\chapter{Useful insights}
\label{C}

\section{The first Detection}
On 14th September 2015 the two LIGO antennas observed for the first time a signal from a gravitational wave produced by the merger of two black holes. This was the very first time that a merger of such massive and elusive objects could be observed.\\
The gravitational-wave signal has been named GW150914 and has been emitted by 2 black hole of masses of 36 $M_{\odot}$ and 29 $M_{\odot}$, which merged at a distance of 410 Mpc (z = 0.09)and produced a final BH of 62 $M_{\odot}$. The remaining 3 $M_{\odot}$ have been radiated in gravitational waves. Fig. \ref{gwsig} shows the signal detected from LIGO Hanford and LIGO Livingston.\\
This detection has been the result of a wide scientific collaboration which efforts made possible a discovery that deserved the Nobel Prize in Physics in 2017 to the pioneers of gravitational wave hunting  \textit{'for decisive contributions to the LIGO detector and the observation of gravitational waves'}.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.5]{images/outreach.png}\\
\includegraphics[scale=0.55]{images/GWsignal.png} 
\caption[First detection of a gravitatonal wave signal.]{First detection of a gravitational wave signal \cite{first}. The event is shown for both observatories at the time of observation 09:50:45 UTC on 14th September 2015. The top row is the gravitational wave amplitude for Hanford (H1) and Livingston (L1). In the L1 panel, there is a visual comparison of the two signals: the wave passe through L1 first, H1 signal (in orange) is shifted by the 6.9 ms of difference, and inverted due to their mutual orientation. The second row shows the consistency of the measured signal with expectations independently computed. Third row shows the residuals after subtraction of the measured time series and the numerical waveform. Bottom row is the same signal in frequency vs time, where it is evident the increase of frequency with time.}
\label{gwsig}
\end{figure}

\begin{figure}
\includegraphics[scale=0.65, angle=90]{images/logos.pdf}
\caption[The gravitational-wave scientific community]{The gravitational-wave scientific community (image kindly provided by \cite{cavaglia}).}
\end{figure}

\section{LIGO duty cycle}
The efficiency of the instrument was shown in Fig. \ref{duty}, and the upper chart is reported here.

\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/duty_cycle.png}
\end{figure}

\noindent
The legend of this pie chart is defined in the detchar summary pages \textit{https://summary.ligo.org/O3/}. From a private conversation with Dr. Jeff Kissel, it is generally intended as in Tab \ref{dutylegend}.

\begin{table}[h!]
\centering
\begin{tabular}{l|l}
\multicolumn{1}{l|}{\textbf{Legend}} & \multicolumn{1}{l}{\textbf{Jeff's definition}} \\ \hline
\hline\\
Observing  & \pbox{10cm}{We are at nominal low noise, no one is messing with the interferometer}\\ 
\hline\\
Ready  & \pbox{10cm} {We are at nominal low noise, but the low-latency processes aren’t functioning normally}\\
\hline\\
Locked & \pbox{10cm} {LIGO is locked, and the automated lock-acquisition system thinks it’s in nominal low noise, but the operator hasn’t confirmed that we’re ready yet}\\
\hline\\
Not locked &  every other time.        
\end{tabular}
\caption[Duty cycle legend of LIGO]{Duty cycle legend of LIGO as explained by Dr. Jeff Kissel (from a private conversation).}
\label{dutylegend}
\end{table}

\noindent
Other definitions and details about duty cycle and performance of the instrument can be found in \cite{duty1} and \cite{duty2}.

\section{The PRCL suspension filters}

The transfer function of the suspensions of the PR cavities, illustrated in the block diagram \ref{prcl} in Chapter 5, are shown in the plot \ref{prclm1}. The complicated shape of this functions makes difficult to manually solve the PRCL block diagram and simulate the motion of the optics. To solve the diagram, the Mathematica software has been used and several tests have been tried to look for the best filters and their effects (as reported on LHO logbook posts 52623, 53160, 53442, 53442).

\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/m1prcl.png}
\caption[Transfer function of the suspensions for PRCL]{Transfer function of the suspensions for PRCL.}
\label{prclm1}
\end{figure}





