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Physics_Thesis_Template/content/chapter-discussion.tex
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\chapter{Discussion \label{sec:discussion}}
M dwarfs, all data, no significant dependency of flare appearance on phase using 10 bins.
30 bins -> either 2 dips during the transition minima <-> maxima or increase of flare occurance during minima and maxima.
Looking at stronger flares only (min 1.25/1.5 flare peak) peaks during minima, stronger peak during phase maxima, in both 10 and 30 bin histograms.
Limiting to max 1.01, makes dip (compared to all data) clearer. Generally more flares during maxima than minima.
Limit to max 1.05, nearly identical histograms to all data. (different result to \cite{connection_starspots_flares_ms_kepler})
\\\\
K dwarfs, all data, siginificant peak at phase minimum, peak dominated by V471 Tau (discussed later). Slightly more flares from maximum to minimum than minimum to maximum in 10 bins. 30 bins larger dips but also larger peaks in second half of phase compared to first half.
limiting to min 1.05 -> three peaks, dip after maximum and on at phase 1 $\pi$. gradual decrease after minimum. V471 Taus peaks at right before and right after phase minimum.
limiting to <1.01 and 1.05, makes histogram look more and more like with all data, similarly to \cite{connection_starspots_flares_ms_kepler} peak in center (compared to their M/K plot), but additionally also peak at phase maximum.
max 1.05 already most flares, very similar to with all data.
G dwarfs, significant results, increase of flare appearance during phase minimum. Most flares are <1.05 (flares on solar like stars that increase brightness by 0.1\% to 1\% already superflares, \cite{solar_like_superflares}) -> most/all detected flares superflares. Overall dependency on phase/spot appearance.
Limiting to flares >1.05 -> flares during minima and transitions between minima <-> maxima, increasing bins -> more data would be required.
%methods: lombscargle generally finds lower periods with higher peaks (e.g. halfs of rotational period), which boxleastsquares does not always detect within the 4 highest
For F dwarfs, overall too little data, but the not siginificant amount detected all during phase minimum, could be similar to G dwarfs?
All data combined, peak at phase minimum dominated by G/K dwarfs, dip in transition maxima -> minima dominated by dip from M dwarf results.
%M dwarfs, all data, no significant dependency of flare appearance on phase using 10 bins.
%30 bins -> either 2 dips during the transition minima <-> maxima or increase of flare occurance during minima and maxima.
%Looking at stronger flares only (min 1.25/1.5 flare peak) peaks during minima, stronger peak during phase maxima, in both 10 and 30 bin histograms.
%Limiting to max 1.01, makes dip (compared to all data) clearer. Generally more flares during maxima than minima.
%Limit to max 1.05, nearly identical histograms to all data. (different result to \cite{connection_starspots_flares_ms_kepler})
%\\\\
Individual star results (subset taken):
BD-08 995 (G type): shows a strong flare/spot dependence for amount, flare peaks not dependent on phase
% K dwarfs, all data, siginificant peak at phase minimum, peak dominated by V471 Tau (discussed later). Slightly more flares from maximum to minimum than minimum to maximum in 10 bins. 30 bins larger dips but also larger peaks in second half of phase compared to first half.
% limiting to min 1.05 -> three peaks, dip after maximum and on at phase 1 $\pi$. gradual decrease after minimum. V471 Taus peaks at right before and right after phase minimum.
% limiting to <1.01 and 1.05, makes histogram look more and more like with all data, similarly to \cite{connection_starspots_flares_ms_kepler} peak in center (compared to their M/K plot), but additionally also peak at phase maximum.
% max 1.05 already most flares, very similar to with all data.
TYC 1360-957-1 (K type): no clear dependence on spots for flare count (1 peak around maximum, 1 during transition, another at minimum), less siginificant with more bins
Shows strongest flares right before phase minimum though.
% G dwarfs, significant results, increase of flare appearance during phase minimum. Most flares are <1.05 (flares on solar like stars that increase brightness by 0.1\% to 1\% already superflares, \cite{solar_like_superflares}) -> most/all detected flares superflares. Overall dependency on phase/spot appearance.
% Limiting to flares >1.05 -> flares during minima and transitions between minima <-> maxima, increasing bins -> more data would be required.
TYC 4595-107-1 (G type): similar to BD-08 995, increase of flares right before minimum, slight (less significant) increase at maximum. (appending folded lightcurves in appendix)
% For F dwarfs, overall too little data, but the not siginificant amount detected all during phase minimum, could be similar to G dwarfs?
V471 Tau: binary with white dwarf, most flares around white dwarf transit -> magnetic interactions likely (ref. to V471 Tau specific papers)
Strongest flares also around that
% All data combined, peak at phase minimum dominated by G/K dwarfs, dip in transition maxima -> minima dominated by dip from M dwarf results.
HK Aqr (M dwarf): not fully trusted results, half period was detected for 2/4 lightcurves (original folding had 2 fit maxima too far away from edges, caused it to check for if half period signal was detected and use that)
only full period results show overall less flares during the maxima
% Individual star results (subset taken):
% BD-08 995 (G type): shows a strong flare/spot dependence for amount, flare peaks not dependent on phase
KOI-256 (M dwarf): similar issue as HK Aqr, in 2/7 Kepler, 2/3 TESS lightcurves, like V471 Tau binary with white dwarf, shows siginficant dependency on spots in with period folded results. (appending folded lightcurves in appendix)
Largest flares, when period folded only, also at around 0.8 $\pi$ (same flare shifted to 2 $\pi$ in spot modulated fold), otherwise flare energies well spread.
% TYC 1360-957-1 (K type): no clear dependence on spots for flare count (1 peak around maximum, 1 during transition, another at minimum), less siginificant with more bins
% Shows strongest flares right before phase minimum though.
% TYC 4595-107-1 (G type): similar to BD-08 995, increase of flares right before minimum, slight (less significant) increase at maximum. (appending folded lightcurves in appendix)
% V471 Tau: binary with white dwarf, most flares around white dwarf transit -> magnetic interactions likely (ref. to V471 Tau specific papers)
% Strongest flares also around that
% HK Aqr (M dwarf): not fully trusted results, half period was detected for 2/4 lightcurves (original folding had 2 fit maxima too far away from edges, caused it to check for if half period signal was detected and use that)
% only full period results show overall less flares during the maxima
% KOI-256 (M dwarf): similar issue as HK Aqr, in 2/7 Kepler, 2/3 TESS lightcurves, like V471 Tau binary with white dwarf, shows siginficant dependency on spots in with period folded results. (appending folded lightcurves in appendix)
% Largest flares, when period folded only, also at around 0.8 $\pi$ (same flare shifted to 2 $\pi$ in spot modulated fold), otherwise flare energies well spread.
Physics_Thesis_Template/content/chapter-introduction.tex
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%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 an introduction to the goals of this study. It also gives a summary of the current knowledge related to this study. Afterwards there will be summaries on topics related to this study, giving explanations on the various spectral types of stars, flares and spots, as well as giving an introduction to the space missions whichs data was used.
This chapter gives an introduction to the goals of this study. Afterwards there will be summaries on topics related to this study, giving explanations on the various spectral types of stars, flares and spots, as well as giving an introduction to the space missions whichs data was used. Last but not least a summary of the current knowledge related to this study is given.
\section{Goals and current knowledge \label{sec:intro:cur_knowledge}}
\section{Goals and current knowledge \label{sec:intro:goals}}
The goal of this study is to relate the appearance of flares/superflares to that of star spots on a large sample of stars of various spectral types. This is done by folding the lightcurves and the normalizing the phases. Due to the appearance of spots on the stars surface, the star is slightly dimmed, causing a local minimum in the lightcurve. This dimming can be observed with the Kepler and TESS (Transiting Exoplanet Survey Satellite) space missions.
The goal of this study is to relate flares/superflares to the appearance of spots on the surfaces of stars of various spectral types. Flares are well studied for the sun (\cite{solar_flares_1}, \cite{solar_flares_2}, \cite{solar_flares_3}) as well as its impact on earths magnetic field (\cite{solar_flare_mag_field}). While the first stellar flares were discovered in middle of the last century (\cite{early_stellar_flares1}, \cite{early_stellar_flares2}), the topic gained a lot of traction with the launch of the likes of Kepler and the Transiting Exoplanet Survey Satellite (TESS). They allowed the survey of thousands of stars. With this, studies of flares and superflares on a large number of stars have been conducted (e.g. \cite{flare_study_1}, \cite{flare_study_2}, \cite{connection_starspots_flares_ms_kepler}, \cite{flare_occurance_periodicity}), but the origin of superflares (flares with an energy above $10^{33}$ erg) is still not clear. So far no superflare has been observed on our sun, but there have been studies focusing on the possible origin on superflares and their likelyhood to happen on our sun (\cite{superflares_on_sun}). They found that superflares on our sun would be rare events (every \textasciitilde800 years for superflares with $10^{34}$ erg).\\
A few proposed caused could be star-planet interaction (SPI) (\cite{au_mic_flaring_spi}, \cite{SPI_1}, \cite{SPI_2}), or just being scaled up version of normal flares which we see from our sun coming from large spots (\cite{superflares_1}, \cite{superflares_2}).\\
\cite{kepler_411_study} focused on Kepler-411 by investigating the relation between superflares and star spots on that star. They found a positive correlation between the energy of flares and the area of star spots (\cite{kepler_411_study}) on Kepler-411. They then compared their results for Kepler-411, which produced multiple superflares, with Kepler-210, which did not produce superflares while having the same number of spots (\cite{kepler_411_210_comparison}). They found the spots on Kepler-210 to be larger, warmer and therefor being magnetically weaker/less complex compared to Kepler-411 and concluded that the area of starspots is not the only relevant parameter for superflare occurance (\cite{kepler_411_210_comparison}).\\
\cite{doyle_2018} studied 34 M dwarfs from the K2 mission, using short cadence observational data. They confirmed that stars with a rotational period of less than 10 days showed more flares, which was already shown previously (\cite{faster_rot_stars_more_flares1}, \cite{faster_rot_stars_more_flares2}). Furthermore they found no star with a preference for when flares occured during the rotational phase (\cite{doyle_2018}). A similar study using TESS 2 minute cadence data has been conducted by \cite{doyle_2019}. In this study they used data of 167 M dwarfs and found a total of 1834 flares. Similar to the study on K2 data, they found no preference for roational phase (\cite{doyle_2019}).\\
Another possible cause for a periodic increase in flares is star-planet interaction (SPI), which is studied by \cite{au_mic_flaring_spi} for the star AU Mic. While they found a signal in their used TESS lightcurves correlating with the orbital period of AU Mic b, they require more observation time to get a $>3\sigma$ detection (\cite{au_mic_flaring_spi}).\\
Further analysis on periodic flare occurance was done by \cite{flare_occurance_periodicity}, who studied lightcurves of 284 M dwarfs. They found three targets (TIC 80427281, TIC 95328477, TIC 220432563) with a confirmed flare periodicity, which correlates to their rotational period or half of it.\\
\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}).
\section{Spectral Types \label{sec:intro:spectral_types}}
The spectral types are 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}).
\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 goes for 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.
\begin{table}
\caption{Table showing the different spectral types, in relation to their minimum and maximum effective temperature ranges in K. Based on the tables found in \cite{astrophysics_group_uk_spectral_types}, \cite{harvard_spectral_types_teff}}
\label{tab:spectral_types_table}
\begin{tabular}{lccl}
\hline
Spectral type & min. T\textsubscript{eff} & max. T\textsubscript{eff} & Color \\
& [K] & [K] & \\
\hline\hline
O & 25000 & - & Blue \\
B & 10000 & 25000 & Blue \\
A & 7500 & 10000 & Blue \\
F & 6000 & 7500 & Blue to White \\
G & 5000 & 6000 & White to Yellow \\
K & 3500 & 5000 & Orange to Red \\
M & - & 3500 & Red \\
\hline
\end{tabular}
\end{table}
% Different Spectral Types
\section{Flares and Starspots \label{sec:intro:flares_and_spots}}
@@ -25,3 +47,7 @@ Further analysis on periodic flare occurance was done by \cite{flare_occurance_p
\section{Space missions \label{sec:intro:space_missions}}
% TESS, Kepler/K2
%\section{Current knowledge \label{sec:intro:current_knowledge}}