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'}.
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@@ -17,3 +18,46 @@ This detection has been the result of a wide scientific collaboration which effo
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}.
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 PRCL cavity illustrated in the block diagram of 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.
\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.}
\caption[LHO duty cycle during O3b]{\textbf{Up:} Example of duty cycle for Hanford Observatory, during O3b \cite{kisseltalk1}. For almost 20\% of the running time the detector was not locked, which means that it was not observing. Of this 20\%, the \textbf{bottom} chart shows the causes of the lockloss: the main ones are seismic and "unknown" The study presented here could possibly reduce both.}
\caption[LHO duty cycle during O3b]{\textbf{Up:} Example of duty cycle for Hanford Observatory, during O3b \cite{kisseltalk1}. For almost 20\% of the running time the detector was not locked, which means that it was not observing\footnotemark. Of this 20\%, the \textbf{bottom} chart shows the causes of the lockloss: the main ones are seismic and "unknown" The study presented here could possibly reduce both.}
\label{duty}
\end{figure}
\subsection{Differential motion between chambers}
We have seen that among the noise sources which contribute to lock loss events there is the ground motion, including earthquakes and microseismic events. \\
In particular, during O3 run, it was observed that the chambers in the corner station (CS) show differential motion with respect to each other \cite{technote1}. It is reasonable to think that if the chambers could have a synchronized motion, the whole interferometer would move following the ground motion, without being affected by it. This would in principle help the cavities to be stable and to maintain the resonance. In case of lock losses due to large earthquakes or high wind, stable resonance could be achieved in shorter times \cite{biswas}.\\
On another side, reducing the differential motion between the chambers means to reduce a source of noise at low frequency (5-30 Hz), as we will show in the next section: this would improve the sensitivity of the interferometer.
\footnotetext{For a full understanding of the legend, refer to Appendix C.}
\subsection{ISI stabilization}
Differential motion affects the ISI of the HAM and BSC chambers in the CS: these are the platforms that we want to stabilize. Several sensors are responsible for sensing the seismic motion, in all degrees of freedom of each stage. We have already introduced the seismic sensors in Section \ref{ligosei} of Chapter \ref{LIGO}: they are T240, L4C, GS13 and CPS \cite{kisselthesis}.\\
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@@ -300,7 +303,7 @@ Figure \ref{t240_inj} shows the T240 signal and its contributors.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/t240inj.png}
\caption[BSC contributions]{Plot of all the single BSC contributions computed from the inertial sensor involved in this chamber. We are certain that the T240 is dominated by tilt effects below 80 mHz, and by sensor-noise at higher frequencies. We interpolated these two bands together to determine an effective input disturbance from the T240.}
\caption[BSC contributions]{Plot of all the single BSC contributions computed from the inertial sensor involved in this chamber. We are certain that the T240 is dominated by tilt effects below 80 mHz, and by sensor-noise at higher frequencies: the $\theta_p$ contribution is the $T240_{inj}$ signal below 80 mHz. We interpolated these two bands together to determine an effective input disturbance from the T240.}
\label{t240_inj}
\end{figure}
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@@ -314,43 +317,42 @@ Figure \ref{gs13_inj} shows the GS13 signal and its contributors.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/gs13inj.png}
\caption[HAM contributions]{Plot of all the single HAM contributions calculated for the inertial sensor involved in this chamber.}
\caption[HAM contributions]{Plot of all the single HAM contributions calculated for the inertial sensor involved in this chamber. Similarly to the previous case, the $\theta_p$ contribution is the $GS13_{inj}$ signal below 80 mHz.}
\label{gs13_inj}
\end{figure}
\subsection{Blending filters}
In order to compute the platform motion for the single chambers in isolation and, later, locked together via CPS, we need the low- and high- pass filters. Many possible blended filters have been found for different combinations of order of magnitudes and blending frequency: the plots in Fig. \ref{blend} show the velocity rms for every combination.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.45]{images/bscblend.png}
\includegraphics[scale=0.3]{images/hamblend.png}
\caption[Blending filters]{Plots of all possible costs built with different combinations of blending filters. The orders of magnitude are indicated by the low and high pass indices l and h of the binomial filter in \ref{binomial} and the are going between l =[1,4] and h = [1,4]. The plateau on both plots is given by the fact that the SC filter is dominating over those frequencies, which induces issues in the choice if the blending frequency. This makes a new way to evaluate blending filters in presence of the SC filter necessary.}
\label{blend}
\end{figure}
\noindent
The best combination has been found computing the orders and the blending frequency which give the minimum of the cost. The optimized blending filter has been then built using the best values of \textit{l} and \textit{h} orders and blending frequency. The cost is given by:
Fig. \ref{cost} shows the cost and its rms obtained with the best blending filters for BSC and HAM chambers.
\begin{figure}[H]
\centering
\includegraphics[scale=0.45]{images/bscblend.png}
\includegraphics[scale=0.3]{images/hamblend.png}
\caption[Blending filters]{Plots of all possible costs built with different combinations of blending filters. The orders of magnitude are indicated by the low and high pass indices l and h of the binomial filter in \ref{binomial} and the are going between l =[1,4] and h = [1,4]. The plateau on both plots is given by the fact that the SC filter is dominating over those frequencies: this means that the chosen cost function has too little power to discriminate between blends. This makes a new way to evaluate blending filters in presence of the SC filter necessary, in particular re-weighting the blends as functions of frequency may help the optimisation process.}
\label{blend}
\end{figure}
\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/bscrms.png}
\includegraphics[scale=0.3]{images/hamrms.png}
\caption[HAM and BSC velocity rms and their contributions]{HAM and BSC velocity rms and their contributions. For BSC, the best blending filter is given by l = 1, h = 4 at a blending frequency of fb = 0.13 Hz. For Ham, the best indeces are l = 1, h = 4 and fb = 1.14 Hz.}
\caption[HAM and BSC cost and their contributions]{HAM and BSC cost and their contributions from. For BSC, the best blending filter is given by l = 1, h = 4 at a blending frequency of fb = 0.13 Hz. For Ham, the best indeces are l = 1, h = 4 and fb = 1.14 Hz. Te green trace is the row, uncontrolled motion of the ISI, for reference.}
\label{cost}
\end{figure}
\subsection{Locking chambers}
With these elements, we can proceed with the analysis of the behaviour of the chambers when locked via CPS. We refer to HAM2 and HAM3 chambers, since in the previous sections we made the computations for them. We recall here that the equations we need are \ref{xp2}, \ref{d2}, \ref{xp3} and \ref{xp3xp2}, where $x_{p_{2}}$ is HAM2 platform motion, $d_{2}$ is the signal from HAM2 to send to HAM3 and $x_{p_{3}}$ is HAM3 motion when attached to HAM2 via CPS.
\noindent
What we need to know is which terms of these equations are coherent, in order to separate them from the incoherent ones, which will need to be summed in quadrature. Since we know that the ground motion is the same everywhere in the CS, the terms involving $x_g$ are coherent. Noises are instead, by definition, independent from each other.\\
The previous equations then become:
What we need to know is which terms of these equations are coherent, in order to separate them from the incoherent ones, which will need to be summed in quadrature. We believe that the ground translation at low-frequencies is the same everywhere in the CS, and we already estimate the tilt separately, so the terms involving $x_g$ can be considered coherent. Noises are instead, by definition, independent from each other. The previous equations then become:
The plot in Fig. \ref{diffham} shows the differential motion of HAM2 and HAM3 in isolation, and Fig. \ref{cpsdiff} shows motions of the chambers when locked to each other and their differential motion. The improvement of the differential motion is evident below 0.1 Hz, but it is not convenient above this frequency: further studies of the blending filters involved could help to find a compromise.
\begin{figure}[h!]
\centering
\includegraphics[scale=0.3]{images/diffham.png}
\caption[HAM chambers in isolation]{Ham chambers in isolation: motion of HAM2 as a reference. The purple trace is the differential motion between HAM2 and HAM3 that we are interested in reducing below $\sim$ 0.1 Hz.}
The plot in Fig. \ref{cpsdiff} shows the differential motion of HAM2 and HAM3 in isolation and the motions when the chambers are locked to each other. The improvement of the differential motion is evident below 0.1 Hz, but it is not efficient above this frequency: further studies of the blending filters involved and a re-weight of the cost in a different part of the spectrum could help to find a compromise.
%\begin{figure}[h!]
%\centering
%\includegraphics[scale=0.3]{images/diffham.png}
%\caption[HAM chambers in isolation]{Ham chambers in isolation: motion of HAM2 as a reference. The purple trace is the differential motion between HAM2 and HAM3 that we are interested in reducing below $\sim$ 0.1 Hz.}
%\label{diffham}
%\end{figure}
\begin{figure}[h!]
\centering
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@@ -472,8 +482,8 @@ This is an interesting result that shows that with the implementation of the cor
With this in mind, a positive consequence of this effect might be the improvement of the LSC signals from LIGO cavities. Among them, DARM is particularly important, because it represents the gravitational wave signal. It might be convenient to make the optics of the LSC cavities, lying on the platforms and subjected to the ISI motion, be controlled by the ISI itself. This ideas has been developed and tested at LHO and is exposed in the following section.
\subsection{LSC offloading}
We saw that the cavities and the optical signals in LIGO are affected by the ISI motion, simply because they lie on them. Given the work done with the CPSs to suppress the ISI motion, we should see an improvement on LSC signals. This is not immediate, though, nor trivial, because the optics are just set on the optical bench, without any communication with the ISI. Despite there is a sort of benefit as testified by Fig. \ref{darmtest}, the motion of the optics on the chambers due to other factors than seismic noise is not seen by the platforms: if we could connect this motion to the platform via software, this would make the optics and the platform more dependent on each other. This means that we can control the stabilization of the cavity lengths also with the ISIs.\\
What we expect is a faster reach of locking and a longer state of lock of the interferometer during observing runs.\\
We saw that the cavities and the optical signals in LIGO are affected by the ISI motion, simply because they lie on them. Given the work done with the CPSs to suppress the ISI motion, we should see an improvement on LSC signals. This is not immediate, though, nor trivial, because the optics are just set on the optical bench, without any communication with the ISI, and there is no active control between the ISI and these optics. Despite there is a sort of benefit as testified by Fig. \ref{darmtest}, the motion of the optics on the chambers due to other factors than seismic noise is not seen by the platforms: if we could connect this motion to the platform via software, this would make the optics and the platform more dependent on each other. This means that we can control the stabilization of the cavity lengths also with the ISIs.\\
What we expect is a faster reach of locking and a longer state of lock of the interferometer during observing runs. Another advantage would lie in a reduction of the forces already used to stabilize the cavities and in less tilt motion.\\
\noindent
This work has been performed on LIGO Hanford in October and November 2019, during the commissioning break between O3a and O3b observing runs. The reason of this choice is that we needed the interferometer to \textit{not} be observing, since we were going to modify some software structure of the instrument.\\
\noindent
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@@ -490,7 +500,7 @@ Through CPSs locking, we reduced the differential motion of HAM2 and HAM3 chambe
The same work is foreseen to be done for the other cavities: the very short period of time available during the commissioning break allowed us to modify only the control loop for PRCL. Moreover, during the commissioning break, time is also used to work on the chambers, profiting of the out-of-lock mode. This means that, for every attempt of software modification, a locking trial was needed, to see if the new configuration of the instrument was giving better performances and, also, if it was affecting negatively other sides of the instrument. To try to lock LIGO, we needed people not to work besides the chambers. This was a huge and collaborative work, which involved many people on site, and their time. Despite these challenges, the results obtained are encouraging and validated the analysis of feasibility exposed.
\paragraph{The Power Recycling Cavity Length (PRCL)}
We need to connect the ISI to the cavity and to do it we need to know how the PR cavity is going to communicate with the ISI (refer to Chapter \ref{LIGO} for details on the PR cavity). The block diagram in Fig. \ref{prcl} illustrates the simplified concept of the PR cavity connected to the ISIs of the block of HAM2 and HAM3 chambers.\\
We need to connect the ISI to the cavity and to do it we need to know how the PR cavity is going to communicate with the ISI (refer to Chapter \ref{LIGO} for details on the PR cavity). The block diagram in Fig. \ref{prcl} illustrates the simplified concept of the PR cavity connected to the ISIs of the block of HAM2 and HAM3 chambers\footnote{Some insights about the shape of the transfer function of the suspensions are in Appendix C.}.\\
The work done in this case is similar to the one done for the HAM chambers, except from the fact that a new filter needs now to be built in order to control how the ISI affect the motion of the PRC optics.
@@ -329,6 +331,10 @@ Beginning of Gravitational Wave Astronomy}
\bibitem{cavaglia} M. Cavaglia, \textit{Logo slide with institution names}, DCC G1300394
\bibitem{duty1} Buikema A. et al., \textit{Sensitivity and Performance of the Advanced LIGO Detectors in the Third Observing Run}, https://dcc.ligo.org/LIGO-P2000122
\bibitem{duty2} Davis D. et al., \textit{LIGO Detector Characterization in the Second and Third Observing Runs}, https://dcc.ligo.org/LIGO-P2000495
