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@@ -42,6 +42,26 @@ journal = {The Astrophysical Journal},
 abstract = {Masuda et al. found a hard X-ray source well above a soft X-ray loop in impulsive compact-loop flares near the limb. This indicates that main energy release is going on above the soft X-ray loop, and suggests magnetic reconnection occurring above the loop, similar to the classical model for two ribbon flares. If the reconnection hypothesis is correct, a hot plasma (or plasmoid) ejection is expected to be associated with these flares. Using the images taken by the soft X-ray telescope aboard Yohkoh, we searched for such plasma ejections in eight impulsive compact-loop flares near the limb, which are selected in an unbiased manner and include also the Masuda flare, 1992 January 13 flare. We found that all these flares were associated with X-ray plasma ejections high above the soft X-ray loop and the velocity of ejections is within the range of 50-400 km s-1. This result gives further support for magnetic reconnection hypothesis of these impulsive compact-loop flares.}
 }
@INPROCEEDINGS{TESS_release,
       author = {{Ricker}, George R. and {Winn}, Joshua N. and {Vanderspek}, Roland and {Latham}, David W. and {Bakos}, G{\'a}sp{\'a}r. {\'A}. and {Bean}, Jacob L. and {Berta-Thompson}, Zachory K. and {Brown}, Timothy M. and {Buchhave}, Lars and {Butler}, Nathaniel R. and {Butler}, R. Paul and {Chaplin}, William J. and {Charbonneau}, David and {Christensen-Dalsgaard}, J{\o}rgen and {Clampin}, Mark and {Deming}, Drake and {Doty}, John and {De Lee}, Nathan and {Dressing}, Courtney and {Dunham}, E.~W. and {Endl}, Michael and {Fressin}, Francois and {Ge}, Jian and {Henning}, Thomas and {Holman}, Matthew J. and {Howard}, Andrew W. and {Ida}, Shigeru and {Jenkins}, Jon and {Jernigan}, Garrett and {Johnson}, John A. and {Kaltenegger}, Lisa and {Kawai}, Nobuyuki and {Kjeldsen}, Hans and {Laughlin}, Gregory and {Levine}, Alan M. and {Lin}, Douglas and {Lissauer}, Jack J. and {MacQueen}, Phillip and {Marcy}, Geoffrey and {McCullough}, P.~R. and {Morton}, Timothy D. and {Narita}, Norio and {Paegert}, Martin and {Palle}, Enric and {Pepe}, Francesco and {Pepper}, Joshua and {Quirrenbach}, Andreas and {Rinehart}, S.~A. and {Sasselov}, Dimitar and {Sato}, Bun'ei and {Seager}, Sara and {Sozzetti}, Alessandro and {Stassun}, Keivan G. and {Sullivan}, Peter and {Szentgyorgyi}, Andrew and {Torres}, Guillermo and {Udry}, Stephane and {Villasenor}, Joel},
        title = "{Transiting Exoplanet Survey Satellite (TESS)}",
     keywords = {Astrophysics - Earth and Planetary Astrophysics, Astrophysics - Solar and Stellar Astrophysics},
    booktitle = {Space Telescopes and Instrumentation 2014: Optical, Infrared, and Millimeter Wave},
         year = 2014,
       editor = {{Oschmann}, Jr., Jacobus M. and {Clampin}, Mark and {Fazio}, Giovanni G. and {MacEwen}, Howard A.},
       series = {Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series},
       volume = {9143},
        month = aug,
          eid = {914320},
        pages = {914320},
          doi = {10.1117/12.2063489},
 archivePrefix = {arXiv},
       eprint = {1406.0151},
 primaryClass = {astro-ph.EP},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2014SPIE.9143E..20R},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
 }
@article{tess_response_curve,
 author = {George R. Ricker and Joshua N. Winn and Roland Vanderspek and David W. Latham and G{\'a}sp{\'a}r  {\'A}. Bakos and Jacob L. Bean and Zachory K. Berta-Thompson and Timothy M. Brown and Lars Buchhave and Nathaniel R. Butler and R. Paul Butler and William J. Chaplin and David B. Charbonneau and J{\o}rgen Christensen-Dalsgaard and Mark Clampin and Drake Deming and John P. Doty and Nathan De Lee and Courtney Dressing and Edward W. Dunham and Michael Endl and Fran{\c{c}}ois Fressin and Jian Ge and Thomas Henning and Matthew J. Holman and Andrew W. Howard and Shigeru Ida and Jon M. Jenkins and Garrett Jernigan and John Asher Johnson and Lisa Kaltenegger and Nobuyuki Kawai and Hans Kjeldsen and Gregory Laughlin and Alan M. Levine and Douglas Lin and Jack J. Lissauer and Phillip MacQueen and Geoffrey Marcy and Peter R. McCullough and Timothy D. Morton and Norio Narita and Martin Paegert and Enric Palle and Francesco Pepe and Joshua Pepper and Andreas Quirrenbach and Stephen A. Rinehart and Dimitar Sasselov and Bun’ei Sato and Sara Seager and Alessandro Sozzetti and Keivan G. Stassun and Peter Sullivan and Andrew Szentgyorgyi and Guillermo Torres and Stephane Udry and Joel Villasenor},
 title = {{Transiting Exoplanet Survey Satellite}},
@@ -176,6 +196,47 @@ volume = {4},
 journal = {Defence S\&T Technical Bulletin}
 }
@ARTICLE{flare_duration,
       author = {{Reep}, Jeffrey W. and {Barnes}, Will T.},
        title = "{Forecasting the Remaining Duration of an Ongoing Solar Flare}",
      journal = {Space Weather},
     keywords = {solar flares, forecasting, Astrophysics - Solar and Stellar Astrophysics, Physics - Space Physics},
         year = 2021,
        month = oct,
       volume = {19},
       number = {10},
          eid = {e02754},
        pages = {e02754},
          doi = {10.1029/2021SW002754},
 archivePrefix = {arXiv},
       eprint = {2103.03957},
 primaryClass = {astro-ph.SR},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2021SpWea..1902754R},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
 }
@article{priest_2,
 author = {Priest, Eric and Forbes, T.G.},
 year = {2002},
 month = {01},
 pages = {313-377},
 title = {The magnetic nature of solar flares},
 volume = {10},
 journal = {Astronomy and Astrophysics Review},
 doi = {10.1007/s001590100013}
 }
@BOOK{priest_1,
       author = {{Priest}, Eric and {Forbes}, Terry},
        title = "{Magnetic Reconnection: MHD Theory and Applications}",
         year = 2000,
          doi = {10.1017/CBO9780511525087},
       adsurl = {https://ui.adsabs.harvard.edu/abs/2000mare.book.....P},
      adsnote = {Provided by the SAO/NASA Astrophysics Data System}
 }
@misc{soho_project_page,
  author = {{The SOHO Team}},
  url = {https://soho.nascom.nasa.gov/},
@@ -1099,7 +1160,7 @@ archivePrefix = {arXiv},
 }
@software{pandas,
-    author       = {The pandas development team},
+    author       = {{The pandas development team}},
    title        = {pandas-dev/pandas: Pandas},
    month        = feb,
    year         = 2020,
@@ -2,6 +2,6 @@
 % 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
-In conclusion the only cumulative results which shows a significant spot dependence are those for G type stars. This distribution shows a significant increase in flares during the phase minimum over the overall flare distribution. The distribution shows a strong similarity to a normal distribution. The same accounts for the two selected G type stars BD-08 995 and TYC 4595-107-1 which were presented and discussed. The histograms for K dwarfs on the other hand do not reveal similarities to a normal distribution. There appears a singular peak in the histogram with 10 bins at the phase minimum, with a few additional narrower peaks in the histogram with 30 bins. This could indicate a dependence of some sort, but a more detailed view at the individual stars is needed. As this category includes V* V471 Tau (close binary system with a white dwarf), similar interactions could happen on other stars. While there is no significant result for a spot dependence of the detected flares on M dwarfs, some individual stars show a behaviour similar to G-stars. HK Aqr and KOI-256 are here good examples, whereas 2MASS J19230963+3739397 shows few flares in the minimum but more flares in the maximum of the phasefolded lightcurve.\\
+In conclusion the only cumulative results which shows a significant spot dependence are those for G type stars. This distribution shows a significant increase in flares during the phase minimum over the overall flare distribution. The distribution shows a strong similarity to a normal distribution. The same accounts for the two selected G type stars BD-08 995 and TYC 4595-107-1 which were presented and discussed individually. The histograms for K dwarfs on the other hand do not reveal similarities to a normal distribution. There appears a singular peak in the histogram with 10 bins at the phase minimum, with a few additional narrower peaks in the histogram with 30 bins. This could indicate a dependence of some sort, but a more detailed view at the individual stars is needed. As this category includes V* V471 Tau (close binary system with a white dwarf), similar interactions could happen on other stars. While there is no significant result for a spot dependence of the detected flares on M dwarfs, some individual stars show a behaviour similar to G-stars. HK Aqr and KOI-256 are here good examples, whereas 2MASS J19230963+3739397 shows few flares in the minimum but more flares in the maximum of the phasefolded lightcurve.\\
-Overall improvements to the folding algorithms are required to handle edge cases better (e.g. KOI-256) , while not breaking for others. This could either be done automatically, or by setting special parameters for individual stars. Even though the latter would require manual user interaction and checking the edge cases manually. Additionally a common folding epoch for multiple fits files of the same star could be implemented. A good example would be V471 Tau, which showed a consistent spot modulation in some of its TESS lightcurves which differed from its rotational period. Implementing something like this could guarantee that the (in this case) transit of the white dwarf would always be at the same position in the phase, and not "jumping" between the center and the edges. Furthermore the energy for the flares could be calculated. For this improvments for the flare duration algorithm is required though, as it currently is just an estimation and does not account for the longest flare durations. It neither makes a distinction between TESS lightcurves with a 2 minute cadence and the Kepler/K2 short cadence data which has a cadence of 1 minute.\\
+Overall improvements to the folding algorithms are required to handle edge cases better (e.g. KOI-256) , while not breaking for others. This could either be done automatically, or by setting special parameters for individual stars. Even though the latter would require manual user interaction and checking the edge cases manually. Additionally a common folding epoch for multiple "fits "files of the same star could be implemented. A good example would be V471 Tau, which showed a consistent spot modulation in some of its TESS lightcurves which differed from its rotational period. Implementing something like this could guarantee that the (in this case) transit of the white dwarf would always be at the same position in the phase, and not "jumping" between the center and the edges. Furthermore the energy for the flares could be calculated. To achieve this, improvement of the flare duration algorithm is required though, as it currently makes just an estimation of the flare duration and does not account for the longest flare durations. It neither makes a distinction between TESS lightcurves with a 2 minute cadence and the Kepler/K2 short cadence data which has a cadence of 1 minute.\\
 Furthermore more stars could be taken into consideration. While the Kepler/K2 missions are complete, the TESS mission is being extended and still observing as of writing this thesis. One could also take into account Kepler long cadence data (30 minute cadence), which would not be able to detect shorter duration flares, but being available for a larger amount of stars.
@@ -8,41 +8,41 @@ In this chapter the selection criteria for the data are explained (section \ref{
 \section{Data selection}
 \label{sec:data:data_selection}
-This study uses a broad selection of Kepler/K2 and TESS lightcurves (427 for Kepler, 27 for K2, 1579 for TESS), which were downloaded from MAST with the help of the astroquery (\cite{astroquery}) python package. For Kepler and its continuation mission K2 short-cadence data were used. Unlike long-cadence data with a cadence of 30 minutes, this allows the resolution of shorter events too, as the duration of flares can vary between a few tens of seconds to a few hours (\cite{flare_duration1}).
+This study uses a broad selection of Kepler/K2 and TESS lightcurves (427 for Kepler, 27 for K2, 1579 for TESS), which were downloaded from MAST with the help of the astroquery \citep{astroquery} python package. For Kepler and its continuation mission K2 short-cadence data were used. Unlike long-cadence data with a cadence of 30 minutes, this allows the resolution of shorter events too, as the duration of flares can vary between a few tens of seconds to a few hours \citep{flare_duration1}.
-The initial dataset was taken from a list of well known flaring stars from \cite{kepler_411_study}, \cite{kepler_411_210_comparison}, \cite{doyle_2018}, \cite{doyle_2019}, \cite{au_mic_flaring_spi} and \cite{flare_occurance_periodicity}. These stars were selected because previous studies revealed that these stars showed detectable flares. This allowed a test of the algorithm described in the next section and a comparison with previous results.
+The initial dataset was taken from a list of well known flaring stars from \citet{kepler_411_study}, \citet{kepler_411_210_comparison}, \citet{doyle_2018}, \citet{doyle_2019}, \citet{au_mic_flaring_spi} and \citet{flare_occurance_periodicity}. These stars were selected because previous studies revealed that these stars showed detectable flares. This allowed a test of the algorithm described in the next section and a comparison with previous results.
-Additionally the dataset of M to F stars of \cite{althukair_starlist} which can be found at \href{https://github.com/akthukair/AFD}{https://github.com/akthukair/AFD} was parsed to the downloader GUI. As not all data were available as short cadence data from Kepler/K2, only a subset of this large sample was added. The full list of stars, for which datasets were downloaded and parsed can be found in appendix \ref{chap:list_of_stars} table \ref{apA:list_of_all_stars}.
+Additionally the dataset of M to F stars of \citet{althukair_starlist} which can be found at \href{https://github.com/akthukair/AFD}{https://github.com/akthukair/AFD} was parsed to the downloader GUI. As not all data were available as short cadence data from Kepler/K2, only a subset of this large sample was added. The full list of stars, for which datasets were downloaded and parsed can be found in appendix \ref{chap:list_of_stars} table \ref{apA:list_of_all_stars}.
 \section{Data reduction algorithms}
 \label{sec:data:data_reduction}
-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 \citep{10.5555/1593511}. It also makes extensive use of the python packages astropy \citep{astropy:2018}, numpy \citep{numpy}, scipy \citep{scipy}, pandas \citep{pandas} and lightkurve \citep{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}
 \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 the function $flatten()$ 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 the function $flatten()$ 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 \citet{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 python 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 (optional) as well as the minimum distance of datapoints (optional). 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 (optional) as well as the minimum distance of datapoints (optional). Afterwards the found peaks are sorted by height, and the highest 100 are returned. This was found to be a good amount as the largest number of flares per "fits" file found in this study were around 70 for CD-56 1032A and B.\\
-Afterwards each individual peak is checked. The first step is to estimate a flare starting and end point. 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 a sufficient number of datapoints for the following steps.\\
+Afterwards each individual peak is checked. The first step is to estimate a flare starting and end point. This is done by checking the datapoints before and after the peak. If it finds that the flux difference 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 a sufficient number of datapoints for the following steps.\\
-Afterwards multiple checks are done. It first checks if the datapoints right before and after the peak are above a threshold of 0.003 (0.3\%) above the mean flattened flux, or if the two datapoints right after the peak are above that 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. This eliminates possible false positives which were found by manually inspecting previously found events, but could not be guaranteed to be two seperate events. In such cases it will only count one flare. Then the flare lightcurve is fitted. For the impulsive phase, a gaussian function is used and for the gradual phase an exponetial function is used to account for the exponential decay in flare lightcurves (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 locations 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 artificial spike (values of 10 or higher when normalized).
+Afterwards multiple checks are done. It first checks if the datapoints right before and after the peak are above a threshold of 0.003 (0.3\%) above the mean flattened flux, or if the two datapoints right after the peak are above that threshold (which is a similar approach to \citet{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. This eliminates possible false positives which were found by manually inspecting previously found events, but could not be guaranteed to be two seperate events. In such cases it will only count one flare. Then the flare lightcurve is fitted. For the impulsive phase, a gaussian function is used and for the gradual phase an exponential function is used to account for the exponential decay in flare lightcurves (similar approach to \citet{au_mic_flaring_spi} and \citet{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 locations 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 artificial spike (values of 10 or higher when normalized).
 \subsection{Lightcurve folding}
 \label{sec:data:data_reduction:lightcurve_folding}
 This section mainly describes how the $getOptimizedFold()$ function works. This function was written to optimize the lightcurve folding, to improve accuracy for the folding and lightcurve fitting process. It uses the normalized lightcurve as well as the preferred fitting function type (see chapter \ref{sec:gui:data_display}) 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 box-least-squares algorithm. Afterwards the four highest peaks of each are taken and converted into periods (unit in days).
+The function at first generates two periodograms with the $to\_periodogram$ function from the lightkurve python package. The first one uses the Lomb-Scargle algorithm, while the second one uses the box-least-squares algorithm. Afterwards the four highest peaks of each are taken and converted into periods (unit in days).
-Then each period found by each algorithm is compared with the periods found by the other, and in the case of a match (absolute value of the difference between the values of the two algorithms is smaller than 5\% of the larger of the two periods) this is now used as the rotational period as well as the spot modulation period. If it does not find a match, it uses the period corresponding to the highest peak in the lombscargle periodogram.
+Then each period found by each algorithm is compared with the periods found by the other, and in the case of a match (absolute value of the difference between the values of the two algorithms is smaller than 5\% of the larger of the two periods) this is now used as the rotational period as well as the spot modulation period. If it does not find a match, it uses the period corresponding to the highest peak in the Lomb-Scargle periodogram.
 Afterwards it calculates the epoch time to the first minimum in the lightcurve using numpys $argrelextrema$ function. In the following loop, which is repeated up to 30 times, the lightcurve is folded (using the lightkurve $fold$ function) with the spot modulation period, and the epoch set to the first minima in the lightcurve. Then a fit is performed using the prefered fitting method. If the fitting process fails for the preferred fitting type, and it was set to "sine", it will fall back to "poly" (polynomial fit), and vice versa. If the resulting fit has two maxima, and they are further away from the edges than 10\% of the used period, the algorithm checks if there is a signal for half the used period in any of the two periodograms. If this is the case, it will use this as the period for spot modulation. It will save the current folded lightcurve as folded by rotational period, and generate a new folded lightcurve with the newly found spot modulation period. Afterwards it checks the location of the minimum of the spot modulation folded lightcurve. If the minimum is within 1\% of half the phase it will stop. If not, it will shift the epoch by the difference of the minimum to zero, which is the center of the folded lightcurve phase, and repeat the folding process.\\
 The function then returns the rotational period, the spot modulation period, the periods found by both periodograms as well as the folded lightcurve, the corresponding phase and the fit and fit type ("sine", "poly" or "linear") as well as the epoch. If the spot modulation differs from the found rotational period, it will also return the folded lightcurve, phase, fit and fit type of the rotational period folded lightcurve. The last returned value is "isValid", which is set to false if the algorithm does not find a fit with its minimum at half the phase for the spot modulation period folded lightcurve within 30 iterations.
-\section{Spectral type identification}
+\section{Spectral type classification}
 \label{sec:data:sptype_identification}
 After the initial download and cross checking with SIMBAD, not all stars had a spectral type assigned. For these stars magnitudes in different wavelength bands were available. The stars with known magnitudes at least in the B and V bands are given in table \ref{tab:unknown_sptypes_bv}, while the stars with only J, H and K bands are given in table \ref{tab:unknown_sptypes_jhk}.
-The B-V color index as well as other color indices (if available) have been compared to the table in \cite{spectral_type_color_table} (\href{https://www.stsci.edu/~inr/intrins.html}{https://www.stsci.edu/~inr/intrins.html}). 
+The B-V color index as well as other color indices (if available) have been compared to the table in \citet{spectral_type_color_table} (\href{https://www.stsci.edu/~inr/intrins.html}{https://www.stsci.edu/\textasciitilde{}inr/intrins.html}).
-This allowed a rough classification of the stars in table \ref{tab:unknown_sptypes_bv}. Additionally, also the effective temperature was taken into account from the TESS Input Catalogue (\cite{revised_tess_input_catalogue}) from Vizier (\cite{vizier}). The classification table for spectral types based on effective temperature has been taken from \cite{harvard_spectral_types_teff} (\href{https://lweb.cfa.harvard.edu/~pberlind/atlas/htmls/note.html}{https://lweb.cfa.harvard.edu/~pberlind/atlas/htmls/note.html}).\\
+This allowed a rough classification of the stars in table \ref{tab:unknown_sptypes_bv}. Additionally, also the effective temperature was taken into account from the TESS Input Catalogue \citep{revised_tess_input_catalogue} from Vizier \citep{vizier}. The classification table for spectral types based on effective temperature has been taken from \citet{harvard_spectral_types_teff} (\href{https://lweb.cfa.harvard.edu/~pberlind/atlas/htmls/note.html}{https://lweb.cfa.harvard.edu/\textasciitilde{}pberlind/atlas/htmls/note.html}).\\
 The final spectral type for the stars can be found in table \ref{tab:unknown_sptypes_final_output}.
 If the spectral type calculated from the effective temperature and the indices is identical, it will use that spectral type as final.
@@ -87,7 +87,7 @@ In the case of those differing, like for BD-08 995, which was found to be an ear
 \begin{landscape}
 \begin{table}
    \centering
-    \caption{Final determined spectral types. Main Identifier taken from SIMBAD. The column B-V contains the value of B-V calculated from the respective magnitudes taken from SIMBAD. The columns T\textsubscript{eff}, MASS and Radius contain the effective temperature, mass and radius for the star taken from the TESS Input Catalogue from Vizier. The column Spectral Type (B-V) contains the determined spectral type based on \cite{spectral_type_color_table}, while the column Spectral Type (T\textsubscript{eff}) contains the spectral type based on the effective temperature from \cite{harvard_spectral_types_teff}. The last column contains the spectral type which is used in this study.}
+    \caption{Final determined spectral types. Main Identifier taken from SIMBAD. The column B-V contains the value of B-V calculated from the respective magnitudes taken from SIMBAD. The columns T\textsubscript{eff}, Mass and Radius contain the effective temperature, mass and radius for the star taken from the TESS Input Catalogue from Vizier. The column Spectral Type (B-V) contains the determined spectral type based on \citet{spectral_type_color_table}, while the column Spectral Type (T\textsubscript{eff}) contains the spectral type based on the effective temperature from \citet{harvard_spectral_types_teff}. The last column contains the spectral type which is used in this study.}
    \label{tab:unknown_sptypes_final_output}
    \begin{tabular}{lccccccc}
    \hline
@@ -1,37 +1,33 @@
 \chapter{Discussion \label{sec:discussion}}
-The investigation of a flare to spot relation 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 which have been 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 iterations 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 investigation of a flare to spot relation 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 which have been 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 \citet{althukair_starlist}), could not produce valid fits (reached 30 iterations 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}.\\
 \section{Analysis}
-The analysis was done with a self written python program (discussed in chapter \ref{sec:gui}). The reason for developing a GUI was to ease the 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. 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 of the flare detection algorithm, as discussed in section \ref{sec:data:data_reduction:flare_detection}, was implemented to prevent failures due to the flattening algorithm massively inverting dips in the lightcurves. This happened for the lightcurves of 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 still generates peaks with values 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 between high and low flare peaks, but it does not calculate the flare energy. But we can say that all flares detected on G type stars  in broad-band photometry such as Kepler/K2 and TESS are superflares, as the lowest detectable flare peak by this algorithm is 1.003, and \cite{solar_like_superflares}, using Kepler data, found that an increase of 0.1\% in flux (flare peak of 1.001) is enough for those flares to be categorized as superflares.\\
+The analysis was done with a self written python program (discussed in chapter \ref{sec:gui}). The reason for developing a GUI was to ease the 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. The algorithms are based on the approaches of \citet{kepler_411_study}, \citet{au_mic_flaring_spi} and \citet{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 of the flare detection algorithm, as discussed in section \ref{sec:data:data_reduction:flare_detection}, was implemented to prevent failures due to the flattening algorithm massively inverting dips in the lightcurves. This happened for the lightcurves of 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 as 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\footnote{\href{https://exoplanetarchive.ipac.caltech.edu/overview/KOI-6423}{https://exoplanetarchive.ipac.caltech.edu/overview/KOI-6423}} \citep{koidr25}. 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 still generates peaks with values 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 between high and low flare peaks, but it does not calculate the flare energy. But we can say that all flares detected on G type stars  in broad-band photometry such as Kepler/K2 and TESS are superflares, as the lowest detectable flare peak by this algorithm is 1.003, and \citet{solar_like_superflares}, using Kepler data, found that an increase of 0.1\% in flux (flare peak of 1.001) is enough for those flares to be categorized as superflares.\\
-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 away 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 in 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 that the minimum of the fit/folded lightcurve can vary by up to \textasciitilde25\% depending on which first minimum is detected in the lightcurve.\\\\
+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 away 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 in 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 that the minimum of the fit/folded lightcurve can vary by up to \textasciitilde25\% depending on which first minimum is detected in the lightcurve.\\\\
 \section{Flares and superflares on M-F stars and their spot dependence}
-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 the algorithm or instruments being possibly not sufficiently sensitive, too noisy data or it could be that there were simply no flares during the observations. For the remaining 49 stars, a total of \textasciitilde3500 flares was 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.
+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 the algorithm or instruments being possibly not sufficiently sensitive, too noisy data or it could be that there were simply no flares during the observations. For the remaining 49 stars, a total of \textasciitilde3500 flares was detected. Using all available flares, there was no significant spot dependency detected in the histogram with 10 bins. In the third bin at phase $0.5 \pi$ 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 around phase $1.1 \pi$ has the most flares detected, and is located at the phase minimum. This could show a possible dependency with more available data, similarly to what was found for K type dwarfs. The data also contain 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}), the folded lightcurves show that for TESS sector 29 the detected minimum ($\pm$ a 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 on 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, revealing 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 \citet{kepler_411_210_comparison} found, the spot area is not the only important parameter.\\
 Limiting the flare by maximum flare peak indicates a dependency of flares on spots, which can be seen in figures \ref{fig:M-Flarecount-10_Bins_1.25_peak} to \ref{fig:M-Flarecount-10_Bins_1.05_maxpeak}. While no flare energies were calculated in this study, this could be parameters to look at in the future. Limiting the flare peaks to a maximum of 1.01 shows a higher count in the phase maxima compared to the phase minima. The same dip as with all flares can be seen here already too. Increasing the flare peak limit to 1.05 shows a nearly identical histogram to the one with all flares. A noteworthy difference here is the peak in the bin at the phase minimum at $1 \pi$. \citet{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.
-While not being significant, the 6th bin has the most flares detected, and is located at the phase minimum.
+Out of a total of \textasciitilde40 K dwarfs in the list of stars to be analyzed, flares could only be detected on 21 stars. This could be due to the algorithm or instruments being possibly not sufficiently sensitive, too noisy data or it could be that there were simply no flares during the observations. Overall the results for the flare distribution of K dwarfs is similar to those of M dwarfs, with the exception of the bin (bins for the histogram with 30 bins) around the phase minimum. This bin shows a significantly increased flare count. One of the causes for this, but not the sole one, is V* V471 Tau (see section \ref{results:v471_tau}), which is in close orbit with a white dwarf \citep{v471tau_revised,V471tau_magnetic_activity}. This can lead to magnetic interactions between the K dwarf and the white dwarf \citep{V471tau_magnetic_activity}, which may lead to the increased flare count seen.\\
 This could show a possible dependency with more available data, similarly to what was found for K type dwarfs. The data also contain 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}), the folded lightcurves show that for TESS sector 29 the detected minimum ($\pm$ a 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, revealing 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 indicates a dependency of flares on spots, which can be seen in figures \ref{fig:M-Flarecount-10_Bins_1.25_peak} to \ref{fig:M-Flarecount-10_Bins_1.05_maxpeak}. While no flare energies were calculated in this study, this could be parameters to look at in the future. Limiting the flare peaks to a maximum of 1.01 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 1.05 shows a nearly identical histogram 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.
 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 the algorithm or instruments being possibly not sufficiently sensitive, too noisy data or it could be that there were simply no flares during the observations. Overall the results for the flare distribution of K dwarfs is similar to those of M dwarfs. With the exception of the bin (bins for the histogram with 30 bins) around the phase minimum. This bin shows a significantly increased flare count. One of the, but not the sole cause 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 may lead to the increased flarecount seen.\\
 Limiting the flare peaks to greater than 1.05 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 1.01 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 1.05 shows a similar pattern, but the gaps between peaks/dips vanishes and the histogram becomes already very similar to the histogram with all flares.
-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 the algorithm or instruments being possibly not sufficiently sensitive, too noisy data or it could be that there were simply no flares during the observations. Most of the flares detected show a peak of below 1.05, but as \cite{solar_like_superflares} found, flares with a flux increase between 0.1 to 1\% (peaks of 1.001 to 1.01) would already be categorized as superflares for G-star flares detected in broad-band photometry such as Kepler/K2 and TESS. Therefore all flares detected for G stars shown in figure \ref{fig:G-Flarecount} are superflares as the threshold of the flare detection algorithm is 0.3\%.
+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 the algorithm or instruments being possibly not sufficiently sensitive, too noisy data or it could be that there were simply no flares during the observations. Most of the flares detected show a peak of below 1.05, but as \citet{solar_like_superflares} found, flares with a flux increase between 0.1 to 1\% (peaks of 1.001 to 1.01) would already be categorized as superflares for G-star flares detected in broad-band photometry such as Kepler/K2 and TESS. Therefore all flares detected for G stars shown in figure \ref{fig:G-Flarecount} are superflares as the threshold of the flare detection algorithm is 0.3\%.
 For the flares found in this study for G type stars, there is 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. As no energies have been deduced from the Kepler/K2 and TESS observations a categorization in flares and superflares is difficult for all stars investigated in the present study.\\
 Limiting the flare peaks to a minimum of 1.05 shows three major peaks. The largest 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 is according to its BV color index and effective temperature a late G type star, reflects this trend well. It shows the same bell curve style histogram as the overall flare number histogram of G-stars. Additionally though it also shows a slight increase in flare number around the phase maximum, its highest flare peak was detected around the phase maximum (see figure \ref{fig:BD-08_995-flarepeaks_1.2}). The maximum flare count for TYC 4595-107-1 on the other hand is slightly offset before the phase minimum (see figure \ref{fig:TYC_4595-107-1-Flarecount-10_Bins}). 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 (see figure \ref{fig:TYC_4595-107-1-flarepeaks_1.27}).
+BD-08 995, which is according to its B-V color index and effective temperature a late G type star, reflects this trend well. It shows the same bell curve style histogram as the overall flare number histogram of G-stars. Additionally though it also shows a slight increase in flare number around the phase maximum, its highest flare peak was detected around the phase maximum (see figure \ref{fig:BD-08_995-flarepeaks_1.2}). The maximum flare count for TYC 4595-107-1 on the other hand is slightly offset before the phase minimum (see figure \ref{fig:TYC_4595-107-1-Flarecount-10_Bins}). 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 (see figure \ref{fig:TYC_4595-107-1-flarepeaks_1.27}).
 Out of a total of \textasciitilde13 F dwarfs in the list of stars to be analyzed, flares could only be detected on four stars. This could be due to the algorithm or instruments being possibly not sufficiently sensitive, too noisy data or it could be that there were simply no flares during the observations. While all flares detected are centered around the phase minimum, the total of 5 flares detected is not a sufficiently large sample to draw a definite conclusion on the spot to flare/superflare relation.
-For two stars, namely the K-dwarf TYC 1360-957-1 and the M-dwarf HK Aqr we find that the most energetic flares occur at the same phase. For TYC 1360-957-1 (see figure \ref{fig:TYC_1360-957-1-flarepeaks_1.31}) the flares with largest flare peak originate all from phase $0.7$ to $0.8 \pi$. Two flares were detected in TESS sector 44 and one two sectors later (sector 46). From the Sun we know that spots can have lifetimes of severeal rotation periods i.e. several months. This maybe also the case for the spot or spot group being the origin of the three strong flares on TYC 1360-957-1.
+For two stars, namely the K-dwarf TYC 1360-957-1 and the M-dwarf HK Aqr we find that the most energetic flares occur at the same phase. For TYC 1360-957-1 (see figure \ref{fig:TYC_1360-957-1-flarepeaks_1.31}) the flares with largest flare peak originate all from phase $0.7$ to $0.8 \pi$. Two flares were detected in TESS sector 44 and one two sectors later (sector 46). From the Sun we know that spots can have lifetimes of several rotation periods i.e. several months. This maybe also the case for the spot or spot group being the origin of the three strong flares on TYC 1360-957-1.
-A similar finding was made on HK Aqr. Also the three strongest flares have been found to occur at the same phase. For HK Aqr this happened in one TESS sector (sector 29, see figure \ref{fig:HKAqr-TESS29_foldedLC_Period}). Also here the it is reasonable to assume that these three flares have been generated by the same spot or spot group. For both stars the phases at which these strong flares have occurred are close to the phase minimum, i.e. correspond to hemispheres of the stars showing a hugh spottedness. 
+A similar finding was made on HK Aqr. Also the three strongest flares have been found to occur at the same phase. For HK Aqr this happened in one TESS sector (sector 29, see figure \ref{fig:HKAqr-TESS29_foldedLC_Period}). Also here it is reasonable to assume that these three flares have been generated by the same spot or spot group. For both stars the phases at which these strong flares have occurred are close to the phase minimum, i.e. correspond to hemispheres of the stars showing a huge spottedness. 
-Looking at all results together, there is a trend that more flares occur when a more spotted stellar hemisphere is visible, than vice versa. This 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 dominates the overall results. 
+Looking at all results together, there is a trend that more flares occur when a more spotted stellar hemisphere is visible, than vice versa. This is mostly influenced by the results for K and G stars. The dip in the otherwise seemingly flat histogram for the results of M dwarfs dominates the overall results.
 There is at the moment no explanation for the significant dip in the histogram and we doubt that it has a physical meaning. %The results of the study support the results from \cite{connection_starspots_flares_ms_kepler} for G+F stars and the overall picture of flares being caused by reconnecting stellar magnetic fields originating in stellar spots rather than being triggered from close-in orbiting planets. As the histogram of G-star flares is representative for superflares the statement above counts for both flares and superflares.
-All results will be published on github. The program will be available at \href{URL}{text} while the data will be available at \href{URL}{text}.
+\\All results will be published on github. The program will be available at \href{URL}{text} while the data will be available at \href{URL}{text}.
@@ -1,18 +1,18 @@
-\chapter{GUI}
+\chapter{GUI application}
 \label{sec:gui}
-In this chapter the usage of the developed GUI application is explained. It was developed to easily download new data, as well as to try various algorithms for flare detection and the usage of various functions of the $lightkurve$ python package (\cite{lightkurve}).
+In this chapter the usage of the newly developed GUI application is explained. It was developed to easily download new data, as well as to try various algorithms for flare detection and the usage of various functions of the $lightkurve$ python package \citep{lightkurve}. The GUI is written in python 3 \citep{10.5555/1593511} and uses the PyQt5 \citep{pyqt5} framework. 
 \section{Data download}
 \label{sec:gui:data_download}
-During the first startup the GUI window (e.g. in figure \ref{fig:full_gui_normal_selection}) is nearly completely empty. An empty local database will be created with SQLite3 (\cite{sqlite}). To show lightcurves, data need to be downloaded first. For that, the "Add" button has to be clicked and a new dialog window appears. This can be seen in figure \ref{fig:download_new_star_data_gui}. This GUI uses the astroquery (\cite{astroquery}) python package to fetch metadata and download fits files from the Mikulski Archive for Space Telescopes (MAST).\\
+During the first startup the GUI window (e.g. in figure \ref{fig:full_gui_normal_selection}) is nearly completely empty. An empty local database will be created with SQLite3 \citep{sqlite}. To show lightcurves, data need to be downloaded first. For that, the "Add" button has to be clicked and a new dialog window appears. This can be seen in figure \ref{fig:download_new_star_data_gui}. This GUI uses the astroquery \citep{astroquery} python package to fetch metadata and download flexible image transport system (fits) files from the Mikulski Archive for Space Telescopes (MAST).\\
-The first step is to enter the identifier of the star(s). In case of multiple identifiers, they have to be seperated by a semicolon. Then the missions from which the data should be fetched can be selected. The supported missions are TESS and Kepler/K2. For Kepler and K2 short and/or long cadence can be selected. The differences are described in section \ref{sec:intro:space_missions}. After the selection has been made, the fetch button needs to be pressed. The program will then request metadata matching the star identifier(s) and selected missions from the MAST archive. The found mission data is then displayed in the preview field. It can then be downloaded by pressing the "Ok" button. The program then proceeds to download the corresponding fits-files. The filename and TESS sector or Kepler/K2 target table ID is appended to the previously fetched metadata and handed back to the main GUI.\\
+The first step is to enter the identifier of the star(s). In case of multiple identifiers, they have to be seperated by a semicolon. Then the missions from which the data should be fetched can be selected. The supported missions are TESS and Kepler/K2. For Kepler and K2 short and/or long cadence can be selected. The differences are described in section \ref{sec:intro:space_missions}. After the selection has been made, the fetch button needs to be pressed. The program will then request metadata matching the star identifier(s) and selected missions from the MAST archive. The found mission data is then displayed in the preview field. It can then be downloaded by pressing the "Ok" button. The program then proceeds to download the corresponding "fits" files. The filename and TESS sector or Kepler/K2 target table ID is appended to the previously fetched metadata and handed back to the main GUI.\\
-There a request to Simbad is made to fetch additional metadata. First the alternative identifiers are fetched from Simbad, which also have a MAIN\_ID attribute. This is to make sure we only have one entry in the local database per star and no duplicates. Afterwards additional data is fetched from Simbad (\cite{simbad}) like spectral type, radial velocity and distance. After the data is gathered, the main identifier, the alternative identifiers, spectral type, rotational velocity and distance (and their respective units) as well as the file path, source (TESS, Kepler or K2), and sector/target table id are saved into a local database using SQLite3 (\cite{sqlite}).
+There a request to SIMBAD is made to fetch additional metadata. First the alternative identifiers are fetched from SIMBAD, which also have a MAIN\_ID attribute. This is to make sure we only have one entry in the local database per star and no duplicates. Afterwards additional data is fetched from SIMBAD \citep{simbad} like spectral type, radial velocity and distance. After the data is gathered, the main identifier, the alternative identifiers, spectral type, rotational velocity and distance (and their respective units) as well as the file path, source (TESS, Kepler or K2), and sector/target table ID are saved as an unique identifier into a local database using SQLite3 \citep{sqlite}. For Kepler/K2 the target table ID was chosen instead of the quarter, as the target table ID is a unique number, whereas there can be multiple "fits" files for the same star and the same quarter.
 \begin{figure}[pt!]
  \includegraphics[width=\linewidth]{gui/download_star_data_gui.png}
-  \caption{GUI window for downloading new fit files with astroquery designed using the Qt5 designer shipped with PyQt5 (\cite{pyqt5}). The star identifier field supports one or more (separated by a semicolon) identifiers. There are checkboxes to select TESS, Kepler (long and/or short cadence) and K2 (long and/or short cadence) data. The preview field shows metadata (Identifier, TESS quarter or Kepler/K2 target table ID) to check the data which was found and which can be downloaded. The "Ok" button then proceeds to download the data and hands information back to the main GUI.}
+  \caption{GUI window for downloading new "fits" files with astroquery designed using the Qt5 designer shipped with PyQt5 \citep{pyqt5}. The star identifier field supports one or more (separated by a semicolon) identifiers. There are checkboxes to select TESS, Kepler (long and/or short cadence) and K2 (long and/or short cadence) data. The preview field shows metadata (Identifier, TESS sector or Kepler/K2 target table ID) to check the data which was found and which can be downloaded. The "Ok" button then proceeds to download the data and hands information back to the main GUI.}
  \label{fig:download_new_star_data_gui}
 \end{figure}
@@ -20,15 +20,15 @@ There a request to Simbad is made to fetch additional metadata. First the altern
 \label{sec:gui:data_display}
 Afterwards the list of stars seen in figure \ref{fig:full_gui_normal_selection} will be refreshed. It shows the alphabetically sorted main identifier determined from SIMBAD.\\
-When one of the stars in the list is selected, the program will show the additionally saved information. This includes all known identifiers for the star (categorized as alternative identifiers in the Alt. IDs list seen in the "Star infos" section of the GUI), the spectral type, its rotational velocity and its distance (from SIMBAD). Additionally a preferred fitting type for the folded lightcurves (which are described in section \ref{sec:data:data_reduction}) can be selected. The default value for this is "sine". The list to the right of the information section shows the available flexible image transport system (fits) files. The formating for the list entries is "TESS - <sequence>" and "Kepler/K2 - <target table id>". The "combine" button combines temporary multiple "fits" files into one, which is then plotted. Selecting one or combining multiple "fits" files, enables the plot options.\\
+When one of the stars in the list is selected, the program will show the additionally saved information. This includes all known identifiers for the star (categorized as alternative identifiers in the Alt. IDs list seen in the "Star infos" section of the GUI), the spectral type, its rotational velocity and its distance (from SIMBAD). Additionally a preferred fitting type for the folded lightcurves (which are described in section \ref{sec:data:data_reduction}) can be selected. The default value for this is "sine". The list to the right of the information section shows the available "fits" files. The formating for the list entries is "TESS - <sequence>" and "Kepler/K2 - <target table id>". The "combine" button combines temporary multiple "fits" files into one, which is then plotted. Selecting one or combining multiple "fits" files, enables the plot options.\\
-The main plot options allow the user to change the type of flux thats plotted. This is either "SAP\_FLUX" (simple aperture photometry) or "PDCSAP\_FLUX" (presearch data conditioning simple aperture photometry) (\cite{lightkurve}) with the latter being the default option. The PDCSAP\_FLUX has parts of its data removed depending on the quality flags (e.g. indicating systematic errors like an attitude tweak or a cosmic ray (\cite{tess_science_data_products}, \cite{kepler_archive_manual})) as well as corrected long-term brightness changes (\cite{lightkurve}). An example of a PDCSAP\_FLUX is shown in figure \ref{fig:full_gui_normal_selection}.\\
+The main plot options allow the user to change the type of flux that is plotted. This is either "SAP\_FLUX" (simple aperture photometry) or "PDCSAP\_FLUX" (presearch data conditioning simple aperture photometry) \citep{lightkurve} with the latter being the default option. The PDCSAP\_FLUX has parts of its data removed depending on the quality flags (e.g. indicating systematic errors like an attitude tweak or a cosmic ray \citep{tess_science_data_products,kepler_archive_manual}) as well as corrected long-term brightness changes \citep{lightkurve}. An example of a PDCSAP\_FLUX is shown in figure \ref{fig:full_gui_normal_selection}.\\
-The lightkurve python package also supports normalizing (to unscaled, percent, parts per thousands (ppt) or parts per million (ppm)) which can be seen in figure \ref{fig:full_gui_normal_selection_normalize_options}. Flattened lightcurves (see figure \ref{fig:full_gui_normal_selection_flattened} as an example for $BD-08\ 995$) are used to identify flares. The "remove outliers", "remove nans/infs" and "bin" features are exposed in the GUI, but are not actively used in this thesis.\\
+The lightkurve python package also supports normalizing (to unscaled, percent, parts per thousands (ppt) or parts per million (ppm)) which can be seen in figure \ref{fig:full_gui_normal_selection_normalize_options}. Flattened lightcurves (see figure \ref{fig:full_gui_normal_selection_flattened} as an example for $BD-08\ 995$) are used to identify flares. The "remove outliers", "remove nans/infs" and "bin" features are available in the GUI, but are not actively used in this thesis.\\
-The checkboxes to flatten the lightcurve, meaning removing all longterm trends like spot/rotational modulation but leaving short term events intact (figure \ref{fig:full_gui_normal_selection_flattened}), folding the lightcurve (figure \ref{fig:full_gui_normal_selection_folded}) and showing the periodogram (figures \ref{fig:full_gui_normal_selection_periodogram_lombscargle} and \ref{fig:full_gui_normal_selection_periodogram_boxleastsquares}) are exclusive of each other. Only one can be used at a time. The values for "Period" and "Epoch Time" are automatically calculated and used as default for the selected lightcurve. If "Optimize" in the "Fold" options is unchecked, the "Epoch Time" represents the first found minimum in the lightcurve, and the "Period" is set to the period of the highest peak found in the lombscargle periodogram. If "Optimize" is checked, it will use the found rotational period of the optimize fold algorithm described in \ref{sec:data:data_reduction:lightcurve_folding}. If "Show Spot Modulation" is selected, it will use the found spot modulation period instead of the rotational period.
+The checkboxes to flatten the lightcurve, meaning removing all longterm trends like spot/rotational modulation but leaving short term events intact (figure \ref{fig:full_gui_normal_selection_flattened}), folding the lightcurve (figure \ref{fig:full_gui_normal_selection_folded}) and showing the periodogram (figures \ref{fig:full_gui_normal_selection_periodogram_lombscargle} and \ref{fig:full_gui_normal_selection_periodogram_boxleastsquares}) are exclusive of each other. Only one can be used at a time. The values for "Period" and "Epoch Time" are automatically calculated and used as default for the selected lightcurve. If "Optimize" in the "Fold" options is unchecked, the "Epoch Time" represents the first found minimum in the lightcurve, and the "Period" is set to the period of the highest peak found in the Lomb-Scargle periodogram. If "Optimize" is checked, it will use the found rotational period of the optimize fold algorithm described in \ref{sec:data:data_reduction:lightcurve_folding}. If "Show Spot Modulation" is selected, it will use the found spot modulation period instead of the rotational period (see section \ref{sec:data:data_reduction:lightcurve_folding}).
 \begin{landscape}
 \begin{figure}[pt!]
  \includegraphics[width=\linewidth]{gui/full_gui_normal_selection.png}
-  \caption{Main GUI window. This window was designed with the Qt5 designer shipped with PyQt5 (\cite{pyqt5}). It shows a list of all available stars with their main identifier (taken from SIMBAD) sorted alphabetically. The "Star infos" box contains additional information on the star gathered from SIMBAD. The "Sequences/Target Table ID" box shows the list of all available lightcurves for the selected star, with an option to combine multiple "fits" files to plot at once. To the right of the list of available lightcurves are different plot options, which utilize the different capabilities of the lightkurve python package (\cite{lightkurve}). In this image the TESS Sector 32 lightcurve of $BD-08\ 995$ is shown. The red crosses show the peaks of the detected flares, while the red solid lines the lightcurve indicate the duration estimate of the flare.}
+  \caption{Main GUI window. This window was designed with the Qt5 designer shipped with PyQt5 \citep{pyqt5}. It shows a list of all available stars with their main identifier (taken from SIMBAD) sorted alphabetically. The "Star infos" box contains additional information on the star gathered from SIMBAD. The "Sequences/Target Table ID" box shows the list of all available lightcurves for the selected star, with an option to combine multiple "fits" files to plot at once. To the right of the list of available lightcurves are different plot options, which utilize the different capabilities of the lightkurve python package \citep{lightkurve}. In this image the TESS Sector 32 lightcurve of $BD-08\ 995$ is shown. The red crosses show the peaks of the detected flares, while the red solid lines the lightcurve indicate the duration estimate of the flare.}
  \label{fig:full_gui_normal_selection}
 \end{figure}
 \end{landscape}
@@ -44,7 +44,7 @@ The checkboxes to flatten the lightcurve, meaning removing all longterm trends l
 \begin{landscape}
 \begin{figure}[pt!]
  \includegraphics[width=\linewidth]{gui/full_gui_normal_selection_normalize_options.png}
-  \caption{Main GUI window. Same as in figure \ref{fig:full_gui_normal_selection}, with the difference that the lightcurve was normalized. It also shows all possible normalize options the lightkurve python package (\cite{lightkurve}) supports.}
+  \caption{Main GUI window. Same as in figure \ref{fig:full_gui_normal_selection}, with the difference that the lightcurve was normalized. It also shows all possible normalize options the lightkurve python package \citep{lightkurve} supports.}
  \label{fig:full_gui_normal_selection_normalize_options}
 \end{figure}
 \end{landscape}
@@ -52,7 +52,7 @@ The checkboxes to flatten the lightcurve, meaning removing all longterm trends l
 \begin{landscape}
 \begin{figure}[pt!]
  \includegraphics[width=\linewidth]{gui/full_gui_normal_selection_flattened.png}
-  \caption{Main GUI window. Showing the same lightcurve as figure \ref{fig:full_gui_normal_selection}, with the difference that it is now flattened. The green line shows a fit of the flare. This is described in chapter \ref{sec:data:data_reduction}.}
+  \caption{Main GUI window. Showing the same lightcurve as figure \ref{fig:full_gui_normal_selection}, with the difference that it is now flattened. The green lines show a fit of the flares. This is described in chapter \ref{sec:data:data_reduction}.}
  \label{fig:full_gui_normal_selection_flattened}
 \end{figure}
 \end{landscape}
@@ -68,7 +68,7 @@ The checkboxes to flatten the lightcurve, meaning removing all longterm trends l
 \begin{landscape}
 \begin{figure}[pt!]
  \includegraphics[width=\linewidth]{gui/full_gui_normal_selection_periodogram_lombscargle.png}
-  \caption{Main GUI window. Showing the periodogram of the lightcurve in figure \ref{fig:full_gui_normal_selection} using the lombscargle algorithm. Furthermore it shows the four highest peaks (which are at least separated by 100 datapoints). The method is explained in chapter \ref{sec:data:data_reduction}.}
+  \caption{Main GUI window. Showing the periodogram of the lightcurve in figure \ref{fig:full_gui_normal_selection} using the Lomb-Scargle algorithm. Furthermore it shows the four highest peaks (which are at least separated by 100 datapoints). The method is explained in chapter \ref{sec:data:data_reduction}.}
  \label{fig:full_gui_normal_selection_periodogram_lombscargle}
 \end{figure}
 \end{landscape}
@@ -84,7 +84,7 @@ The checkboxes to flatten the lightcurve, meaning removing all longterm trends l
 \FloatBarrier
 \section{Data processing \label{sec:gui:data_processing}}
-Pressing the button "New FC" will start the processing of all fits files in the current loaded database. It will sequentially go through all files and apply the flare detection algorithms described in section \ref{sec:data:data_reduction} to the lightcurves, as well as generate the periodogram and optimized folded lightcurves. This is done for the PDCSAP\_FLUX. Additionally plots for each individual lightcurve and processing step are generated. The data provides:
+Pressing the button "New FC" will start the processing of all "fits" files in the current loaded database. It will sequentially go through all files and apply the flare detection algorithms described in section \ref{sec:data:data_reduction} to the lightcurves, as well as generate the periodogram and optimized folded lightcurves. This is done for the PDCSAP\_FLUX. Additionally plots for each individual lightcurve and processing step are generated. The data provides:
 \begin{itemize}
  \item Flares (peak, timestamp, datapoint index in the lightcurve, TESS/Kepler data quality flags)
@@ -103,10 +103,10 @@ Pressing the button "New FC" will start the processing of all fits files in the
 And in the case the period and spot modulation of the star differs, it will seperately save the folded lightcurves and related data for the stars period as well.
 After this process is finished, a new window will open. It allows to show multiple different debugging statistics like flares per file, flares per star (total, or normalized to a 7 day period) or mean periods for each star. This window can be seen in figure \ref{fig:summary_statistics_window}.
-The data can then be saved by clicking "File" and then "Save As", which uses the pandas (\cite{pandas}) "to\_pickle" function. Similarly it can be loaded again using the "read\_pickle" function which is called either by "File" and then "Open" in the debugging statistics window, or by clicking "Open" in the main window next to "New FC".
+The data can then be saved by clicking "File" and then "Save As", which uses the pandas \citep{pandas} "to\_pickle" function. Similarly it can be loaded again using the "read\_pickle" function which is called either by "File" and then "Open" in the debugging statistics window, or by clicking "Open" in the main window next to "New FC".
 \begin{figure}[pt!]
  \includegraphics[width=\linewidth]{gui/statistics_summary_window.png}
-  \caption{Debugging statistics window. It has the option to filter data by sources and spectral type for Kepler/K2/TESS pdcsap flux data. It has the ability to show various statistics like flares per fits file, flares per star (total or normalized to a period of 7 days), or the mean period detected. The figure shows sttistics generated by pressing the "Show Flares/File" button.}
+  \caption{Debugging statistics window. It has the option to filter data by sources and spectral type for Kepler/K2/TESS pdcsap flux data. It has the ability to show various statistics like flares per "fits" file, flares per star (total or normalized to a period of 7 days), or the mean period detected. The figure shows statistics generated by pressing the "Show Flares/File" button.}
  \label{fig:summary_statistics_window}
 \end{figure}
@@ -2,28 +2,28 @@
 %Example chapter on Asteroseismology
 \chapter{Introduction \label{sec:intro}}
 %\cleanchapterquote{Shoot for the moon. Even if you miss, you'll land among the stars.}{Les Brown} %optional, if you want to place something here.
-This chapter gives brief introduction to the goals of this study, the state of the art, scientific backgrounds such as spectral types, spots and flares, as well as to the space missions from which data has been extensively used for the present study.\\
+This chapter gives a brief introduction to the goals of this study, the state of the art, scientific backgrounds such as spectral types, spots and flares, as well as to the space missions from which data has been extensively used for the present study.\\
-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}) with the first recorded event being the Carrington event from September 1859 (\cite{Carrington_event}). The same accounts for the impact of stellar activity on Earths magnetic field (\cite{solar_flare_mag_field}). A detailed description of spots and flares is given in section \ref{sec:intro:flares_and_spots}.
+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 \citep{solar_flares_1,solar_flares_2,solar_flares_3} with the first recorded event being the Carrington event from September 1859 \citep{Carrington_event}. The same accounts for the impact of stellar activity on Earths magnetic field \citep{solar_flare_mag_field}. A detailed description of spots and flares is given in section \ref{sec:intro:flares_and_spots}.
-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 attraction 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 a bolometric 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). Even more recently \cite{superflare_shapiro} estimated the occurance rate of superflares with $>10^{34}$ erg on Sun-like stars to roughly once per century.\\
+While the first stellar flares were discovered in middle of the last century \citep{early_stellar_flares1,early_stellar_flares2}, the topic gained a lot of attraction with the launch of the likes of Kepler \citep{Kepler_first_results} and the Transiting Exoplanet Survey Satellite (TESS) \citep{TESS_release}. They allowed the survey of thousands of stars. With this, studies of flares and superflares on a large number of stars have been conducted \citep{flare_study_1,flare_study_2,connection_starspots_flares_ms_kepler,flare_occurance_periodicity}, but the origin of superflares (flares with a bolometric 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 \citep{superflares_on_sun}. They found that superflares on our Sun would be rare events (every \textasciitilde800 years for superflares with $10^{34}$ erg). Even more recently \citet{superflare_shapiro} estimated the occurrence rate of superflares with $>10^{34}$ erg on Sun-like stars to roughly once per century.\\
-A few proposed causes for superflares 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 generation mechanisms for superflares could be star-planet interaction (SPI) \citep{au_mic_flaring_spi,SPI_1,SPI_2}, or just being scaled up version of normal flares which we see from our Sun coming from large spots \citep{superflares_1,superflares_2}. In the case of the latter, we would expect to see a correlation between the appearance of superflares and the phase.\\
 \section{State of the art \label{sec:intro:goals}}
-\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 than stars with longer roation periods, 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}).\\
+\citet{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 than stars with longer roation periods, which was already shown previously \citep{faster_rot_stars_more_flares1,faster_rot_stars_more_flares2}. Furthermore they found no star with a preference for when flares occured during the rotational phase \citep{doyle_2018}. A similar study using TESS 2 minute cadence data has been conducted by \citet{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 rotational phase \citep{doyle_2019}.\\
-\cite{connection_starspots_flares_ms_kepler} investigated a sample of 119 stars from spectral types M to F. They used a subset of the Kepler long-cadence data. 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}).\\
+\citet{connection_starspots_flares_ms_kepler} investigated a sample of 119 stars from spectral types M to F. They used a subset of the Kepler long-cadence data. 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 \citep{connection_starspots_flares_ms_kepler}.\\
-Further analysis on periodic flare occurance was done by \cite{flare_occurance_periodicity}, who studied TESS lightcurves of 284 cool 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 occurrence was done by \citet{flare_occurance_periodicity}, who studied TESS lightcurves of 284 cool 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.\\
-There have also been studies on individual stars, for example \cite{kepler_411_study} focused on Kepler-411, which is a K2V dwarf, 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 (a K dwarf with two planets), 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 therefore 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}).\\
+There have also been studies on individual stars, for example \citet{kepler_411_study} focused on Kepler-411, which is a K2V dwarf, 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 \citep{kepler_411_study} on Kepler-411. They then compared their results for Kepler-411, which produced multiple superflares, with Kepler-210 (a K dwarf with two planets), which did not produce superflares while having the same number of spots \citep{kepler_411_210_comparison}. They found the spots on Kepler-210 to be larger, warmer and therefore being magnetically weaker/less complex compared to Kepler-411 and concluded that the area of starspots is not the only relevant parameter for superflare occurrence \citep{kepler_411_210_comparison}.\\
-Star-planet interaction was 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 state that a $>3\sigma$ detection requires more observations (\cite{au_mic_flaring_spi}).\\
+Star-planet interaction was studied by \citet{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 state that a $>3\sigma$ detection requires more observations \citep{au_mic_flaring_spi}.\\
-In conclusion, many flares and superflares have been found on stars, but the origin of the latter is still not clear. Although it is widely accepted that superflares may be scaled up normal flares, still the issue of star-planet interaction is discussed. Furthermore, the above mentioned studies could not relate flare/superflare occurance distinctively to the spottedness of stars. With a large data set comprised of Kepler, K2 and TESS data we aim for a more distinct relation flare/superflare occurance and spottedness of stars.
+In conclusion, many flares and superflares have been found on stars, but the origin of the latter is still not clear. Although it is widely accepted that superflares may be scaled up normal flares, still the issue of star-planet interaction is discussed. Furthermore, the above mentioned studies could not relate flare/superflare occurrence distinctively to the spottedness of stars. With a large data set comprised of Kepler, K2 and TESS data we aim for a more distinct relation of flare/superflare occurrence and spottedness of stars.
 \section{Spectral Types \label{sec:intro:spectral_types}}
-Spectral classification is a way to classify the vast amount of stars into various types. The original definition of the currently used Harvard System was developed by \cite{orig_harvard_system_sptype_definition}. It characterized stars by their most prominent spectral lines. The different spectral types introduced are O, B, A, F, G, K and M. In this system the stars were differentiated by their different prominent spectral lines. For example B type stars were described to have faint hydrogen lines, but numerous helium lines. Another example would be spectral class A, which was described to have the most prominent hydrogen lines (\cite{orig_harvard_system_sptype_definition}). Furthermore the spectral classes were divided into 10 subtypes, with 1 to 9 attached to the letter. In a later revision, the spectral types without a numeral had a 0 attached, for example B to B0 or A to A0 (\cite{orig_harvard_system_sptype_definition2}). If the exact spectral type can not be determined, the numeral should be left out (\cite{orig_harvard_system_sptype_definition2}). 
+Spectral classification is a way to classify the vast amount of stars into various types. The original definition of the currently used Harvard System was developed by \citet{orig_harvard_system_sptype_definition}. It characterized stars by their most prominent spectral lines. The different spectral types introduced are O, B, A, F, G, K and M. In this system the stars were differentiated by their different prominent spectral lines. For example B type stars were described to have faint hydrogen lines, but numerous helium lines. Another example would be spectral class A, which was described to have the most prominent hydrogen lines \citep{orig_harvard_system_sptype_definition}. Furthermore the spectral classes were divided into 10 subtypes, with 1 to 9 attached to the letter. In a later revision, the spectral types without a numeral had a 0 attached, for example B to B0 or A to A0 \citep{orig_harvard_system_sptype_definition2}. If the exact spectral type can not be determined, the numeral should be left out \citep{orig_harvard_system_sptype_definition2}. 
-\cite{spectral_lines_temperature_correlation} then found that this specification links to the effective temperature of stars, with O being the hottest, and M being the coolest. The same applies to the subtypes, with 0 being the hottest, and 9 the coolest of their respective type (\cite{harvard_spectral_types_teff}). Additionally the terms "early" and "late" are often used and can refer to the spectral type itself, with the hotter O, B, or A stars being "early" type, and cooler F, G, K, M stars being "late" types, or if used in combination with a spectral type, it refers to hotter or colder subtypes like K0 being an early K type or G9 being a late G type (\cite{astrophysics_group_uk_spectral_types}). Table \ref{tab:spectral_types_table} shows the spectral types with their respective approximate temperature range as well as color.
+\citet{spectral_lines_temperature_correlation} then found that this specification links to the effective temperature of stars, with O being the hottest, and M being the coolest. The same applies to the subtypes, with 0 being the hottest, and 9 the coolest of their respective type \citep{harvard_spectral_types_teff}. Additionally the terms "early" and "late" are often used and can refer to the spectral type itself, with the hotter O, B, or A stars being "early" type, and cooler F, G, K, M stars being "late" types, or if used in combination with a spectral type, it refers to hotter or colder subtypes like K0 being an early K type or G9 being a late G type \citep{astrophysics_group_uk_spectral_types}. Table \ref{tab:spectral_types_table} shows the spectral types with their respective approximate temperature range as well as color.
 \begin{table}
    \centering
-    \caption{Table showing the different spectral types, in relation to their minimum and maximum effective temperature ranges in K. Based on the tables given in \cite{astrophysics_group_uk_spectral_types}, \cite{harvard_spectral_types_teff}}
+    \caption{Table showing the different spectral types, in relation to their minimum and maximum effective temperature ranges in Kelvin. Based on the tables given in \citep{astrophysics_group_uk_spectral_types,harvard_spectral_types_teff}.}
    \label{tab:spectral_types_table}
    \begin{tabular}{lccl}
    \hline
@@ -49,39 +49,39 @@ This section gives a short overview of starspots/flares by explaining it based o
 \subsection{Spots}
-Sunspots, or genereally speaking spots, are magnetic regions on the surface of a star that are cooler than their surroundings. Spots generally have an umbra, which is the center, and the penumbra, which is surrounding the umbra and separating it from the rest of the surface of the star (\cite{sunspots_overview}). If a spot does not have a penumbra, it is called a pore (\cite{sunspots_overview}). The size of spots varies greately, and can be up to a diameter of 60000 km on the Sun and have lifetimes from a few days up to several months (\cite{sunspots_overview}). The umbra can be 1000 to 1900K cooler than the solar surface, while the penumbra can be 250 to 400 K cooler, which also causes them to be less bright than the rest of the photosphere (values for the Sun, \cite{sunspots_overview}). This is because the strong magnetic fields (1800 to 3700 G in the umbra and 700 to 1000 G in the penumbra, compared to a few gauss in the photosphere (\cite{sunspots_overview})) limit the convection process, effecitvely reducing the thermal energy in this area (\cite{sunspots_overview}, \cite{sun_photosphere_mag_field_strength}). An example of a sunspot can be seen in figure \ref{fig:sunspot_soho}. The image was taken by SOHO (Solar \& Heliospheric Observatory, \cite{soho_project_page}, \cite{soho_esa}, \cite{soho_nasa}). It shows a sunspot, with its umbra (black area) being slightly larger than Earth. The penumbra is visible in orange, and the surrounding solar photosphere is colored in yellow. Additionally an image of full solar disk at the same time the spot image was taken is included in the top right. The sunspot is located slightly left of the center.\\
+Sunspots, or genereally speaking spots, are magnetic regions on the surface of a star that are cooler than their surroundings. Spots generally have an umbra, which is the center, and the penumbra, which is surrounding the umbra and separating it from the rest of the surface of the star \citep{sunspots_overview}. If a spot does not have a penumbra, it is called a pore \citep{sunspots_overview}. The size of spots varies greatly, and can be up to a diameter of 60000 km on the Sun and have lifetimes from a few days up to several months \citep{sunspots_overview}. The umbra can be 1000 to 1900K cooler than the solar surface, while the penumbra can be 250 to 400 K cooler, which also causes them to be less bright than the rest of the photosphere (values for the Sun, \citealp{sunspots_overview}). This is because the strong magnetic fields (1800 to 3700 G in the umbra and 700 to 1000 G in the penumbra, compared to a few gauss in the photosphere \citep{sunspots_overview}) limit the convection process, effecitvely reducing the thermal energy in this area \citep{sunspots_overview,sun_photosphere_mag_field_strength}. An example of a sunspot can be seen in figure \ref{fig:sunspot_soho}. The image was taken by SOHO (Solar \& Heliospheric Observatory)\footnote{\href{https://soho.nascom.nasa.gov/}{https://soho.nascom.nasa.gov/}}\textsuperscript{,}\footnote{\href{https://www.esa.int/Science_Exploration/Space_Science/SOHO}{https://www.esa.int/Science\_Exploration/Space\_Science/SOHO}}\textsuperscript{,}\footnote{\href{https://science.nasa.gov/mission/soho/}{https://science.nasa.gov/mission/soho/}}. It shows a sunspot, with its umbra (black area) being slightly larger than Earth. The penumbra is visible in orange, and the surrounding solar photosphere is colored in yellow. Additionally an image of the full solar disk at the same time the spot image was taken is included in the top right. The sunspot is located slightly left of the center.\\
 Figure \ref{fig:sunspot_magnetic_field_lines} shows a sketch of a sunspot, with its umbra and penumbra and magnetic field lines, with more field lines at the umbra representing a stronger magnetic field. Each spot is also magnetically linked to one or more spots of the opposite polarity, with the magnetic field varying in complexity. A simple example of this can be seen in figure \ref{fig:sunspot_magnetic_field_lines_connecting}.
 \begin{figure}[pt!]
    \centering
    \includegraphics[width=.6\linewidth]{gfx/spots/sunspot00.png}
-    \caption{Image showing a sunspot from the 23. September 2000. Comparison of its size to Earth in the bottom left. The whole visible photosphere of the Sun is visible in the top right corner. Image taken from the SOHO image gallery (\cite{soho_project_page}).}
+    \caption{Image showing a sunspot from 23 September 2000. Comparison of its size to Earth in the bottom left. The whole disk of the Sun is visible in the top right corner. Image taken from the SOHO image gallery \citep{soho_project_page}.}
    \label{fig:sunspot_soho}
 \end{figure}
 \begin{figure}[pt!]
    \centering
    \includegraphics[width=.7\linewidth]{gfx/spots/magnetic_fields_above_sunspot.png}
-    \caption{Image showing magnetic field lines coming out of a sunspot. Field lines are denser in the umbra compared to the penumbra, representing stronger magnetic fields. Image from \cite{sunspot_magfieldlines_image}.}
+    \caption{Image showing magnetic field lines coming out of a sunspot. Field lines are denser in the umbra compared to the penumbra, representing stronger magnetic fields. Image from \citet{sunspot_magfieldlines_image}.}
    \label{fig:sunspot_magnetic_field_lines}
 \end{figure}
 \begin{figure}[pt!]
    \centering
    \includegraphics[width=.6\linewidth]{gfx/spots/image1_3.png}
-    \caption{Image showing two sunspots being connected by magnetic field lines. Image from \cite{sunspot_mag_field_connecting_to_second}.}
+    \caption{Image showing two sunspots being connected by magnetic field lines. Image from \citet{sunspot_mag_field_connecting_to_second}.}
    \label{fig:sunspot_magnetic_field_lines_connecting}
 \end{figure}
 \subsection{Flares}
-Flares are a sudden release of a huge amount of magnetic energy, which happens due to magnetic reconnection (\cite{flares_1}) with the first flare observed on the 1. September 1859 by \cite{Carrington_event} and \cite{Carrington_event2}. \cite{Carrington_event3} estimated the energy release of the flare to $5.77 \pm 2.89 * 10^{32} erg$, which would .
+Flares are a sudden release of a huge amount of magnetic energy, which happens due to magnetic reconnection \citep{flares_1} with the first flare observed on 1 September 1859 by \citet{Carrington_event} and \citet{Carrington_event2}. \citet{Carrington_event3} estimated the energy release of the flare to $5.77 \pm 2.89 * 10^{32}$ erg, with an estimated GOES classification of X46 to X126 with a median of X80.
-The energy which is released, is the so called free magnetic energy. This is the excess energy above the ground state of the magnetic field. During a period of days to weeks this free energy is accumulated. This is done by braiding, sheering and twisting the frozen-in magnetic fields. The more the magnetic field now differs from the unmodified state, the more energy is built up. To release the stored energy, magnetic reconnection has to happen. For this two magnetic field lines of opposing direction need to come close. This causes a current sheet to form due to the strong current flow. In this region the frozen-in state is broken. The energy that is released during the reconnection process causes a temperature increase of the surrounding plasma (multiple 10 million K). This is then observed in soft X-ray, EUV, FUV, UV as well as some lines in the visible spectrum and in radio. Additionally particles are accelerated and when they hit the denser chromosphere, those particles are decelerated quickly, producing hard X-ray (Bremsstrahlung). The energy release can take just a few tens of seconds, but can also last up to a few hours on the Sun. An imagine of this process can be seen in figure \ref{fig:solar_flare}.
+The energy which is released, is the so called free magnetic energy \citep{priest_1,priest_2}. This is the excess energy above the ground state of the magnetic field. During a period of days to weeks this free energy is accumulated by braiding, sheering and twisting the frozen-in magnetic fields \citep{priest_1,priest_2}. The more the magnetic field now differs from the unmodified state, the more energy is built up which is then released in a magnetic reconnection \citep{priest_1,priest_2}. For this two magnetic field lines of opposing direction need to come close \citep{priest_1,priest_2}. This causes a current sheet to form due to the strong current flow \citep{priest_1,priest_2}. In this region the frozen-in state is broken \citep{priest_1,priest_2}. The energy that is released during the reconnection process causes a temperature increase of the surrounding plasma (multiple 10 million K) \citep{priest_1,priest_2}. This is then observed in soft X-ray, EUV, FUV, UV as well as some lines in the visible spectrum and in radio \citep{priest_1,priest_2}. Additionally particles are accelerated and when they hit the denser chromosphere, those particles are decelerated quickly, producing hard X-ray (Bremsstrahlung) \citep{priest_1,priest_2}. The energy release can take just a few tens of seconds, but can also last up to a few hours on the Sun \citep{flare_duration}. An illustration of this process can be seen in figure \ref{fig:solar_flare}.
 \begin{figure}[pt!]
    \centering
    \includegraphics[width=.6\linewidth]{gfx/flares/Color-online-Standard-model-of-a-solar-flare-The-flare-is-triggered-by-the-ascension.png}
-    \caption{Imagine showing the standard model for a solar flare. The blue arrows indicate inflow of cool plasma. The green arrows indicate outflow of hot plasma. Image from \cite{flare_image}.}
+    \caption{Illustration showing the standard model for a solar flare. The blue arrows indicate inflow of cool plasma. The green arrows indicate outflow of hot plasma. Image from \citet{flare_image}.}
    \label{fig:solar_flare}
 \end{figure}
@@ -94,25 +94,25 @@ This section gives a short overview on the space mission from which the data was
 \subsection{Kepler and K2}
-The Kepler space telesope was named after Johannes Kepler and was launched in 2009\footnote{\label{fn:nasa_kepler_in_depth}\href{https://science.nasa.gov/mission/kepler/in-depth/}{https://science.nasa.gov/mission/kepler/in-depth/}} and its primary mission lasted till May 2013\footnote{\label{fn:kepler_missions_and_data_mast}\href{https://archive.stsci.edu/missions-and-data/kepler}{https://archive.stsci.edu/missions-and-data/kepler}}. Its main scientific goal was the discovery of exoplanets, especially Earth-sized ones, in the habitable zone around their host star\footnote{\label{fn:kepler_missions_caltech}\href{https://exoplanetarchive.ipac.caltech.edu/docs/KeplerMission.html}{https://exoplanetarchive.ipac.caltech.edu/docs/KeplerMission.html}} (\cite{Kepler_first_results}). This was done by observing transits of planets around their host star\cref{fn:kepler_missions_caltech}\textsuperscript{,}\cref{fn:kepler_missions_and_data_mast} (\cite{Kepler_first_results}).\\
+The Kepler space telesope was named after Johannes Kepler and was launched in 2009\footnote{\label{fn:nasa_kepler_in_depth}\href{https://science.nasa.gov/mission/kepler/in-depth/}{https://science.nasa.gov/mission/kepler/in-depth/}} and its primary mission lasted till May 2013\footnote{\label{fn:kepler_missions_and_data_mast}\href{https://archive.stsci.edu/missions-and-data/kepler}{https://archive.stsci.edu/missions-and-data/kepler}}. Its main scientific goal was the discovery of exoplanets, especially Earth-sized ones, in the habitable zone around their host star using the transit method\footnote{\label{fn:kepler_missions_caltech}\href{https://exoplanetarchive.ipac.caltech.edu/docs/KeplerMission.html}{https://exoplanetarchive.ipac.caltech.edu/docs/KeplerMission.html}} \citep{Kepler_first_results}.\\
-It provides two different types of data: short cadence (1 minute exposure) and long cadence (30 minute exposure) data\cref{fn:kepler_missions_and_data_mast} (\cite{Kepler_first_results}). While short cadence data provides a higher temporal resolution, it was used for fewer targets (\cite{Kepler_first_results}). It had a fixed exposure time of 6.02 seconds for its photometer with a field of view of 115 $deg^{2}$ near the cygnus constellation\cref{fn:kepler_missions_and_data_mast} (\cite{Kepler_first_results}) and is most sensitive in the visual to near infrared as seen in figure \ref{fig:kepler_bands}. The data was then accumulated for selected targets to either short or long cadence, and then downloaded (\cite{Kepler_first_results}). The space telescope could accomondate data of around 170,000 targets with long cadence and 512 targets with short cadence (\cite{Kepler_first_results}). The spacial resolution of each of the 42 CCDs was 4 arcseconds per pixel (\cite{doyle_2019}, \cite{kepler_mission_stellar_and_instrument_noise}).\\
+It provides two different types of data: short cadence (1 minute exposure) and long cadence (30 minute exposure) data\cref{fn:kepler_missions_and_data_mast} \citep{Kepler_first_results}. While short cadence data provides a higher temporal resolution, it was used for fewer targets \citep{Kepler_first_results}. It had a fixed exposure time of 6.02 seconds for its photometer with a field of view of 115 deg\textsuperscript{2} near the Cygnus constellation\cref{fn:kepler_missions_and_data_mast} \citep{Kepler_first_results} and is most sensitive in the visual to near infrared as seen in figure \ref{fig:kepler_bands}. The data was then accumulated for selected targets to either short or long cadence, and then downloaded \citep{Kepler_first_results}. The space telescope could accomodate data of around 170,000 targets with long cadence and 512 targets with short cadence \citep{Kepler_first_results}. The spatial resolution of each of the 42 CCDs was 4 arcseconds per pixel \citep{doyle_2019,kepler_mission_stellar_and_instrument_noise}.\\
-The K2 mission is the continuation mission of Kepler after the second of four of its reaction wheels broke in 2013\cref{fn:nasa_kepler_in_depth} (\cite{k2_missions_and_data_mast}). Due to this, a follow-up mission was proposed, keeping the now limited capabilities in mind\cref{fn:nasa_kepler_in_depth}. The mission was active from February 2014 till September 2018 when its fuel ran out\footnote{\label{fn:k2_missions_and_data_mast}\href{https://archive.stsci.edu/missions-and-data/k2}{https://archive.stsci.edu/missions-and-data/k2}}\textsuperscript{,}\footnote{\label{fn:kepler_end_nytimes}\href{https://web.archive.org/web/20181030211627/https://www.nytimes.com/2018/10/30/science/nasa-kepler-exoplanet.html}{https://web.archive.org/web/20181030211627/https://www.nytimes.com/2018/10/30/science/nasa-kepler-exoplanet.html}}\textsuperscript{,}\footnote{\label{fn:kepler_end_nasa_press}\href{https://www.jpl.nasa.gov/news/nasa-retires-kepler-space-telescope/}{https://www.jpl.nasa.gov/news/nasa-retires-kepler-space-telescope/}}. It discovered a total of over 2600 confirmed planets as of 2018\cref{fn:kepler_end_nytimes}\textsuperscript{,}\cref{fn:kepler_end_nasa_press}.
+The K2 mission is the continuation mission of Kepler after the second of four of its reaction wheels broke in 2013\cref{fn:nasa_kepler_in_depth} \citep{k2_missions_and_data_mast}. Due to this, a follow-up mission was proposed, keeping the now limited capabilities in mind\cref{fn:nasa_kepler_in_depth}. The mission was active from February 2014 till September 2018 when its fuel ran out\footnote{\label{fn:k2_missions_and_data_mast}\href{https://archive.stsci.edu/missions-and-data/k2}{https://archive.stsci.edu/missions-and-data/k2}}\textsuperscript{,}\footnote{\label{fn:kepler_end_nytimes}\href{https://web.archive.org/web/20181030211627/https://www.nytimes.com/2018/10/30/science/nasa-kepler-exoplanet.html}{https://web.archive.org/web/20181030211627/https://www.nytimes.com/2018/10/30/science/nasa-kepler-exoplanet.html}}\textsuperscript{,}\footnote{\label{fn:kepler_end_nasa_press}\href{https://www.jpl.nasa.gov/news/nasa-retires-kepler-space-telescope/}{https://www.jpl.nasa.gov/news/nasa-retires-kepler-space-telescope/}}. It discovered a total of over 2600 confirmed planets as of 2018\cref{fn:kepler_end_nytimes}\textsuperscript{,}\cref{fn:kepler_end_nasa_press}.
 \begin{figure}[pt!]
    \centering
    \includegraphics[width=.6\linewidth]{gfx/kepler/kepler_bandpass_jason1.jpg}
-    \caption{Johnson B, V, R and I in comparison to the Kepler, MOST and CoRoT missions response curves. Also shown is a A2V and a M2V spectrum. Image from \cite{kepler_sensitivity}.}
+    \caption{Johnson B, V, R and I in comparison to the Kepler, MOST and CoRoT missions response curves. Also shown is a A2V and a M2V spectrum. Image from \citet{kepler_sensitivity}.}
    \label{fig:kepler_bands}
 \end{figure}
 \subsection{TESS}
-The Transiting Exoplanet Survey Satellite (TESS) was launched in 2018, with its primary mission lasting two years\footnote{\href{https://exoplanets.nasa.gov/tess/}{https://exoplanets.nasa.gov/tess/}}. Since 2020 TESS is in its extended mission, the first being from 2020 to 2022\footnote{\label{fn:tess_extended_mission_1}\href{https://archive.stsci.edu/contents/newsletters/august-2020/tess-extended-mission}{https://archive.stsci.edu/contents/newsletters/august-2020/tess-extended-mission}}, the second from 2022 to 2024\cref{fn:tess_tess}. TESS has four identical cameras, with each providing a 24 times 24 degree field of view\footnote{\label{fn:tess_tess}\href{https://tess.mit.edu/science/}{https://tess.mit.edu/science/}} (\cite{TESS2014}). TESS's CCDs have a pixel scale of 21 arcseconds (\cite{TESS2014}, \cite{doyle_2019}) and is most sensitive in the red and infrared (see figure \ref{fig:tess_bands}). The data is provided in 2 minute cadence for individual stars and 30 minute cadence for full frame images (\cite{tess_tess}).\\
+The Transiting Exoplanet Survey Satellite (TESS) was launched in 2018, with its primary mission lasting two years\footnote{\href{https://exoplanets.nasa.gov/tess/}{https://exoplanets.nasa.gov/tess/}}, and was designed to detected exoplanets using the transit method. Since 2020 TESS is in its extended mission, the first being from 2020 to 2022\footnote{\label{fn:tess_extended_mission_1}\href{https://archive.stsci.edu/contents/newsletters/august-2020/tess-extended-mission}{https://archive.stsci.edu/contents/newsletters/august-2020/tess-extended-mission}}, the second from 2022 to 2024\cref{fn:tess_tess}. TESS has four identical cameras, with each providing a 24 times 24 degree field of view\footnote{\label{fn:tess_tess}\href{https://tess.mit.edu/science/}{https://tess.mit.edu/science/}} \citep{TESS2014}. TESS's CCDs have a pixel scale of 21 arcseconds \citep{TESS2014,doyle_2019} and is most sensitive in the red and near infrared (see figure \ref{fig:tess_bands}). The data is provided in 2 minute cadence for individual stars and 30 minute cadence for full frame images\cref{fn:tess_tess}. Since the first extended mission, the cadence for full frame images has been reduced to 200 seconds, and additionally 20 second cadence data is available\cref{fn:tess_tess}.\\
 TESS observes its targets in so called sectors. Each sector is observed for 27 days\cref{fn:tess_tess}.
 \begin{figure}[pt!]
    \centering
    \includegraphics[width=.6\linewidth]{gfx/tess/The-TESS-spectral-response-function-black-line-defined-as-the-product-of-the-long-pass.png}
-    \caption{Johnson V, R\textsubscript{C}, I\textsubscript{C} and SDSS z (colored dashed lines) response curves and in comparison to TESS (solid black line). Image from \cite{kepler_sensitivity}.}
+    \caption{Johnson V, R\textsubscript{C}, I\textsubscript{C} and SDSS z (colored dashed lines) response curves and in comparison to TESS (solid black line). Image from \citet{tess_response_curve}.}
    \label{fig:tess_bands}
 \end{figure}
@@ -1,15 +1,15 @@
 \chapter{Results \label{sec:results}}
-This chapter includes the main results of this study. The data for the plots in this section were generated using the "New FC" Button from the main GUI described in section \ref{sec:gui:data_processing}. As every star has a different rotational/spot modulation period, the value range for the phases of the folded lightcurves do not match. To compare different stars (or spot modulation periods for the same star) with each other, the phase was normalized to $0$ to $2 \pi$.\\
+This chapter includes the main results of this study. The data for the plots in this section were generated using the "New FC" Button from the main GUI described in section \ref{sec:gui:data_processing}. As every star has a different rotational/spot modulation period, the value range for the phases of the folded lightcurves do not match. To compare different stars (or spot modulation periods for the same star) with each other, the phase was normalized from $0$ to $2 \pi$.\\
 The results contain plots for the different spectral types M, K, G, and F as well as combined results of every possible combination. Additionally for all these possible combinations, plots with data limits, e.g. only stars with a rotational period of less than 2 days or minimal/maximal normalized flare peak limits, were also generated. Moreover plots for stars according to their spectral sub type like M0 or G5 were created. Furthermore there is a selection of individual star results. For every plot group a CSV file is generated, which contains information about every star and flare used to generate the plot.
 The results also only contain the data of folded lightcurves which could be fitted with a sine function and less than 30 iterations of the fold optimization. The data which uses polynomial fits or both sine and polynomial fits as well as all plots and the accompanying CSV files are available at \href{link}{<link to github>}.
 \section{M dwarfs \label{sec:results:m_dwarfs}}
 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 flare count histograms, with 10 and 30 phase bins respectively, of the number of flares during the normalized phase.\\
+Figures \ref{fig:M-Flarecount-10_Bins} and \ref{fig:M-Flarecount-30_Bins} show flare count histograms, with 10 and 30 phase bins respectively, of the number of flares depending on the normalized phase.\\
-Looking at figure \ref{fig:M-Flarecount-10_Bins} there is an even distribution within the 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 the error, of flares across the normalized phase, with the exception 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 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 significantly below the surrounding bins. The same is true for the dips at phases $0.7 \pi$ and $1.3 \pi$. The dip at phase $1.4 \pi$ on the other is not significant. Due to the dips surrounding the center, it may look like there is an increased number of flares in the center.
+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 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 significantly below the surrounding bins. The same is true for the dips at phases $0.7 \pi$ and $1.3 \pi$. The dip at phase $1.4 \pi$ on the other hand is not significant. Due to the dips surrounding the minimum at phase $1 \pi$, it looks like there is an increased number in flares around the phase minimum as well as phase maximum.
 \begin{figure}[pt!]
    \centering
@@ -25,7 +25,7 @@ Looking at the same data, just with 30 instead of 10 bins (figure \ref{fig:M-Fla
        \caption{30 bins}
        \label{fig:M-Flarecount-30_Bins}
    \end{subfigure}
-    \caption{Histogram showing the number 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 $1 \pi$.}
+    \caption{Histogram showing the number of flares per phase of 49 M dwarfs for which a total of 3523 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 idealized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
    \label{fig:M-Flarecount}
 \end{figure}
@@ -50,7 +50,7 @@ Increasing the number of bins to 30 (see figure \ref{fig:M-Flarecount-30_Bins_1.
        \caption{30 bins}
        \label{fig:M-Flarecount-30_Bins_1.25_peak}
    \end{subfigure}
-    \caption{Histograms showing the number 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 $1 \pi$.}
+    \caption{Histograms showing the number of flares with a normalized peak of greater than 1.25 per phase of 27 M dwarfs for which a total of 127 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 idealized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
    \label{fig:M-Flarecount-peaks_1.25_peak}
 \end{figure}
 \begin{figure}[pt!]
@@ -67,7 +67,7 @@ Increasing the number of bins to 30 (see figure \ref{fig:M-Flarecount-30_Bins_1.
        \caption{30 bins}
        \label{fig:M-Flarecount-30_Bins_1.5_peak}
    \end{subfigure}
-    \caption{Histograms showing the number 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 $1 \pi$.}
+    \caption{Histograms showing the number of flares with a normalized peak of greater than 1.5 per phase for 20 M dwarfs for which a total of 40 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 idealized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
    \label{fig:M-Flarecount-peaks_1.5_peak}
 \end{figure}
@@ -90,7 +90,7 @@ The difference becomes less obvious when increasing the bin size 30 (figure \ref
        \caption{30 bins}
        \label{fig:M-Flarecount-30_Bins_1.01_maxpeak}
    \end{subfigure}
-    \caption{Histograms showing the number 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 $1 \pi$.}
+    \caption{Histograms showing the number of flares with a normalized peak of less than 1.01 per phase of 17 M dwarfs for which a total of 480 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 idealized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
    \label{fig:M-Flarecount-peaks_1.01_maxpeak}
 \end{figure}
@@ -108,7 +108,7 @@ The difference becomes less obvious when increasing the bin size 30 (figure \ref
        \caption{30 bins}
        \label{fig:M-Flarecount-30_Bins_1.05_maxpeak}
    \end{subfigure}
-    \caption{Histograms showing the number 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 $1 \pi$.}
+    \caption{Histograms showing the number of flares with a normalized peak of less than 1.05 per phase of 32 M dwarfs for which a total of 2621 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 idealized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
    \label{fig:M-Flarecount-peaks_1.05_maxpeak}
 \end{figure}
@@ -133,13 +133,13 @@ Looking at the same dataset with 30 bins for the histogram (figure \ref{fig:K-Fl
        \caption{30 bins}
        \label{fig:K-Flarecount-30_Bins}
    \end{subfigure}
-    \caption{Histogram showing the number 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 $1 \pi$.}
+    \caption{Histogram showing the number of flares per phase of 21 K dwarfs for which a total of 742 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 idealized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
    \label{fig:K-Flarecount}
 \end{figure}
 The histograms with normalized flare peaks limited to >1.05 are shown in figure \ref{fig:K-Flarecount-peaks_1.5_peak}. In figure \ref{fig:K-Flarecount-10_Bins_1.05_peak} the histogram with 10 bins is shown, while figure \ref{fig:K-Flarecount-30_Bins_1.05_peak} shows the histogram with 30 bins.
 There are multiple significant peaks visible in figure \ref{fig:K-Flarecount-10_Bins_1.05_peak}. The two highest being at phases $0.7 \pi$ as well as $1.1 \pi$. From phase $1.1 \pi$ onwards we see a decrease in the number of flares. These two peaks are seperated by a bin at phase $0.9 \pi$ which is significantly lower (roughly twice the error). Moreover, we also see a peak at phase $0 \pi$ which is slightly smaller than the other two at $0.7$ and $1.1 \pi$.\\
-A similar picture forms when increasing the resolution to 30 bins (figure \ref{fig:K-Flarecount-30_Bins_1.05_peak}). The main differences to figure \ref{fig:K-Flarecount-10_Bins_1.05_peak} is though that the heights of the afformentioned peaks is now the same, and that the errorbars are ofcourse larger than for the 10 bin representation. Additionally a new peak in the last bin, during the phase maximum, appeared having the same height as the other three peaks.
+A similar picture forms when increasing the resolution to 30 bins (figure \ref{fig:K-Flarecount-30_Bins_1.05_peak}). The main differences to figure \ref{fig:K-Flarecount-10_Bins_1.05_peak} is though that the heights of the aformentioned peaks is now the same, and that the errorbars are of course larger than for the 10 bin representation. Additionally a new peak in the last bin, during the phase maximum, appeared having the same height as the other three peaks.
 \begin{figure}[pt!]
    \centering
@@ -155,11 +155,11 @@ A similar picture forms when increasing the resolution to 30 bins (figure \ref{f
        \caption{30 bins}
        \label{fig:K-Flarecount-30_Bins_1.05_peak}
    \end{subfigure}
-    \caption{Histograms showing the number 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 $1 \pi$.}
+    \caption{Histograms showing the number of flares with a normalized peak of greater than 1.05 per phase of 13 K dwarfs for which a total of 60 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 idealized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
    \label{fig:K-Flarecount-peaks_1.5_peak}
 \end{figure}
-Similar to figures \ref{fig:M-Flarecount-peaks_1.01_maxpeak} and \ref{fig:M-Flarecount-peaks_1.05_maxpeak}, we also show the histograms of flares with a normalized peak threshold of 1.01 and 1.05. In figure \ref{fig:K-Flarecount-10_Bins_1.01_maxpeak}, where we show the histogram of flares with a peak <1.01, there appears a siginificantly large peak around phase $1.2 \pi$ which is at the phase minimum. Another, slightly smaller peak appears at the phase maximum at $1.9 \pi$. Both of these peaks are significant when comparing them to their surrounding bins. Checking for more specific phases for the peaks, by increasing the resolution to 30 bins, shows siginificant peaks at phases $1.6 \pi$ and $1.9 \pi$. These two bins stand out with respect to their neighbouring bins.\\
+Similar to figures \ref{fig:M-Flarecount-peaks_1.01_maxpeak} and \ref{fig:M-Flarecount-peaks_1.05_maxpeak}, we also show the histograms of flares with a normalized peak threshold of less than 1.01 and 1.05. In figure \ref{fig:K-Flarecount-10_Bins_1.01_maxpeak}, where we show the histogram of flares with a peak <1.01, there appears a siginificantly large peak around phase $1.2 \pi$ which is at the phase minimum. Another, slightly smaller peak appears at the phase maximum at $1.9 \pi$. Both of these peaks are significant when comparing them to their surrounding bins. Checking for more specific phases for the peaks, by increasing the resolution to 30 bins, shows siginificant peaks at phases $1.6 \pi$ and $1.9 \pi$. These two bins stand out with respect to their neighbouring bins.\\
 Increasing the maximum flare peak threshold to 1.05 in figure \ref{fig:K-Flarecount-peaks_1.05_maxpeak} reveals a similar pattern as shown in figure \ref{fig:M-Flarecount-peaks_1.05_maxpeak} with the data for M dwarfs. The histogram is similar to the ones using all available flare data for K dwarfs (figure \ref{fig:K-Flarecount}). The differences of figure \ref{fig:K-Flarecount-10_Bins_1.05_maxpeak}, which shows the histogram with 10 bins with flare peaks limited to <1.05, and \ref{fig:K-Flarecount-10_Bins}, which shows the histogram with 10 bins for all detected flares of K dwarfs, is that that the two bins at around phase $0.3 \pi$ to $0.5 \pi$ are now more pronounced, even though still not outside of the error of their surrounding bins. Similarly the last bin at around phase $1.9 \pi$ is more pronounced.\\
 Increasing the bins to 30 (figure \ref{fig:K-Flarecount-30_Bins_1.05_maxpeak}) shows a very similar figure compared to figure \ref{fig:K-Flarecount-30_Bins}.
@@ -177,7 +177,7 @@ Increasing the bins to 30 (figure \ref{fig:K-Flarecount-30_Bins_1.05_maxpeak}) s
        \caption{30 bins}
        \label{fig:K-Flarecount-30_Bins_1.01_maxpeak}
    \end{subfigure}
-    \caption{Histograms showing the number 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 $1 \pi$.}
+    \caption{Histograms showing the number of flares with a normalized peak of less than 1.01 per phase of 20 K dwarfs for which a total of 375 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 idealized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
    \label{fig:K-Flarecount-peaks_1.01_maxpeak}
 \end{figure}
@@ -197,7 +197,7 @@ Increasing the bins to 30 (figure \ref{fig:K-Flarecount-30_Bins_1.05_maxpeak}) s
        \caption{30 bins}
        \label{fig:K-Flarecount-30_Bins_1.05_maxpeak}
    \end{subfigure}
-    \caption{Histograms showing the number 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 $1 \pi$.}
+    \caption{Histograms showing the number of flares with a normalized peak of less than 1.05 per phase of 20 K dwarfs for which a total of 682 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 idealized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
    \label{fig:K-Flarecount-peaks_1.05_maxpeak}
 \end{figure}
@@ -223,7 +223,7 @@ Limiting the flare peaks to <1.05 (figure \ref{fig:G-Flarecount-peaks_1.05_maxpe
        \caption{30 bins}
        \label{fig:G-Flarecount-30_Bins}
    \end{subfigure}
-    \caption{Histogram showing the number 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 $1 \pi$.}
+    \caption{Histogram showing the number of flares per phase of 21 G dwarfs for which a total of 700 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 idealized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
    \label{fig:G-Flarecount}
 \end{figure}
@@ -244,7 +244,7 @@ Increasing the bins to 30, which is seen in figure \ref{fig:G-Flarecount-30_Bins
        \caption{30 bins}
        \label{fig:G-Flarecount-30_Bins_1.05_maxpeak}
    \end{subfigure}
-    \caption{Histograms showing the number 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 $1 \pi$.}
+    \caption{Histograms showing the number of flares with a normalized peak of less than 1.05 per phase of 16 G dwarfs for which a total of 656 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 idealized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
    \label{fig:G-Flarecount-peaks_1.05_maxpeak}
 \end{figure}
@@ -262,14 +262,14 @@ Increasing the bins to 30, which is seen in figure \ref{fig:G-Flarecount-30_Bins
        \caption{30 bins}
        \label{fig:G-Flarecount-30_Bins_1.05_peak}
    \end{subfigure}
-    \caption{Histograms showing the number 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 $1 \pi$.}
+    \caption{Histograms showing the number of flares with a normalized peak of greater than 1.05 per phase of 13 G dwarfs for which a total of 44 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 idealized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
    \label{fig:G-Flarecount-peaks_1.5_peak}
 \end{figure}
 \FloatBarrier
 \section{F dwarfs \label{sec:results:f_dwarfs}}
-This section shows the results for four 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}.\\
+This section shows the results for four F dwarfs for which a total of 5 flares could be detected. The list of F type stars can be found in table \ref{apA:list_of_f_stars}.\\
 The detected number of flares in the already low number of F type stars in this study in figures \ref{fig:F-Flarecount-10_Bins} and \ref{fig:F-Flarecount-30_Bins} is very low which causes large errorbars of the histogram. Nontheless all detected flares were around the minimum of the phasefolded lightcurves. However, due to the above mentioned large errorbars, the results of F-type main-sequence stars is not significant.
 \begin{figure}[pt!]
@@ -286,7 +286,7 @@ The detected number of flares in the already low number of F type stars in this
        \caption{30 bins}
        \label{fig:F-Flarecount-30_Bins}
    \end{subfigure}
-    \caption{Histogram showing the number of flares per phase of four 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 $1 \pi$.}
+    \caption{Histogram showing the number of flares per phase of four 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 idealized phase (sine curve), with the maximum at phase $0 \pi$/$2 \pi$ and the minimum at phase $1 \pi$.}
    \label{fig:F-Flarecount}
 \end{figure}
@@ -294,8 +294,8 @@ The detected number of flares in the already low number of F type stars in this
 \section{Combined results \label{sec:results:combined}}
 The results combined for all 95 stars in the study for which flares could be detected is presented in this section. 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 number of the individual stars per bin are stacked on top of each other resulting in a total flare number histogram. Each color (red for M, orange for K, yellow for G and green for F type stars) represents the number of flares counted in the bin by the respective spectral type. For easier comparison, the histograms shown in the previous sections for M, K and G stars are shown again in figures \ref{fig:MKGF-Flarecount-10_Bins_M} to \ref{fig:MKGF-Flarecount-30_Bins_G}.\\
-The dip at phase $0.5 \pi$ which was present in the histogram for the M type stars (see figure \ref{fig:MKGF-Flarecount-10_Bins_M}) dominates the total flarenumber histogram. From figures \ref{fig:MKGF-Flarecount-10_Bins_K}/\ref{fig:MKGF-Flarecount-30_Bins_K} and \ref{fig:MKGF-Flarecount-10_Bins_G}/\ref{fig:MKGF-Flarecount-30_Bins_G} one can see that no local minimum at phase $0.5 \pi$ exists. 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 peak in the center at phase $1 \pi$ is significant.\\
+The dip at phase $0.5 \pi$ which was present in the histogram for the M type stars (see figure \ref{fig:MKGF-Flarecount-10_Bins_M}) dominates the total flare count histogram. From figures \ref{fig:MKGF-Flarecount-10_Bins_K}/\ref{fig:MKGF-Flarecount-30_Bins_K} and \ref{fig:MKGF-Flarecount-10_Bins_G}/\ref{fig:MKGF-Flarecount-30_Bins_G} one can see that no local minimum at phase $0.5 \pi$ exists. The peak at phase $1 \pi$ is a result of the data from the K and G type stars, as those show significant peaks in this bin. Due to the large number of overall flares, the errorbars are small and the peak in the center at phase $1 \pi$ is significant.\\
-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:MKGF-Flarecount-30_Bins_K}) and G (figure \ref{fig:MKGF-Flarecount-30_Bins_G}) 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 histogram is shaped mostly by the data of the M type stars, which 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:MKGF-Flarecount-30_Bins_K}) and G (figure \ref{fig:MKGF-Flarecount-30_Bins_G}) 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 $1.5 \pi$.
 \begin{figure}[pt!]
    \centering
@@ -347,7 +347,7 @@ Looking at the same data with 30 bins over the phase in figure \ref{fig:MKGF-Fla
        \caption{G type stars, 30 bins}
        \label{fig:MKGF-Flarecount-30_Bins_G}
    \end{subfigure}
-    \caption{Histograms showing the number of flares per phase for all 95 dwarfs for which flares could be detected in panels \subref{fig:MKGF-Flarecount-10_Bins} and \subref{fig:MKGF-Flarecount-30_Bins}. Panels \subref{fig:MKGF-Flarecount-10_Bins_M} to \subref{fig:MKGF-Flarecount-30_Bins_G} show the histograms for spectral types M, K and G respectively as direct comparison (same as histograms shown in figures \ref{fig:M-Flarecount}, \ref{fig:K-Flarecount} and \ref{fig:G-Flarecount}).}
+    \caption{Histograms showing the number of flares per phase for all 95 dwarfs for which flares could be detected in panels \subref{fig:MKGF-Flarecount-10_Bins} and \subref{fig:MKGF-Flarecount-30_Bins}. Panels \subref{fig:MKGF-Flarecount-10_Bins_M} to \subref{fig:MKGF-Flarecount-30_Bins_G} repeat the histograms for spectral types M, K and G respectively as direct comparison (same as histograms shown in figures \ref{fig:M-Flarecount}, \ref{fig:K-Flarecount} and \ref{fig:G-Flarecount}).}
    \label{fig:MKGF-Flarecount}
 \end{figure}
@@ -358,7 +358,7 @@ This section contains a selection of results for individual stars. The results f
 \subsection{BD-08   995}
-BD-08 995, also known as TIC 43472154, is a G type main-sequence star with a surface temperature of 5316 K (\cite{revised_tess_input_catalogue}), and a distance of \textasciitilde87 pc (\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 in sectors 5 and 32.\\
+BD-08 995, also known as TIC 43472154, is a G type main-sequence star with a surface temperature of 5316 K \citep{revised_tess_input_catalogue}, and a distance of \textasciitilde87 pc \citep{simbad}. It is a very active solar like star, producing over 200 superflares per year \citep{tess_1st_year_superflares}. It has a rotational period of 2.8 days \citep{tess_1st_year_superflares}. There are two TESS lightcurves available in 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, one can see a clear peak at phase $1 \pi$. The bins forming the peak are significantly enhanced with respect to the neighbouring bins.
 The bins of the phase maxima also show a slight increase in flare activity at phase $0/2 \pi$ compared to the phase transition regions around phase $0.5 \pi$ (maximum to minimum) and $1.5 \pi$ (minimum to maximum). The peaks at the phase maxima are not as significant as the peaks in phase minimum.\\
 Figure \ref{fig:BD-08_995-Flarecount-30_Bins} shows the same data just with 30 bins instead of 10, but less significant. It shows a similar picture as the previous figure. But due to the low number of total detected flares, and a 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$1.1 \pi$, which errorbars only overlap with other larger bins like the ones at phase \textasciitilde$0.9 \pi$ and \textasciitilde$1.4 \pi$.
@@ -378,7 +378,7 @@ Figure \ref{fig:BD-08_995-Flarecount-30_Bins} shows the same data just with 30 b
        \caption{30 bins}
        \label{fig:BD-08_995-Flarecount-30_Bins}
    \end{subfigure}
-    \caption{Histograms of BD-08 995 across the phase showing the number of flares in each bin. The error bar shows the standard deviation for the histogram. The blue lines show the various fits for the folded lightcurves used to generate the data, with the phase minimum at $1 \pi$ and phase maximum at $0 \pi$/$2 \pi$.}
+    \caption{Histograms of BD-08 995 across the phase showing the number of flares in each bin with a total of 59 flares. 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:BD-08_995-Flarecount}
 \end{figure}
@@ -386,7 +386,7 @@ The distribution of normalized flare peaks for BD-08 995 in figure \ref{fig:BD-0
 \begin{figure}[pt!]
    \includegraphics[width=.95\textwidth]{plots/sine/BD-08_995/BD-08\space\space\space995-Flarepeaks_maxY-1.2.png}
-    \caption{Distribution of flare peaks in relation to the normalized phase at which they occured for BD-08 995. The y-Axis shows the flare peak and the x-axis shows the normalized phase.}
+    \caption{Distribution of flare peaks in relation to the normalized phase at which they occured for BD-08 995. The y-axis shows the flare peak and the x-axis shows the normalized phase.}
    \label{fig:BD-08_995-flarepeaks_1.2}
 \end{figure}
@@ -413,8 +413,8 @@ Looking at the folded TESS lightcurves of sector 5 (\ref{fig:BD-08_995-TESS5_fol
 \FloatBarrier
 \subsection{TYC 1360-957-1}
-Not much is published about TYC 1360-957-1. It has been categorized as spectral type K on SIMBAD (\cite{simbad}). It has the TESS Input Catalogue number 247117382, and has been observed by TESS in sectors 44, 45 and 46.\\
+Not much is published about TYC 1360-957-1. It has been categorized as spectral type K on SIMBAD \citep{simbad}. It has the TESS Input Catalogue number 247117382, and has been observed by TESS in sectors 44, 45 and 46.\\
-Looking at the flare distribution histogram with 10 bins for this star in figure \ref{fig:TYC_1360-957-1-Flarecount-10_Bins} one can see that the largest peaks in order are at phase \textasciitilde$0.7 \pi$, \textasciitilde$0.4 \pi$ and \textasciitilde$1.2 \pi$. The last one being two bins wide. The first two are significant with respect to their neighboring bins and errors, while the third peak is only partly significant.
+Looking at the flare distribution histogram with 10 bins for this star in figure \ref{fig:TYC_1360-957-1-Flarecount-10_Bins} one can see that the largest peaks in order are at phase \textasciitilde$0.7 \pi$, \textasciitilde$0.4 \pi$ and \textasciitilde$1.2 \pi$, the last one being two bins wide. The first two are significant with respect to their neighboring bins and errors, while the third peak is only partly significant.
 Looking at the histogram with 30 bins of the same dataset (figure \ref{fig:TYC_1360-957-1-Flarecount-30_Bins}), the first 2 peaks mentioned for the histogram with 10 bins are still pronounced. But compared to figure \ref{fig:TYC_1360-957-1-Flarecount-10_Bins}, the low number of flares and the large number of bins result in a rather large error. Therefore these two peaks are not significant as those are within the error of the histogram.
 \begin{figure}[pt!]
@@ -431,15 +431,15 @@ Looking at the histogram with 30 bins of the same dataset (figure \ref{fig:TYC_1
        \caption{30 bins}
        \label{fig:TYC_1360-957-1-Flarecount-30_Bins}
    \end{subfigure}
-    \caption{Histograms of TYC 1360-957-1 across the phase showing the number of flares in each bin. The error bars show 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 $0 \pi$/$2 \pi$.}
+    \caption{Histograms of TYC 1360-957-1 across the phase showing the number of flares in each bin with a total of 40 flares. The error bars show 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:TYC_1360-957-1-Flarecount}
 \end{figure}
-Figure \ref{fig:TYC_1360-957-1-flarepeaks_1.31} presents the overall distribution of the normalized phase detected for TYC 1360-957-1 in this study. The three largest flare peaks detected were at a normalized phase of \textasciitilde$0.8 \pi$, which is close to the phase minimum at $1 \pi$. This could indicate that they originate from the same spot or spot group. Three more larger flare peaks stand out at phase $1.2 \pi$. While they are not as large as the previous three, they have a higher peak than the rest of the detected flares.
+Figure \ref{fig:TYC_1360-957-1-flarepeaks_1.31} presents the overall distribution of flares across the normalized phase detected for TYC 1360-957-1 in this study. The three largest flare peaks detected were at a normalized phase of \textasciitilde$0.8 \pi$, which is close to the phase minimum at $1 \pi$. This could indicate that they originate from the same spot or spot group. Three more larger flare peaks stand out at phase $1.2 \pi$. While they are not as large as the previous three, they have a higher peak than the rest of the detected flares.
 \begin{figure}[pt!]
    \includegraphics[width=.95\textwidth]{plots/sine/TYC_1360-957-1/TYC 1360-957-1-Flarepeaks_maxY-1.5.png}
-    \caption{Distribution of flare peaks in relation to the normalized phase at which they occured for TYC 1360-957-1. The y-Axis shows the flare peak and the x-axis shows the normalized phase.}
+    \caption{Distribution of flare peaks in relation to the normalized phase at which they occured for TYC 1360-957-1. The y-axis shows the flare peak and the x-axis shows the normalized phase.}
    \label{fig:TYC_1360-957-1-flarepeaks_1.31}
 \end{figure}
@@ -473,8 +473,8 @@ No such large flares can be seen in sector 45 (upper right panel of figure \ref{
 \FloatBarrier
 \subsection{TYC 4595-107-1}
-TYC 4595-107-1, also known as TIC 394030788, is an active G-type main-sequence star with an effective temperature of 5231 K, a radius of 0.9 $R_\odot$ (\cite{tess_2nd_year_superflares}, \cite{superflare_rate_variation_g_type}), a mass of 0.89 $M_\odot$ (\cite{superflare_rate_variation_g_type}) and a rotational period of 3.3 days (\cite{tess_2nd_year_superflares}, \cite{superflare_rate_variation_g_type}) and was observed in 20 TESS sectors. The folded lightcurves for TYC 4595-107-1 can be found in appendix \ref{apB:TYC_4595-107-1}.\\
+TYC 4595-107-1, also known as TIC 394030788, is an active G-type main-sequence star with an effective temperature of 5231 K, a radius of 0.9 $R_\odot$ \citep{tess_2nd_year_superflares,superflare_rate_variation_g_type}, a mass of 0.89 $M_\odot$ \citep{superflare_rate_variation_g_type} and a rotational period of 3.3 days \citep{tess_2nd_year_superflares,superflare_rate_variation_g_type} and was observed in 20 TESS sectors. The folded lightcurves for TYC 4595-107-1 can be found in appendix \ref{apB:TYC_4595-107-1}.\\
-The first histogram, figure \ref{fig:TYC_4595-107-1-Flarecount-10_Bins}, with 10 bins shows the accumulated data for all 20 observed lightcurves. Due to the high number of available lightcurves, and TYC 4595-107-1 being a very active star (\cite{tess_2nd_year_superflares}, \cite{superflare_rate_variation_g_type}), the total flare count is very high. There seem to be a base level of flares per bin of around 30 over the phase, with a large and two bin wide peak at around phase $0.6$ to $0.8 \pi$. This increase in flare number is sufficiently large to be outside of the error of the average distribution. Another peak, even though less significant as its errorbar overlaps with the surrounding bins, appears at the bin at phase $1.9 \pi$. A similar, but a bit weaker increase in flares can be seen at the bin at $0.2 \pi$.\\
+The first histogram, figure \ref{fig:TYC_4595-107-1-Flarecount-10_Bins}, with 10 bins shows the accumulated data for all 20 observed lightcurves. Due to the high number of available lightcurves, and TYC 4595-107-1 being a very active star \citep{tess_2nd_year_superflares,superflare_rate_variation_g_type}, the total flare count is very high. There seems to be a base level of flares per bin of around 30 over the phase, with a large and two bin wide peak at around phase $0.6$ to $0.8 \pi$. This increase in flare number is sufficiently large to be outside of the error of the average distribution. Another peak, even though less significant as its errorbar overlaps with the surrounding bins, appears at the bin at phase $1.9 \pi$. A similar, but a bit weaker increase in flares can be seen at the bin at $0.2 \pi$.\\
 The histogram with 30 bins (figure \ref{fig:TYC_4595-107-1-Flarecount-30_Bins}) shows a similar result. It shows an increase in flare number around phase $0.6$ to $1 \pi$, as well as at $1.9$ to $0.1 \pi$ and $0.4 \pi$. Only the first mentioned peak managed to be large enough though, to be significantly above the error of the average distribution.
 \begin{figure}[pt!]
@@ -491,7 +491,7 @@ The histogram with 30 bins (figure \ref{fig:TYC_4595-107-1-Flarecount-30_Bins})
        \caption{30 bins}
        \label{fig:TYC_4595-107-1-Flarecount-30_Bins}
    \end{subfigure}
-    \caption{Histograms of TYC 4595-107-1 across the phase showing the number of flares in each bin. The error bar shows the standard deviation for the histogram. The blue lines show the various fits for the folded lightcurves used to generate the data, with the phase minimum at $1 \pi$ and phase maximum at $0 \pi$/$2 \pi$.}
+    \caption{Histograms of TYC 4595-107-1 across the phase showing the number of flares in each bin with a total of 365 flares. 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:TYC_4595-107-1-Flarecount}
 \end{figure}
@@ -500,7 +500,7 @@ All of the folded lightcurves of TYC 4595-107-1 can be found in appendix \ref{ap
 \begin{figure}[pt!]
    \includegraphics[width=.95\textwidth]{plots/sine/TYC_4595-107-1/TYC 4595-107-1-Flarepeaks_maxY-1.5.png}
-    \caption{Distribution of flare peaks in relation to the normalized phase at which they occured for TYC 1360-957-1. The y-Axis shows the flare peak and the x-axis shows the normalized phase.}
+    \caption{Distribution of flare peaks in relation to the normalized phase at which they occured for TYC 4595-107-1. The y-axis shows the flare peak and the x-axis shows the normalized phase.}
    \label{fig:TYC_4595-107-1-flarepeaks_1.27}
 \end{figure}
@@ -508,12 +508,11 @@ All of the folded lightcurves of TYC 4595-107-1 can be found in appendix \ref{ap
 \subsection{V* V471 Tau}
 \label{results:v471_tau}
-V471 Tau is a post-common envelope binary system consiting of a K2 and a white dwarf (\cite{v471tau_revised}). The K2 dwarf has a dominant spot facing the white dwarf all the time, as the system shows a bound rotation (\cite{V471tau_magnetic_activity}).
+V471 Tau is a post-common envelope binary system consiting of a K2 and a white dwarf \citep{v471tau_revised}. The K2 dwarf has a dominant spot facing the white dwarf all the time, as the system shows a bound rotation \citep{V471tau_magnetic_activity}.
 Figures \ref{fig:V471Tau-Flarecount-10_Bins} and \ref{fig:V471Tau-Flarecount-30_Bins} show the histograms of five TESS folded lightcurves for V471 Tau with 10 and 30 bins respectively. The TESS lightcurves used are from sectors 42, 43, 44, 70 and 71. The lightcurve of K2 target table ID 80 was rejected by the algorithm described in section \ref{sec:data:data_reduction}. Due to the lightcurve spanning 90 days, and the variability due to spots, the folding and fitting algorithm could not produce a reliable output.
 The blue lines show the used fits for the individual folded lightcurves.
 In the first figure, there appear two different peaks. The first being at phase $0.5 \pi$, and the second one at phase $1.1 \pi$. These bins are significantly higher than the remaining bins with 13/15 flares respectively compared to 1 to 8 in the other bins.\\
-Increasing the bins to 30 (figure \ref{fig:V471Tau-Flarecount-30_Bins}) does not change the result much. Due to the individual flare count being lower per bin compared to figure \ref{fig:V471Tau-Flarecount-10_Bins}, the errorbars are comparatively larger. There are still peaks at \textasciitilde$0.5 \pi$ and $1 \pi$.\\
+Increasing the bins to 30 (figure \ref{fig:V471Tau-Flarecount-30_Bins}) does not change the result much. Due to the individual flare count being lower per bin compared to figure \ref{fig:V471Tau-Flarecount-10_Bins}, the errorbars are comparatively larger. There are still peaks at \textasciitilde$0.5 \pi$ and $1 \pi$.
 As seen in figures \ref{fig:V471Tau-TESS42_foldedLC}, \ref{fig:V471Tau-TESS43_foldedLC} and \ref{fig:V471Tau-TESS44_foldedLC} the transit of the white dwarf (dip in the lightcurves) occurs phase 0 (in these figures) which translates to phase $1 \pi$ in the normalized phase. 
 \begin{figure}[pt!]
    \centering
@@ -529,7 +528,7 @@ As seen in figures \ref{fig:V471Tau-TESS42_foldedLC}, \ref{fig:V471Tau-TESS43_fo
        \caption{30 bins}
        \label{fig:V471Tau-Flarecount-30_Bins}
    \end{subfigure}
-    \caption{Histograms of V471 Tau across the phase showing the number of flares in each bin. The error bar shows the standard deviation for the histogram. The blue lines show the various fits for the folded lightcurves used to generate the data, with the phase minimum at $1 \pi$ and phase maximum at $0 \pi$/$2 \pi$.}
+    \caption{Histograms of V471 Tau across the phase showing the number of flares in each bin with a total of 66 flares. 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:V471Tau-Flarecount}
 \end{figure}
@@ -560,11 +559,11 @@ Looking at the folded lightcurves for this star (see figures \ref{fig:V471Tau-TE
 \end{figure}
-In figure \ref{fig:V471Tau-flarepeaks_1.1} the flare peak of the normalized phase distribution can be seen. It reveals that the largest flares occured around phase $0.5 \pi$, $1 \pi$ and $1.5 \pi$. The phase in which the white dwarf transit occurs is around phase $1 \pi$.
+In figure \ref{fig:V471Tau-flarepeaks_1.1} the flare peak across the normalized phase distribution can be seen. It reveals that the largest flares occured around phase $0.5 \pi$, $1 \pi$ and $1.5 \pi$. The phase in which the white dwarf transit occurs is around phase $1 \pi$.
 \begin{figure}[pt!]
    \includegraphics[width=.95\textwidth]{plots/sine/V471Tau/V_star_ V471 Tau-Flarepeaks_maxY-1.1.png}
-    \caption{Distribution of flare peaks in relation to the normalized phase at which they occured. The y-Axis shows the flare peak and the x-axis shows the normalized phase.}
+    \caption{Distribution of flare peaks in relation to the normalized phase at which they occured. The y-axis shows the flare peak and the x-axis shows the normalized phase.}
    \label{fig:V471Tau-flarepeaks_1.1}
 \end{figure}
@@ -572,10 +571,10 @@ In figure \ref{fig:V471Tau-flarepeaks_1.1} the flare peak of the normalized phas
 \subsection{V* HK Aqr}
 \label{results:hk_aqr}
-HK Aqr is an M dwarf with a mass of 0.57 $M_\odot$, a radius of 0.53 $R_\odot$ and a distance of 22.3 pc. Its effective temperature is 3800 K (\cite{conch_shell_m_dwarfs}). It was observed in four TESS sectors.
+HK Aqr is an M dwarf with a mass of 0.57 $M_\odot$, a radius of 0.53 $R_\odot$ and a distance of 22.3 pc. Its effective temperature is 3800 K \citep{conch_shell_m_dwarfs}. It was observed in four TESS sectors.
 For the analysis of HK Aqr the optimize fold algorithm partially broke. This happened for its lightcurves for TESS 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.\\
 In figure \ref{fig:HKAqr-Flarecount-10_Bins} one can see an increase in flare number at phase $1.3 \pi$. This peak is sufficiently large to be outside the error range of the lower flare count bins between phase $0$ to $1 \pi$. Figure \ref{fig:HKAqr-Flarecount-30_Bins} shows a similar picture. Additionally it shows a peak at phase $0 \pi$ though, which means during the phase maximum, as well as one around phase $1.6 \pi$ which is in the transition from minimum to maximum.\\
-Figures \ref{fig:HKAqr-Flarecount-10_Bins_Period} and \ref{fig:HKAqr-Flarecount-30_Bins_Period} show the histograms for the data of the two folded TESS lightcurves of sectors 29 and 42 which were flagged as period folded with 10 and 30 bins respectively. The folded lightcurves can be found in figure \ref{fig:HKAqr-TESS_foldedLCs_Period}.
+Figures \ref{fig:HKAqr-Flarecount-10_Bins_Period} and \ref{fig:HKAqr-Flarecount-30_Bins_Period} show the histograms for the data of the two folded TESS lightcurves of sectors 29 and 42 which were period folded with 10 and 30 bins respectively. The folded lightcurves can be found in figure \ref{fig:HKAqr-TESS_foldedLCs_Period}.
 In figure \ref{fig:HKAqr-Flarecount-10_Bins_Period} the overall flare distribution seems to be relatively high from phase $0.2 \pi$ to $1.4 \pi$, with a peak at phase $1.2 \pi$. The number of detected flares during the maximum of the lightcurves at phase $1.8$ to $0.2 \pi$ is low compared to that. An additional dip of the same flare count can be seen at phase $1.5 \pi$.
 The flare count in figure \ref{fig:HKAqr-Flarecount-30_Bins_Period} together with larger number of bins results in large errors. Nontheless there are two bins which stand out at phases \textasciitilde$0.4 \pi$ and \textasciitilde$1.25 \pi$ which would be in the transition from maximum to minimum, and shortly after the minimum respectively. In figure \ref{fig:HKAqr-TESS_foldedLCs1} we see that the three strongest (according to their flare peak) flares all occur at the same phase. Also here, and similar to the strong flares seen in figure \ref{fig:TYC_1360-957-1-flarepeaks_1.31}, those may originate from the same spot or spot group.
@@ -593,7 +592,7 @@ The flare count in figure \ref{fig:HKAqr-Flarecount-30_Bins_Period} together wit
        \caption{30 bins}
        \label{fig:HKAqr-Flarecount-30_Bins}
    \end{subfigure}
-    \caption{Histograms of V* HK Aqr across the phase showing the number of flares in each bin. The error bar shows the standard deviation for the histogram. The blue lines show the various fits for the folded lightcurves used to generate the data, with the phase minimum at $1 \pi$ and phase maximum at $0 \pi$/$2 \pi$.}
+    \caption{Histograms of V* HK Aqr across the phase showing the number of flares in each bin with a total of 79 flares. The error bar shows the standard deviation for the histogram. The blue lines show the various fits for the folded lightcurves used to generate the data, with the phase minimum at $1 \pi$ and phase maximum at $0 \pi$/$2 \pi$.}
    \label{fig:HKAqr-Flarecount}
 \end{figure}
@@ -646,7 +645,7 @@ The flare count in figure \ref{fig:HKAqr-Flarecount-30_Bins_Period} together wit
        \caption{30 bins}
        \label{fig:HKAqr-Flarecount-30_Bins_Period}
    \end{subfigure}
-    \caption{Histograms of V* HK Aqr across the phase showing the number of flares in each bin. The error bar shows the standard deviation for the histogram. The blue lines show the various fits for the folded lightcurves used to generate the data, with the phase minimum at $1 \pi$ and phase maximum at $0 \pi$/$2 \pi$.}
+    \caption{Histograms of V* HK Aqr across the phase showing the number of flares in each bin with a total of 38 flares. The error bar shows the standard deviation for the histogram. The blue lines show the various fits for the folded lightcurves used to generate the data, with the phase minimum at $1 \pi$ and phase maximum at $0 \pi$/$2 \pi$.}
    \label{fig:HKAqr-Flarecount_Period}
 \end{figure}
@@ -672,7 +671,7 @@ The flare count in figure \ref{fig:HKAqr-Flarecount-30_Bins_Period} together wit
 \subsection{KOI-256}
 \label{results:koi_256}
-KOI-256 is, similarly to V471 Tau, a binary system consisting of an 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 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 an M dwarf and a white dwarf \citep{eclipsing_binaries_koi_256,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 \citep{eclipsing_binaries_koi_256}. Similarly to HK Aqr, a second periodicity was detected, which was 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 wrongly detected. This figure shows an increase in flare count around phase $1 \pi$, which peaks at phases $0.7 \pi$ and a bit weaker around $1.4 \pi$. Additionally there appears a peak at phase $1.7 \pi$. 
 Increasing the bins to 30 (figure \ref{fig:KOI-256-Flarecount-30_Bins}) shows more distinct peaks at phase $0.7 \pi$ as well as at $1.2 \pi$. The mentioned peaks of both figures are significantly above their surrounding bins.
@@ -690,13 +689,13 @@ Increasing the bins to 30 (figure \ref{fig:KOI-256-Flarecount-30_Bins}) shows mo
        \caption{30 bins}
        \label{fig:KOI-256-Flarecount-30_Bins}
    \end{subfigure}
-    \caption{Histograms of KOI-256 across the phase showing the number of flares in each bin. The error bar shows the standard deviation for the histogram. The blue lines show the various fits for the folded lightcurves used to generate the data, with the phase minimum at $1 \pi$ and phase maximum at $0 \pi$/$2 \pi$.}
+    \caption{Histograms of KOI-256 across the phase showing the number of flares in each bin with a total of 167 flares. The error bar shows the standard deviation for the histogram. The blue lines show the various fits for the folded lightcurves used to generate the data, with the phase minimum at $1 \pi$ and phase maximum at $0 \pi$/$2 \pi$.}
    \label{fig:KOI-256-Flarecount}
 \end{figure}
 Figures \ref{fig:KOI-256-Flarecount-10_Bins_Period} and \ref{fig:KOI-256-Flarecount-30_Bins_Period} show the histograms based on the, by the optimized fold algorithm determined, period folded lightcurves. Therefore 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 the histogram with 10 bins for the flare distribution across the normalized phase, there is a clear increase of flare number seen around the minimum at phase $1 \pi$. The distribution is nearly comparable to a normal distribution, except for the last two bins.\\
-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 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 shows gradual increases/descreases before and after, with the exception of the dip in the bin right before 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 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 other hand shows gradual increases/decreases before and after, with the exception of the dip in the bin right before phase $0.9 \pi$.
 \begin{figure}[pt!]
    \centering
@@ -712,7 +711,7 @@ Looking at figure \ref{fig:KOI-256-Flarecount-30_Bins_Period} which shows the sa
        \caption{30 bins}
        \label{fig:KOI-256-Flarecount-30_Bins_Period}
    \end{subfigure}
-    \caption{Histograms of KOI-256 across the phase showing the number of flares in each bin. The error bar shows the standard deviation for the histogram. The blue lines show the various fits for the folded lightcurves used to generate the data, with the phase minimum at $1 \pi$ and phase maximum at $0 \pi$/$2 \pi$.}
+    \caption{Histograms of KOI-256 across the phase showing the number of flares in each bin with a total of 66 flares. The error bar shows the standard deviation for the histogram. The blue lines show the various fits for the folded lightcurves used to generate the data, with the phase minimum at $1 \pi$ and phase maximum at $0 \pi$/$2 \pi$.}
    \label{fig:KOI-256-Flarecount_Period}
 \end{figure}
@@ -740,7 +739,7 @@ Comparing the results of the flare peak distributions across the normalized phas
 \subsection{2MASS J19230963+3739397}
 \label{results:2MASS_J19230963p3739397}
-2MASS J19230963+3739397, also known as KIC 2300039 or TIC 122672447, is an M dwarf around 213 pc away from our solar system (\cite{simbad}). It was observed in three Kepler target table IDs as well as four 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 the opposite of what is expected. As seen in the histogram with 10 bins (figure \ref{fig:2MASS_J19230963p3739397-Flarecount-10_Bins}) it shows an increased flare occurence 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 lowest. Increasing the bin count to 30 (see figure \ref{fig:2MASS_J19230963p3739397-Flarecount-30_Bins}) creates a similarly shaped histogram. The errorbars are larger, and the distribution less significant. 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. 
+2MASS J19230963+3739397, also known as KIC 2300039 or TIC 122672447, is an M dwarf around 213 pc away from our solar system \citep{simbad}. It was observed in three Kepler target table IDs as well as four 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 the opposite of what is expected. As seen in the histogram with 10 bins (figure \ref{fig:2MASS_J19230963p3739397-Flarecount-10_Bins}) it shows an increased flare occurrence 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 lowest. Increasing the bin count to 30 (see figure \ref{fig:2MASS_J19230963p3739397-Flarecount-30_Bins}) creates a similarly shaped histogram. The errorbars are larger, and the distribution less significant. 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
@@ -756,7 +755,7 @@ Comparing the results of the flare peak distributions across the normalized phas
        \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 $0 \pi$/$2 \pi$.}
+    \caption{Histograms of 2MASS J19230963+3739397 across the phase showing the number of flares in each bin with a total of 63 flares. 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}