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@@ -7,12 +7,12 @@ This chapter gives an introduction to the goals of this study. Afterwards there
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\section{Goals and current knowledge \label{sec:intro:goals}}
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The goal of this study is to relate flares/superflares to the appearance of spots on the surfaces of stars of various spectral types. Flares are well studied for the sun (\cite{solar_flares_1}, \cite{solar_flares_2}, \cite{solar_flares_3}) as well as its impact on earths magnetic field (\cite{solar_flare_mag_field}). While the first stellar flares were discovered in middle of the last century (\cite{early_stellar_flares1}, \cite{early_stellar_flares2}), the topic gained a lot of traction with the launch of the likes of Kepler and the Transiting Exoplanet Survey Satellite (TESS). They allowed the survey of thousands of stars. With this, studies of flares and superflares on a large number of stars have been conducted (e.g. \cite{flare_study_1}, \cite{flare_study_2}, \cite{connection_starspots_flares_ms_kepler}, \cite{flare_occurance_periodicity}), but the origin of superflares (flares with an energy above $10^{33}$ erg) is still not clear. So far no superflare has been observed on our sun, but there have been studies focusing on the possible origin on superflares and their likelyhood to happen on our sun (\cite{superflares_on_sun}). They found that superflares on our sun would be rare events (every \textasciitilde800 years for superflares with $10^{34}$ erg).\\
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A few proposed caused could be star-planet interaction (SPI) (\cite{au_mic_flaring_spi}, \cite{SPI_1}, \cite{SPI_2}), or just being scaled up version of normal flares which we see from our sun coming from large spots (\cite{superflares_1}, \cite{superflares_2}).\\
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\cite{kepler_411_study} focused on Kepler-411 by investigating the relation between superflares and star spots on that star. They found a positive correlation between the energy of flares and the area of star spots (\cite{kepler_411_study}) on Kepler-411. They then compared their results for Kepler-411, which produced multiple superflares, with Kepler-210, which did not produce superflares while having the same number of spots (\cite{kepler_411_210_comparison}). They found the spots on Kepler-210 to be larger, warmer and therefor being magnetically weaker/less complex compared to Kepler-411 and concluded that the area of starspots is not the only relevant parameter for superflare occurance (\cite{kepler_411_210_comparison}).\\
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\cite{doyle_2018} studied 34 M dwarfs from the K2 mission, using short cadence observational data. They confirmed that stars with a rotational period of less than 10 days showed more flares, which was already shown previously (\cite{faster_rot_stars_more_flares1}, \cite{faster_rot_stars_more_flares2}). Furthermore they found no star with a preference for when flares occured during the rotational phase (\cite{doyle_2018}). A similar study using TESS 2 minute cadence data has been conducted by \cite{doyle_2019}. In this study they used data of 167 M dwarfs and found a total of 1834 flares. Similar to the study on K2 data, they found no preference for roational phase (\cite{doyle_2019}).\\
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Another possible cause for a periodic increase in flares is star-planet interaction (SPI), which is studied by \cite{au_mic_flaring_spi} for the star AU Mic. While they found a signal in their used TESS lightcurves correlating with the orbital period of AU Mic b, they require more observation time to get a $>3\sigma$ detection (\cite{au_mic_flaring_spi}).\\
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A few proposed causes could be star-planet interaction (SPI) (\cite{au_mic_flaring_spi}, \cite{SPI_1}, \cite{SPI_2}), or just being scaled up version of normal flares which we see from our sun coming from large spots (\cite{superflares_1}, \cite{superflares_2}).\\
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\cite{doyle_2018} studied 34 M dwarfs from the K2 mission, using short cadence observational data. They confirmed that the stars in their dataset with a rotational period of less than 10 days showed more flares, which was already shown previously (\cite{faster_rot_stars_more_flares1}, \cite{faster_rot_stars_more_flares2}). Furthermore they found no star with a preference for when flares occured during the rotational phase (\cite{doyle_2018}). A similar study using TESS 2 minute cadence data has been conducted by \cite{doyle_2019}. In this study they used data of 167 M dwarfs and found a total of 1834 flares. Similar to the study on K2 data, they found no preference for roational phase (\cite{doyle_2019}).\\
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Further analysis on periodic flare occurance was done by \cite{flare_occurance_periodicity}, who studied lightcurves of 284 M dwarfs. They found three targets (TIC 80427281, TIC 95328477, TIC 220432563) with a confirmed flare periodicity, which correlates to their rotational period or half of it.\\
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\cite{connection_starspots_flares_ms_kepler} investigated a sample of 119 stars from spectral types M to F. They found that flares which increase the stellar flux by 1\% to 5\% appear more often while larger starspots are visible, while flares which increase the flux by more that 5\% do not seem to have this dependency (\cite{connection_starspots_flares_ms_kepler}).
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\cite{connection_starspots_flares_ms_kepler} investigated a sample of 119 stars from spectral types M to F. They found that flares which increase the stellar flux by 1\% to 5\% appear more often while larger starspots are visible, while flares which increase the flux by more that 5\% do not seem to have this dependency (\cite{connection_starspots_flares_ms_kepler}).\\
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There have also been studies on individual stars, for example \cite{kepler_411_study} focused on Kepler-411 by investigating the relation between superflares and star spots on that star. They found a positive correlation between the energy of flares and the area of star spots (\cite{kepler_411_study}) on Kepler-411. They then compared their results for Kepler-411, which produced multiple superflares, with Kepler-210, which did not produce superflares while having the same number of spots (\cite{kepler_411_210_comparison}). They found the spots on Kepler-210 to be larger, warmer and therefor being magnetically weaker/less complex compared to Kepler-411 and concluded that the area of starspots is not the only relevant parameter for superflare occurance (\cite{kepler_411_210_comparison}). Star-planet interaction is studied by \cite{au_mic_flaring_spi} for the star AU Mic. While they found a signal in their used TESS lightcurves correlating with the orbital period of AU Mic b, they require more observation time to get a $>3\sigma$ detection (\cite{au_mic_flaring_spi}).\\
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In coclusion, many flares and superflares have been found on stars, but the origin of the later is still not clear. There are a few ongoing possible origins like star-planet interaction (or interactions with other close companions) or them coming from larger, more complex starspots.
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\section{Spectral Types \label{sec:intro:spectral_types}}
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@@ -40,7 +40,7 @@ The spectral types are a way to classify the vast amount of stars into various t
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% Different Spectral Types
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\section{Flares and Starspots \label{sec:intro:flares_and_spots}}
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\section{Flares and Spots \label{sec:intro:flares_and_spots}}
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% Stellar Activity,
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@@ -48,6 +48,14 @@ The spectral types are a way to classify the vast amount of stars into various t
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% TESS, Kepler/K2
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\subsection{Kepler}
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\subsection{K2}
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\subsection{TESS}
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%\section{Current knowledge \label{sec:intro:current_knowledge}}
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