite{faster_rot_stars_more_flares1}, \cite{faster_rot_stars_more_flares2}). Furthermore they found no star with a preference for when flares occured during the rotational phase (\cite{doyle_2018}). A similar study using TESS 2 minute cadence data has been conducted by \cite{doyle_2019}. In this study they used data of 167 M dwarfs and found a total of 1834 flares. Similar to the study on K2 data, they found no preference for roational phase (\cite{doyle_2019}).\\
Another possible cause for a periodic increase in flares is star-planet interaction (SPI), which is studied by \cite{au_mic_flaring_spi} for the star AU Mic. While they found a signal in their used TESS lightcurves correlating with the orbital period of AU Mic b, they require more observation time to get a $>3\sigma$ detection (\cite{au_mic_flaring_spi}).\\
Further analysis on periodic flare occurance was done by \cite{flare_occurance_periodicity}, who studied lightcurves of 284 M dwarfs. They found three targets (TIC 80427281, TIC 95328477, TIC 220432563) with a confirmed flare periodicity, which correlates to their rotational period or half of it.\\ Further analysis on periodic flare occurance was done by \cite{flare_occurance_periodicity}, who studied lightcurves of 284 M dwarfs. They found three targets (TIC 80427281, TIC 95328477, TIC 220432563) with a confirmed flare periodicity, which correlates to their rotational period or half of it.\\
\cite{connection_starspots_flares_ms_kepler} investigated a sample of 119 stars from spectral types M to F. They found that flares which increase the stellar flux by 1\% to 5\% appear more often while larger starspots are visible, while flares which increase the flux by more that 5\% do not seem to have this dependency (\cite{connection_starspots_flares_ms_kepler}). \cite{connection_starspots_flares_ms_kepler} investigated a sample of 119 stars from spectral types M to F. They found that flares which increase the stellar flux by 1\% to 5\% appear more often while larger starspots are visible, while flares which increase the flux by more that 5\% do not seem to have this dependency (\cite{connection_starspots_flares_ms_kepler}).\\
There have also been studies on individual stars, for example \cite{kepler_411_study} focused on Kepler-411 by investigating the relation between superflares and star spots on that star. They found a positive correlation between the energy of flares and the area of star spots (\cite{kepler_411_study}) on Kepler-411. They then compared their results for Kepler-411, which produced multiple superflares, with Kepler-210, which did not produce superflares while having the same number of spots (\cite{kepler_411_210_comparison}). They found the spots on Kepler-210 to be larger, warmer and therefor being magnetically weaker/less complex compared to Kepler-411 and concluded that the area of starspots is not the only relevant parameter for superflare occurance (\cite{kepler_411_210_comparison}). Star-planet interaction is studied by \cite{au_mic_flaring_spi} for the star AU Mic. While they found a signal in their used TESS lightcurves correlating with the orbital period of AU Mic b, they require more observation time to get a $>3\sigma$ detection (\cite{au_mic_flaring_spi}).\\
In coclusion, many flares and superflares have been found on stars, but the origin of the later is still not clear. There are a few ongoing possible origins like star-planet interaction (or interactions with other close companions) or them coming from larger, more complex starspots.
\section{Spectral Types \label{sec:intro:spectral_types}} \section{Spectral Types \label{sec:intro:spectral_types}}
@@ -40,7 +40,7 @@ The spectral types are a way to classify the vast amount of stars into various t
% Different Spectral Types % Different Spectral Types
\section{Flares and Starspots \label{sec:intro:flares_and_spots}} \section{Flares and Spots \label{sec:intro:flares_and_spots}}
% Stellar Activity, % Stellar Activity,
@@ -48,6 +48,14 @@ The spectral types are a way to classify the vast amount of stars into various t
% TESS, Kepler/K2 % TESS, Kepler/K2
\subsection{Kepler}
\subsection{K2}
\subsection{TESS}
%\section{Current knowledge \label{sec:intro:current_knowledge}} %\section{Current knowledge \label{sec:intro:current_knowledge}}
Physics_Thesis_Template/content/chapter-results.tex
+76 -24
View File
@@ -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}} \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.\\ 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 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. 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} \caption{30 bins}
\label{fig:M-Flarecount-30_Bins} \label{fig:M-Flarecount-30_Bins}
\end{subfigure} \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} \label{fig:M-Flarecount}
\end{figure} \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} \caption{30 bins}
\label{fig:M-Flarecount-30_Bins_1.25_peak} \label{fig:M-Flarecount-30_Bins_1.25_peak}
\end{subfigure} \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} \label{fig:M-Flarecount-peaks_1.25_peak}
\end{figure} \end{figure}
\begin{figure}[pt!] \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} \caption{30 bins}
\label{fig:M-Flarecount-30_Bins_1.5_peak} \label{fig:M-Flarecount-30_Bins_1.5_peak}
\end{subfigure} \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} \label{fig:M-Flarecount-peaks_1.5_peak}
\end{figure} \end{figure}
@@ -90,7 +90,7 @@ The difference becomes less obvious when increasing the bin size 30 (figure \ref
\caption{30 bins} \caption{30 bins}
\label{fig:M-Flarecount-30_Bins_1.01_maxpeak} \label{fig:M-Flarecount-30_Bins_1.01_maxpeak}
\end{subfigure} \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} \label{fig:M-Flarecount-peaks_1.01_maxpeak}
\end{figure} \end{figure}
@@ -108,14 +108,14 @@ The difference becomes less obvious when increasing the bin size 30 (figure \ref
\caption{30 bins} \caption{30 bins}
\label{fig:M-Flarecount-30_Bins_1.05_maxpeak} \label{fig:M-Flarecount-30_Bins_1.05_maxpeak}
\end{subfigure} \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} \label{fig:M-Flarecount-peaks_1.05_maxpeak}
\end{figure} \end{figure}
\FloatBarrier \FloatBarrier
\section{K dwarfs \label{sec:results:k_dwarfs}} \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}.\\ 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. 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} \caption{30 bins}
\label{fig:K-Flarecount-30_Bins} \label{fig:K-Flarecount-30_Bins}
\end{subfigure} \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} \label{fig:K-Flarecount}
\end{figure} \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} \caption{30 bins}
\label{fig:K-Flarecount-30_Bins_1.05_peak} \label{fig:K-Flarecount-30_Bins_1.05_peak}
\end{subfigure} \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} \label{fig:K-Flarecount-peaks_1.5_peak}
\end{figure} \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} \caption{30 bins}
\label{fig:K-Flarecount-30_Bins_1.01_maxpeak} \label{fig:K-Flarecount-30_Bins_1.01_maxpeak}
\end{subfigure} \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} \label{fig:K-Flarecount-peaks_1.01_maxpeak}
\end{figure} \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} \caption{30 bins}
\label{fig:K-Flarecount-30_Bins_1.05_maxpeak} \label{fig:K-Flarecount-30_Bins_1.05_maxpeak}
\end{subfigure} \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} \label{fig:K-Flarecount-peaks_1.05_maxpeak}
\end{figure} \end{figure}
\FloatBarrier \FloatBarrier
\section{G dwarfs \label{sec:results:g_dwarfs}} \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 $1.1 \pi$.\\ 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. 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} \caption{30 bins}
\label{fig:G-Flarecount-30_Bins} \label{fig:G-Flarecount-30_Bins}
\end{subfigure} \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} \label{fig:G-Flarecount}
\end{figure} \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} \caption{30 bins}
\label{fig:G-Flarecount-30_Bins_1.05_maxpeak} \label{fig:G-Flarecount-30_Bins_1.05_maxpeak}
\end{subfigure} \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} \label{fig:G-Flarecount-peaks_1.05_maxpeak}
\end{figure} \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} \caption{30 bins}
\label{fig:G-Flarecount-30_Bins_1.05_peak} \label{fig:G-Flarecount-30_Bins_1.05_peak}
\end{subfigure} \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} \label{fig:G-Flarecount-peaks_1.5_peak}
\end{figure} \end{figure}
\FloatBarrier \FloatBarrier
\section{F dwarfs \label{sec:results:f_dwarfs}} \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. 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!] \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} \caption{30 bins}
\label{fig:F-Flarecount-30_Bins} \label{fig:F-Flarecount-30_Bins}
\end{subfigure} \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} \label{fig:F-Flarecount}
\end{figure} \end{figure}
\FloatBarrier \FloatBarrier
\section{Combined results \label{sec:results:combined}} \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.\\ 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 $1.5 \pi$. 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} \caption{30 bins}
\label{fig:MKGF-Flarecount-30_Bins} \label{fig:MKGF-Flarecount-30_Bins}
\end{subfigure} \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} \label{fig:MKGF-Flarecount}
\end{figure} \end{figure}
@@ -323,7 +323,7 @@ This section contains a selection of results for individual stars. The results f
\subsection{BD-08 995} \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 $0 \pi$. 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.\\ 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$1.4 \pi$. 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} \label{fig:TYC_4595-107-1-Flarecount}
\end{figure} \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!] \begin{figure}[pt!]
\includegraphics[width=.95\textwidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1-Flarepeaks_maxY-1.2782052782832685.png} \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 \FloatBarrier
\subsection{V* V471 Tau} \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}). 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. 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 \FloatBarrier
\subsection{V* HK Aqr} \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 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.\\ 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 \FloatBarrier
\subsection{KOI-256} \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.\\ 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 $1.7 \pi$. 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} \label{fig:KOI-256-Flarecount}
\end{figure} \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.\\ 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 $0.9 \pi$. 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} \label{fig:KOI-256-Flarecount_Period}
\end{figure} \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!] \begin{figure}[pt!]
\centering \centering
@@ -694,6 +698,54 @@ Comparing the results of the flare peak distributions across the normalized phas
\caption{Period folded} \caption{Period folded}
\label{fig:KOI-256-flarepeaks_1.3_period} \label{fig:KOI-256-flarepeaks_1.3_period}
\end{subfigure} \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} \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} \end{figure}
Physics_Thesis_Template/main.bbl-SAVE-ERROR
+4850
View File
File diff suppressed because it is too large Load Diff
Physics_Thesis_Template/main.pdf
BIN
View File
Binary file not shown.
Physics_Thesis_Template/plots/KOI-6423/2MASS J19033576+3941263_TESS-40-lc.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 63 KiB

Physics_Thesis_Template/plots/KOI-6423/2MASS J19033576+3941263_TESS-41-lc.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 58 KiB

Physics_Thesis_Template/plots/KOI-6423/2MASS J19033576+3941263_TESS-53-lc.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 58 KiB

Physics_Thesis_Template/plots/KOI-6423/2MASS J19033576+3941263_TESS-54-lc.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 59 KiB

Physics_Thesis_Template/plots/V452Lyr/V_star_ V452 Lyr_Kepler-55-flattened_lc-marked_flares.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 37 KiB

Physics_Thesis_Template/plots/V452Lyr/V_star_ V452 Lyr_Kepler-55-lc-marked_flares.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 34 KiB

Physics_Thesis_Template/plots/V471Tau/V_star_ V471 Tau_TESS-42-periodFoldedLC-marked_fit_flares.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 84 KiB

Physics_Thesis_Template/plots/V471Tau/V_star_ V471 Tau_TESS-43-periodFoldedLC-marked_fit_flares.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 71 KiB

Physics_Thesis_Template/plots/V471Tau/V_star_ V471 Tau_TESS-44-periodFoldedLC-marked_fit_flares.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 94 KiB

Physics_Thesis_Template/plots/sine/2MASS J19230963+3739397/2MASS J19230963+3739397-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 35 KiB

Physics_Thesis_Template/plots/sine/2MASS J19230963+3739397/2MASS J19230963+3739397-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 34 KiB

Physics_Thesis_Template/plots/sine/2MASS J19230963+3739397/2MASS J19230963+3739397_Kepler-47-foldedLC-marked_fit_flares.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 42 KiB

Physics_Thesis_Template/plots/sine/2MASS J19230963+3739397/2MASS J19230963+3739397_Kepler-48-foldedLC-marked_fit_flares.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 42 KiB

Physics_Thesis_Template/plots/sine/2MASS J19230963+3739397/2MASS J19230963+3739397_Kepler-49-foldedLC-marked_fit_flares.png
BIN
View File
Binary file not shown.
Side by Side

After

Width:  |  Height:  |  Size: 41 KiB

Physics_Thesis_Template/plots/sine/F/F-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 36 KiB

After

Width:  |  Height:  |  Size: 36 KiB

Physics_Thesis_Template/plots/sine/F/F-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 35 KiB

After

Width:  |  Height:  |  Size: 35 KiB

Physics_Thesis_Template/plots/sine/G/G-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 38 KiB

After

Width:  |  Height:  |  Size: 38 KiB

Physics_Thesis_Template/plots/sine/G/G-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 40 KiB

After

Width:  |  Height:  |  Size: 41 KiB

Physics_Thesis_Template/plots/sine/G/G_maxFlarePeak_1.05-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 38 KiB

After

Width:  |  Height:  |  Size: 38 KiB

Physics_Thesis_Template/plots/sine/G/G_maxFlarePeak_1.05-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 40 KiB

After

Width:  |  Height:  |  Size: 41 KiB

Physics_Thesis_Template/plots/sine/G/G_minFlarePeak_1.05-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 37 KiB

After

Width:  |  Height:  |  Size: 37 KiB

Physics_Thesis_Template/plots/sine/G/G_minFlarePeak_1.05-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 35 KiB

After

Width:  |  Height:  |  Size: 36 KiB

Physics_Thesis_Template/plots/sine/K/K-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 40 KiB

After

Width:  |  Height:  |  Size: 40 KiB

Physics_Thesis_Template/plots/sine/K/K-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 39 KiB

After

Width:  |  Height:  |  Size: 39 KiB

Physics_Thesis_Template/plots/sine/K/K_maxFlarePeak_1.01-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 39 KiB

After

Width:  |  Height:  |  Size: 39 KiB

Physics_Thesis_Template/plots/sine/K/K_maxFlarePeak_1.01-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 38 KiB

After

Width:  |  Height:  |  Size: 38 KiB

Physics_Thesis_Template/plots/sine/K/K_maxFlarePeak_1.05-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 39 KiB

After

Width:  |  Height:  |  Size: 39 KiB

Physics_Thesis_Template/plots/sine/K/K_maxFlarePeak_1.05-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 41 KiB

After

Width:  |  Height:  |  Size: 41 KiB

Physics_Thesis_Template/plots/sine/K/K_minFlarePeak_1.05-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 38 KiB

After

Width:  |  Height:  |  Size: 38 KiB

Physics_Thesis_Template/plots/sine/K/K_minFlarePeak_1.05-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 37 KiB

After

Width:  |  Height:  |  Size: 37 KiB

Physics_Thesis_Template/plots/sine/M/M-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 41 KiB

After

Width:  |  Height:  |  Size: 42 KiB

Physics_Thesis_Template/plots/sine/M/M-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 40 KiB

After

Width:  |  Height:  |  Size: 41 KiB

Physics_Thesis_Template/plots/sine/M/M_maxFlarePeak_1.01-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 38 KiB

After

Width:  |  Height:  |  Size: 38 KiB

Physics_Thesis_Template/plots/sine/M/M_maxFlarePeak_1.01-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 37 KiB

After

Width:  |  Height:  |  Size: 37 KiB

Physics_Thesis_Template/plots/sine/M/M_maxFlarePeak_1.05-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 40 KiB

After

Width:  |  Height:  |  Size: 40 KiB

Physics_Thesis_Template/plots/sine/M/M_maxFlarePeak_1.05-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 39 KiB

After

Width:  |  Height:  |  Size: 39 KiB

Physics_Thesis_Template/plots/sine/M/M_minFlarePeak_1.1-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 38 KiB

After

Width:  |  Height:  |  Size: 38 KiB

Physics_Thesis_Template/plots/sine/M/M_minFlarePeak_1.1-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 37 KiB

After

Width:  |  Height:  |  Size: 37 KiB

Physics_Thesis_Template/plots/sine/M/M_minFlarePeak_1.25-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 36 KiB

After

Width:  |  Height:  |  Size: 36 KiB

Physics_Thesis_Template/plots/sine/M/M_minFlarePeak_1.25-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 36 KiB

After

Width:  |  Height:  |  Size: 36 KiB

Physics_Thesis_Template/plots/sine/M/M_minFlarePeak_1.5-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 35 KiB

After

Width:  |  Height:  |  Size: 36 KiB

Physics_Thesis_Template/plots/sine/M/M_minFlarePeak_1.5-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 35 KiB

After

Width:  |  Height:  |  Size: 35 KiB

Physics_Thesis_Template/plots/sine/MKGF-Flarecount-10_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 47 KiB

After

Width:  |  Height:  |  Size: 47 KiB

Physics_Thesis_Template/plots/sine/MKGF-Flarecount-30_Bins.png
BIN
View File
Binary file not shown.
Side by Side Swipe Overlay

Before

Width:  |  Height:  |  Size: 46 KiB

After

Width:  |  Height:  |  Size: 46 KiB