% !TEX root = ../thesis-example.tex
%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.

Binary stars play a major role in astrophysics since their analysis by different means enables astronomers to deduce various stellar properties. In this thesis the binary system KIC 10614012 is analysed by combining asteroseismic techniques with radial velocity measurements and light curve analysis. This star system, also referred to as TYC 3561-1138-1, is part of the Kepler Input Catalog (KIC), a catalogue for potential target stars of the \textit{Kepler} mission. KIC 10614012 is an eclipsing binary (EB), i.e. an eclipse is visible in its light curve \citep[as written in][]{Kirk2016}. Furthermore, \cite{Beck2014} has shown that this star exhibits tidally induced flux modulations during periastron passage, on its eccentric ($e = 0.71$) orbit. Such binary stars, theorized by \citet{Kumar:1995}, are colloquially referred to as \textit{Heartbeat stars}, a term coined by \citet{Thompson2012}.

\begin{figure}[t!]
  \includegraphics[width=\linewidth]{gfx/rghbHRD.pdf}
  \caption{Position of the 18 red giant heartbeat stars from Tables 1 and 2 in
the HR diagram, where the colour shows the mass of the red giant, derived from seismology. The size of the dots represents the orbital period,
ranging between 20 and 438 d. The contour surfaces reflect the density
distribution of 1000 pulsating red giants. The darkest areas mark the
position of the densely populated red clump. Numbers in red indicate
the star count per bin, for which the contour surfaces have been drawn.
Lines of equal radii in the HR diagram have been drawn for selected
stellar radii between 5 and 30 R. \citep[Figure taken from][]{Beck2014}}
  \label{fig:singelPanelPlot}
\end{figure}

This case study is divided into 7 sections. The first section (Sec.\,\ref{sec:intro}) gives a brief introduction into some of the underlying astrophysics of this analysis. Sec.\,\ref{sec:data} presents the three datasets used for this case study (light curves, asteroseismic power spectra and radial velocity measurements) and the instruments which obtained them (\textit{Kepler} and HERMES). The analysis of KIC 10614012 by means of asteroseismology is described in Sec.\,\ref{sec:data}, while the next chapter (Sec.\,\ref{sec:results}) deals with the system's analysis regarding its binary features. The fifth section (Sec.\,\ref{sec:results}) combines results from the previous two sections and estimates stellar properties of both, the primary and the secondary. A discussion of those results and a comparison to other studies are given in Sec.\,\ref{sec:discussion}. Eventually, in Sec.\,\ref{sec:conclusion} some conclusions are drawn, suggestions for further analysis of KIC 10614012 are given and a brief outlook on future prospects in asteroseismology is provided.


Calculating the hypotenuse follows the sentence of Pythagoras, 
\begin{eqnarray}
c^2 &=& a^2 + b^2, \label{eq:pyth1}\\
c &=& \sqrt{a^2 + b^2} \label{eq:pyth2},
\end{eqnarray}
whereby $a$ and $b$ are the cathetus and $c$ the hypotenuse of a right-angled triangle. Please note that $a$ and $b$ are typically in the range of 10$^{-9}$\,$\lesssim$\,R/R$_\odot$\,$\lesssim$\,10$^6$.


\lipsum[1]
