\caption[Mounting the wires and their support]Mounting the wires for the test mass suspension on their support. Right: Jeff and I while installing the wire support into the suspension cage.}
\caption[Mounting the wires and their support]{Mounting the wires for the test mass suspension on their support. Right: Jeff and I while installing the wire support into the suspension cage.}
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.\\
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.\\
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'}.
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'}.
\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.}
\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.}
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 debated during dedicated workshops which the author of this thesis attended since 2018.
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 debated during dedicated workshops which the author of this thesis attended since 2018.
\subsection{Sources of gravitational waves}
\section{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.
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!]
\begin{figure}[h!]
...
@@ -17,7 +17,7 @@ The best modelled sources are binary systems, typically Neutron Stars (NS), Whit
...
@@ -17,7 +17,7 @@ The best modelled sources are binary systems, typically Neutron Stars (NS), Whit
\begin{figure}[h!]
\begin{figure}[h!]
\centering
\centering
\includegraphics[scale=1]{images/bin.png}
\includegraphics[scale=0.8]{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.}
\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}
\label{binary}
\end{figure}
\end{figure}
...
@@ -27,7 +27,29 @@ Gravitational waves from binary systems can provide several information about th
...
@@ -27,7 +27,29 @@ Gravitational waves from binary systems can provide several information about th
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.\\
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
\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.
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 \footnote{The working principles of the interferometers and details about the US instrument are exposed in Chapter \ref{LIGO}}.
\section{Opening the low frequency window}
As we will see in the next chapter, the grund-based detectors involved in the search of gravitational waves are cover a wide range of frequencies, but they are affected by some noises which make them unable to detect waves from sources emitting below 30 Hz. We will see later the nature of these noises. The reason why it is important to open the lower frequency window is that it can give access to the detection of gravitational waves emitted by sources which physical structure and astrophysical features are still unknown.\\
This is the effort towards which a huge part of the scientific collaboration is involved.
\subsection{Frequencies of emission}
We saw in the previous chapter that the emitted amplitude depends on the masses and the orbital frequency involved: the emitted frequency is also linked to these parameters. For mergers of binary systems, the frequency of a gravitational wave is twice the orbital frequency of its source \cite{mag} and hence it can be used to know the relation between the masses and the time to coalescence, i.e. the time to the merger \footnote{A simple example based on point-like masses in circular orbits is explained in details in \cite{mag}.}. For masses in circular orbits, this is given by:
\begin{equation}
\centering
\tau\simeq 2.18 s \left(\dfrac{1.21 M_{\odot}}{M_c}\right)^{5/3}\left(\dfrac{100 Hz}{f_{gw}}\right)^{8/3}.
\end{equation}
\noindent
This equation is particularly useful if we want to know information about the radiation emitted my a certain mass, at a certain frequency at a certain time before the merger. Predictions about this time and the frequency where it is possible to detect the radiation is essential for several reasons, from efficiency of the detector in terms of variety of sources to Multimessenger astronomy, in which timing is important to assure a correct localization of the source CITA MULTI.\\
In our case of interest, if we apply the lowest range of frequency available by ground-based detectors ($\sim$ 10 Hz in order of magnitude and consider M$_c$ = 1.21 M$_{\odot}$, it is possible to observe the radiation emitted at $\tau$ = 17 minutes to coalescence. This equation says that the larger is the time to coalescence, the smaller is the masses involved \footnote{A useful exercise to prove this is by applying the Kepler's law for different emitting frequencies and masses. Some interesting examples are given in \cite{mag}.}.\\
Recalling Fig. \ref{spec}, the range of the frequencies of emission below 10 Hz lies almost all in the space-based detectors dominion. Opening this frequency window would allow the ground-based detectors to access to a frequency bandwidth which is still not investigated and would allow the detection from sources whose physics is still unknown.
\subsection{Duty cycle of the detector}
\section{The goals of the collaboration}
\section{Hidden GW sources}
PER QUESTA SEZIONE, FARE RIFERIMENTO A TUTTI I VARI WORKSHOP.
\title{Innovative perspectives for seismic isolation of gravitational-wave detectors}
\title{Innovative perspectives for seismic isolation of gravitational-wave detectors}
\author{Myself}
\author{Chiara Di Fronzo}
\date{}
\date{}
\titlehead{A Thesis submitted for the degree of Philosophiae Doctor}
\titlehead{A Thesis submitted for the degree of Philosophiae Doctor}
\publishers{School of Something\\University of Somewhere}
\publishers{School of Physics and Astronomy\\Gravitational Waves Department\\ University of Birmingham}
\begin{document}
\begin{document}
\maketitle
\maketitle
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@@ -28,25 +28,41 @@
...
@@ -28,25 +28,41 @@
\frontmatter
\frontmatter
\chapter{Statement of originality}
\chapter{Statement of originality}
Here I will certify that the work done is original from myself.
I confirm that the work presented in this thesis is original and has been entirely carried out by the author, started and completed at the University of Birmingham. The work done in collaboration with other scientific groups and/or abroad has been suitably highlighted.
\chapter{Abstract}
\begin{flushright}
Chiara Di Fronzo
\end{flushright}
A brief summary of the project goes here, with main results.
\chapter{Abstract}
%dedica va qui
The discovery of gravitational waves opened a new way to look at the Universe and offered new opportunities to shed light on the still unknown aspects of physical sciences. The work presented in this thesis wants to give a contribution to the development of this new type of research: the author chose to focus on the improvement of the instruments able to detect the gravitational waves. This field is important to make the detectors more sensitive, in order to see more gravitational-wave sources and help to complete the mosaic of the astrophysical science. In particular, the detectors currently in use are interferometers, which are especially blind in a range of frequency below 30 Hz: this affects the chance to detect sources emitting in this frequency band.\\
This lack of sensitivity is mainly due to seismic motion, and the work exposed in this thesis focussed on new techniques to lower this noise source and allow the instruments to be sensitive below 30 Hz.\\
During the studies, the development and test of devices able to to potentially reduce the seismic motion have been performed, such as optical levers for tilt motion reduction and laser stabilization for low frequency readout; a new concept of the seismic system on one of the interferometers (LIGO) has also been proposed.\\
The results are promising to provide suppression of the seismic motion in the bandwidth of interest and show that it is possible for a ground-based instrument to be seismically more stable and able to detect gravitational waves where it is now forbidden.
\clearpage
\chapter*{}
\begin{flushright}
\thispagestyle{empty}
\vspace*{1cm}
\textit{Ai miei genitori e a mia sorella.}
\vspace*{\fill}
\end{flushright}
\clearpage
\chapter{Acknowledgements}
\chapter{Acknowledgements}
Here I need to acknowledge for any funding (UoB, RAS, IOP, Caltech).
%I am particularly grateful to Dr. Conor Mow-Lowry and the University of Birmingham for giving me the opportunity and the funding to join the Gravitational waves group and contribute to the development of exciting science. This was also possible thanks to the support of the Royal Astronomical Society and the Institute of Physics which allowed me to take part to conferences and workshops abroad.\\
%ricordati anche di ringraziare per l'estensione
%During my stay at LIGO Hanford site, I need to warmly thank Caltech for providing me accommodation and travel: this experience was very important for my studies.\\
%The completion of the work presented in this thesis would not have been possible without the action of the University of Birmingham, which accepted my application for an extension of my studies: the lockdown in 2020 stopped my lab work and the support of the UoB has been crucial to accomplish my project in the best way.\\
\tableofcontents
\tableofcontents
\listoffigures
\listoffigures
\listoftables
\listoftables
\chapter{Notations}
\chapter{Notations}
Useful notations, constants and formulas go here.\\
An introduction to frame the work and structure of the thesis go here.\\
STRUCTURE OF THESIS [DRAFT]\\
\chapter*{Structure of this thesis}
PART I: Gravitational astrophysics\\
This thesis presents a study for the enhancement of the detectors for gravitational waves. It is then divided in two parts: Part 1 introduces the context of the work done and frames the study into the specific field of the low frequency window; this part is crucial to fully embrace the study performed in the laboratories. Part 2 is entirely focussed on the work done during the years between 2017 and 2021, covering the experience at LIGO Hanford and at the Albert Einstein Institute. This part includes the details of the experiments performed and their results.\\
Chapter 1: Gravitational waves and sources\\
Chapter 2: low frequency window and multimessenger astronomy\\
Chapter 3: Interferometry and Advanced LIGO\\
PART II: Lowering seismic noise\\
\noindent
Chapter 4: Inertial sensors and optical levers\\
Chapter 1. This chapter briefly introduces the gravitational waves as the astrophysical phenomenon proposed by Albert Einstein in 1915 and discovered in 2017.\\
Chapter 5: Seismic isolation at LHO\\
Chapter 6: Laser stabilization for 6D seismic isolation\\
Appendix A: Assembling suspension chains for A+ at LHO\\
\noindent
Appendix B: control loops\\
Chapter 2. In this chapter we will see that there are some gravitational-wave sources emitting at lower frequency for which the current detectors are blind: it is in this frame that the experiments proposed in this thesis have been done. The final and ambitious goal is to improve the sensitivity of the detectors at lower frequencies.\\
Appendix C: first GW detection
\mainmatter
\noindent
Chapter 3. This chapter describes briefly how an interferometric detector for gravitational waves works. In particular, the detector LIGO for which this work collaborated is illustrated. Specific details of the instruments on which the author has contributed are explained and referred to throughout the experimental work of the following chapters.\\
\noindent
Chapter 4. In this chapter there is the first experimental study performed in the first year of my PhD study: an optical lever for the reduction of tilt motion has been design and build at UoB, and then tested at the AEI. The details of the experiment and the results are explained in details.\\
\noindent
Chapter 5. This chapter is focussed entirely on the work done during my collaboration at LIGO Hanford site in 2019: during the O3a and O3b runs I had the chance to contribute to the improvement of the detectors by studying a new configuration of the seismic system in order to make the instrument more stable and allow a longer observing time. The details of this study includes original computations and tests on LIGO sites.\\
\noindent
Chapter 6. During the last year of the PhD studies, I contributed to the development of a new device for seismic control; in particular, I focussed on the stabilization in frequency of the laser source of the device, making use of new technology and advanced techniques. The experiment has been fully carried out at UoB between September 2020 and September 2021 and it is described in details.\\
\noindent
There are three appendices useful to make the work more complete: appendix A illustrates the work done at LIGO Hanford laboratory in building the suspensions for the A+ upgrade; appendix B gives some useful directions about control loops and block diagrams; appendix C aims to celebrate the first gravitational wave discovery.
\part{Gravitational-wave frontiers}
\part{Gravitational-wave frontiers}
\include{GW}
\include{GW}
...
@@ -168,6 +190,13 @@ Appendix C: first GW detection
...
@@ -168,6 +190,13 @@ Appendix C: first GW detection
\bibitem{first} B. P. Abbott, \textit{Observation of Gravitational Waves from a Binary Black Hole Merger}, Phys. Rev. Lett. 116, 061102, 2016
\bibitem{first} B. P. Abbott, \textit{Observation of Gravitational Waves from a Binary Black Hole Merger}, Phys. Rev. Lett. 116, 061102, 2016
\bibitem{lf1} P. Fritschel, B. Lantz, \textit{Report on the workshop on Low Frequency Noise in LIGO, April 6 -7, 2021}, Low Frequency Workshop, April 2021 DCC L2100055
\bibitem{lf2} ERC Workshop, Frebruary 2021
\bibitem{lf3} Low Frequency Workshop, University of Birmingham, August 2018
%chapt 3
%chapt 3
\bibitem{ligo} Advanced LIGO Systems Group, \textit{Advanced LIGO Systems Design}, DCC document T010075-v3, 2017
\bibitem{ligo} Advanced LIGO Systems Group, \textit{Advanced LIGO Systems Design}, DCC document T010075-v3, 2017
...
@@ -275,6 +304,9 @@ Beginning of Gravitational Wave Astronomy}
...
@@ -275,6 +304,9 @@ Beginning of Gravitational Wave Astronomy}
