\chapter{The low frequency window}
\label{LF}
The scientific research exposed in this thesis focusses on the improvement of ground-based gravitational-wave detectors at low frequency. This chapter intends to frame the work done in this context and highlight why the lower frequency window is so important. The discussion around this topic is relatively recent and it has been widely discussed during dedicated workshops which the author of this thesis attended since 2018.

\subsection{Sources of gravitational waves}
Fig. \ref{spec} summarizes the possible objects that can be gravitational waves sources, their frequency emission and what kind of instrument can detect them. The terrestrial interferometric detectors are the most involved at present times, but the efforts of the scientific community are going towards the development of new detectors both ground- and space-based in order to widen the frequency window of observation.

\begin{figure}[h!]
\centering
\includegraphics[scale=1.6]{images/spectrum}
\caption[Sources of gravitational waves]{Spectrum of emission of sources of gravitational waves (adapted from https://lisa.nasa.gov).}
\label{spec}
\end{figure}

\noindent
The best modelled sources are binary systems, typically Neutron Stars (NS), White Dwarfs and Black Holes (BH), orbiting each other. Fig. \ref{binary} shows the main phases of the evolution of the systems, emitting gravitational waves at different frequencies, depending on the phase.

\begin{figure}[h!]
\centering
\includegraphics[scale=1]{images/bin.png}
\caption[Phases of gravitational waves emission by a binary system]{The three phases of a BH-BH binary system emitting gravitational waves (amplitude vs time) \cite{first}. \textbf{Inspiral phase}: the orbits shrink, velocity increases and frequency of the waves emitted increases as $f_{gw} = 2f_{orbital}$. \textbf{Merging phase}: the objects merge and the signal is maximum. \textbf{Ring-down phase}: a new BH is formed and the signal emitted decreases in frequency as a damped sinusoid.}
\label{binary}
\end{figure}

\noindent
Gravitational waves from binary systems can provide several information about the equation of state of Neutron stars, masses and spin of Black holes, test of General Relativity theory.\\
Currently, the ground-based observatories are tuned to detect binary systems sources: interferometers are the instruments that have been able to detect gravitational waves from binary systems.\\

\noindent
The first detection of gravitational waves happened on the 14th September 2015 and confirmed the Theory General Relativity, opening a new window on the Universe: the signal from a merger of two black holes have been observed thanks to the emission of gravitational waves, confirming the existence of these objects, still mostly unknown \cite{first}. The detector responsible of the new discovery is based in the USA and it is one of the terrestrial interferometers currently in use for gravitational waves detection.

\section{Hidden GW sources}
PER QUESTA SEZIONE, FARE RIFERIMENTO A TUTTI I VARI WORKSHOP.