In this chapter I will briefly introduce the key concept that established the goals of the work exposed in this thesis and moved all its steps. My research has been devoted to the enhancement of the instruments currently in use to detect gravitational waves, which is one of the most advanced fields of astrophysics research of our time.\\
A detailed structure of the thesis is then following.
In this chapter I will briefly introduce the key concepts that establish the goals of the work presented in this thesis and moved all its steps. My research has been devoted to the enhancement of the instruments currently used to detect gravitational waves, which is one of the most advanced fields of astrophysics research of our time.\\
A detailed structure of the thesis then follows.
\section{Gravitational waves and their detection}
Gravitational waves are an astrophysical event that takes place when massive objects move and deform the fabric of the spacetime \cite{mag}\footnote{An in-depth source about how gravitational waves have been computed and their features is \cite{mag}.}. They have been theorized by Einstein in 1915 and discovered a hundred years later by a joint collaboration of two detectors \cite{nar}\cite{first}, which was worth of the Nobel Prize for Physics in 2017 \footnote{See Appendix C for some information about the first detection of gravitational waves.}.\\
Gravitational waves are an astrophysical event that takes place when massive objects move and deform the fabric of spacetime \footnote{An in-depth source about how gravitational waves have been computed and their features is \cite{mag}.}. They have been theorized by Albert Einstein in 1915 and discovered a hundred years later by a joint collaboration of two detectors \cite{nar}\cite{first}, which was worthy of the Nobel Prize for Physics in 2017 \footnote{See Appendix C for some information about the first detection of gravitational waves.}.\\
\noindent
The effect of the gravitational waves when they pass through an object is to produce a deformation on the physical lengths (L). This effect is very small ($\Delta$L/L $\sim$ 10$^{-21}$): masses able to deform the fabric of the spacetime and generate gravitational waves are of the order of more than the solar mass $M_{\odot}$, so they need to be looked for in the Universe.\\
The effect of gravitational waves when they pass through an object is to produce a deformation of the physical lengths (L). This effect is very small ($\Delta$L/L $\sim$ 10$^{-21}$): masses able to deform the fabric of spacetime and generate gravitational waves are of the order of more than the solar mass $M_{\odot}$, so such massive objects need to be looked for in the Universe.\\
\subsection{A challenging detection}
Detecting gravitational waves is particularly hard, because the effect is very small, and the sensitivity required for an instrument to see it must be suitable.\\
Detecting gravitational waves is particularly challenging, because the effect is very small, and the sensitivity required for an instrument to see it must be suitably high.\\
The challenging goal of detecting gravitational waves opened a research field dedicated to the development of new technologies, that could help to obtain the sensitivity necessary for the detection to happen.\\
This research is important, because detecting gravitational waves means looking at the sources which produced them. There is still a gap in the knowledge of many astrophysical objects, such as Black Holes (BH), Neutron Stars (NS), Supernova events: this new-born branch of astrophysics will help to fill the gap and increase our knowledge of the Universe.\\
This research is important, because detecting gravitational waves provides information on the sources which produced them. There is still a gap in the knowledge of many astrophysical objects, such as Black Holes (BH), Neutron Stars (NS) and Supernova events: this new-born branch of astrophysics will help to fill the gap and increase our knowledge of the Universe.\\
\noindent
The detectors currently in use are sensitive to events from sources emitting at frequencies above $\sim$ 10 Hz, but there is still a broad range of frequencies to which the detectors are blind. Looking at different frequencies of emission means looking at different objects emitting gravitational waves. This would broaden the catalogue of observed objects and the chances to better understand their nature.\\
\noindent
The work carried on during my PhD studies and exposed in this thesis has been dedicated to the improvement of the sensitivity of the detectors at frequencies below 10 Hz, by the development of new ideas and technologies to reduce noise sources affecting the low-frequency bandwidth, in particular the seismic motion.
The work carried on during my PhD studies and presented in this thesis has been dedicated to the improvement of the sensitivity of the detectors at frequencies below 10 Hz, by the development of new ideas and technologies to reduce noise sources affecting the low-frequency bandwidth, in particular the seismic motion.
\section{Structure of this thesis}
This thesis presents a study for the enhancement of the detectors for gravitational waves. It is 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 and illustrate some features of the detectors useful 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.\\
This thesis presents a study for the enhancement of the detectors for gravitational waves. It is divided into two parts: Part 1 introduces the context of the work done and frames the study into the specific field of the low frequency window and illustrates some features of the detectors useful to fully understand the work done 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.\\
\noindent
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.\\
Chapter 2. In this chapter we will see that there are some gravitational-wave sources emitting at lower frequency to 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.\\
\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.\\
Chapter 3. This chapter describes briefly how an interferometric detector for gravitational waves works. In particular, the detector LIGO, with which I collaborated, is illustrated. Specific details of the instruments to which the author has contributed are explained and referred to throughout the experimental work in 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.\\
Chapter 4. This chapter contains the first experimental work performed in the first year of my PhD study: an optical lever for the reduction of tilt motion has been designed and built at UoB, and then tested at the AEI. The details of the experiment and the results are explained in detail.\\
\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.\\
Chapter 5. This chapter is focused entirely on the work done during my collaboration at LIGO Hanford 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 include original computations and tests at the 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.
Chapter 6. During the last year of my PhD studies, I contributed to the development of a new device for seismic control; in particular, I focused 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 detail.
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 presented in this thesis focuses 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.
\section{Sources of gravitational waves}
Fig. \ref{spec} summarizes the possible objects that can be gravitational waves sources, their frequency of 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 of emission and what kind of instrument can detect them. The terrestrial interferometric detectors are the most involved at present, but the efforts of the scientific community are directed towards the development of new detectors, both ground- and space-based, in order to widen the frequency window of observation.
\begin{figure}[h!]
\centering
...
...
@@ -18,27 +18,27 @@ The best modelled sources are binary systems, orbiting each other around a commo
\begin{figure}[h!]
\centering
\includegraphics[scale=0.8]{images/bin.png}
\caption[Phases of gravitational waves emission by a binary system]{The three phases of a Black Hole (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 Black Hole (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 at 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 and test of General Relativity \cite{wei}\cite{mag}. The interest of the scientific community for these events and their detectors is therefore linked to the possibility of new astrophysical discoveries.\\
Currently, the ground-based observatories are tuned to detect binary systems sources: the interferometers are the instruments that have been able to detect gravitational waves from these kind of sources.\\
Gravitational waves from binary systems can provide information about the equation of state of Neutron stars, masses and spin of Black Holes and allow for test of General Relativity \cite{wei}\cite{mag}. The interest of the scientific community for these events and their detectors is therefore linked to the possibility of new astrophysical discoveries.\\
Currently, the ground-based observatories are tuned to detect emission from binary systems: the interferometers are the only instruments that have been able to detect gravitational waves from these kind of sources.\\
\noindent
The first detection of gravitational waves happened on the 14th September 2015 and confirmed the Theory of the 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 first detection of gravitational waves happened on the 14th September 2015 and confirmed the Theory of 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}.\\
\noindent
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}}.
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-wave 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 ground-based detectors involved in the search of gravitational waves 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.\\
As we will see in the next chapter, the ground-based detectors involved in the search of gravitational waves 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 later see 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 whose physical structure and astrophysical features are still unknown.\\
\noindent
This is the effort towards which a huge part of the scientific collaboration is involved.
This is the end towards which a significant part of the scientific collaboration is directed.
\subsection{Frequencies of emission}
The emitted frequency from a source of gravitational waves depends on the masses and the orbital frequency involved\footnote{A detailed derivation of the gravitational-wave equation and how the frequencies of emission depend on the features of the sources can be found in \cite{mag}.} and for mergers of binary systems, the frequency of a gravitational wave is twice the orbital frequency of its source \cite{mag}. Therefore, it can be used to know the relation between the masses and the time to coalescence, i.e. the time when the to objects merge \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:\\
The emitted frequency from a source of gravitational waves depends on the masses and the orbital frequency involved\footnote{A detailed derivation of the gravitational-wave equation and how the frequencies of emission depend on the features of the sources can be found in \cite{mag}.} and for mergers of binary systems, the frequency of a gravitational wave is twice the orbital frequency of its source \cite{mag}. Therefore, it can be used to determine the relation between the masses and the time to coalescence, i.e. the time when the two objects merge \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
...
...
@@ -48,11 +48,11 @@ The emitted frequency from a source of gravitational waves depends on the masses
\noindent
where $M_c$ is the combination of the two involved masses $m_1$ and $m_2$, defined as \textit{chirp mass}$M_c$ = ($m_1$$\cdot$$m_2$)$^{3/5}$/($m_1$ + $m_2$)$^{1/5}$.\\
This equation is particularly useful if we want to know information about the radiation emitted by 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 are essential for several reasons, going from efficiency of the detector in detecting different of sources to Multimessenger astronomy, in which timing is important to assure a correct localization of the source \cite{branchesi}.\\
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 hence says that the larger is the time to coalescence, the smaller are 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.
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. Hence the equation says that the larger the time to coalescence is, the smaller the masses involved are\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 entirely in the domain of the space-based detectors. Opening this frequency window would allow the ground-based detectors to access to a frequency bandwidth which has still not been investigated and would allow the detection from sources whose physics is still unknown.
\subsection{Redshifted frequencies}
When dealing with cosmological objects, we need to take into account the contribution of the redshift z: in the case of gravitational waves, the redshift acts on the observed frequency. In a cosmological context, the time-scale is redshifted, and so it is the frequency observed $f_{obs}$ with respect to the emitted one $f_{gw}$ by \cite{mag}\cite{nar}:
When dealing with cosmological objects, we need to take into account the contribution of the redshift z: in the case of gravitational waves, the redshift acts on the observed frequency. In a cosmological context, the time-scale is redshifted, and so is the frequency observed $f_{obs}$ with respect to the emitted one $f_{gw}$ by \cite{mag}\cite{nar}:
\begin{equation}
\centering
...
...
@@ -67,7 +67,7 @@ An important consequence is that if the instrument could be able to detect in a
Multi-messenger astronomy is a branch of astronomy born with the discovery of the first gravitational wave. It has been seen that the signal of a gravitational wave can be followed up by observatories operating in other frequency bands (say, the electromagnetic bandwidth), to localize and study the source under several other points of view \footnote{A general overview about multi-messenger astronomy can be found in \cite{branchesi}. An interesting paper about a multi-messenger GW-source detection and its implications is \cite{multi}.}.\\
It is then important that the communication between these observatories is the best of the efficiency: the joint-collaboration is determinant to provide a precise localization of the source in the sky and a complete set of data to study the object in all its details \cite{bird}.\\
The main challenge when an electromagnetic observatory tries to follow up a signal from a gravitational-wave detector is the time spent in the communication of the signal, and in the adjustments of the instrument towards the right position in the sky. This can be achieved faster and precisely if the gravitational-wave detector is able to provide coordinates quickly and accurately.\\
A significant contribution to this goal could be added by the opening of the lower frequency window of ground-based gravitational-wave detectors. As see in the previous section, the time to coalescence scales with frequency as $f^{-8/3}$. Lowering the frequency of observation would increase the time of observation before the coalescence. This would give more time for the electromagnetic detectors to adjust the position once received the coordinates. Moreover, the more the two inspirilling objects are far from coalescence, the more are they far from each other, increasing the volume of observation in the sky.
A significant contribution to this goal could be added by the opening of the lower frequency window of ground-based gravitational-wave detectors. As seen in the previous section, the time to coalescence scales with frequency as $f^{-8/3}$. Lowering the frequency of observation would increase the time of observation before the coalescence. This would give more time for the electromagnetic detectors to adjust the position once they have received the coordinates. Moreover, the further the two inspiraling objects are from coalescence, the further they are from each other, thus increasing the volume of observation in the sky.
\subsection{Duty cycle of the detector}
...
...
@@ -79,17 +79,17 @@ N_c = \int f_{gw}(t) dt.
\end{equation}
\noindent
This quantity defines for how many cycles (and hence how much time) the detector can follow the evolution of a signal in a given frequency band. The ground-based detectors are sensitive to operate for thousands of cycles \footnote{Interesting examples on typical duty cycles for ground- and space-based detectors can be found in \cite{mag}.}. Lowering the frequency band and increasing the sensitivity would increase the number of cycles, allowing to follow a signal for more time \cite{mag}. The consequent advantage is more precise waveform predictions based on these observations, besides to the detection of objects still unknown.
This quantity defines for how many cycles (and hence how much time) the detector can follow the evolution of a signal in a given frequency band. The ground-based detectors are sensitive to operate for thousands of cycles \footnote{Interesting examples on typical duty cycles for ground- and space-based detectors can be found in \cite{mag}.}. Lowering the frequency band and increasing the sensitivity would increase the number of cycles, allowing the following of a signal for longer \cite{mag}. The consequent advantage is more precise waveform predictions based on these observations, in addition to the detection of objects still unknown.
\section{The goals of the gravitational-wave collaboration}
The efforts of the scientific collaboration, towards the opening of the low frequency window, are devoted to the development of new technologies for active control of the noise sources, responsible of the lack of sensitivity below 30 Hz \cite{lf1}\cite{lf2}\cite{lf3}. This has been the target focussed on during the workshops dedicated to the low frequency band, which I attended between 2018 and 2021.\\
The efforts of the scientific collaboration, towards the opening of the low frequency window, are devoted to the development of new technologies for active control of the noise sources, responsible for the lack of sensitivity below 30 Hz \cite{lf1}\cite{lf2}\cite{lf3}. This has been the target of focus during the workshops dedicated to the low frequency band, which I attended between 2018 and 2021.\\
The goal of these meetings is to update the state-of-the-art of the topic and work together on new ideas and possible new solutions.\\
We will see in the next chapters that one of the most important noise sources, affecting the detectors in the low frequency range, is the seismic noise. The strategy investigated is based on the subtraction of this noise source: in particular, modelling, controls and reduction of the noise of seismic platforms are currently under exam for increasing the sensitivity below 30 Hz. Besides this, the study for the development of lower-noise sensors is also an up-to-date topic of discussion.\\
We will see in the next chapters that one of the most important noise sources, affecting the detectors in the low frequency range, is the seismic noise. The strategy investigated is based on the subtraction of this noise source: in particular, modelling, controls and reduction of the noise of seismic platforms are currently under examination for increasing the sensitivity below 30 Hz. Besides this, the study for the development of lower-noise sensors is also an up-to-date topic of discussion.\\
\noindent
The importance of the opening of the lower frequency window has been widely outlined and highlighted \cite{lantztalk}: the final goal is to reduce the noise coupling into the gravitational-wave signal, and an important contribution could be provided by the efforts of the people working on the seismic noise suppression. \\
\noindent
It is in this frame that the work exposed in this thesis finds place. The experiments carried on cover both the studies for noise suppression of seismic platforms on gravitational-wave detectors, and the development of new devices for sensing and reducing seismic motion.
It is in this frame that the work presented in this thesis takes place. The experiments carried out cover both the studies for noise suppression of seismic platforms on gravitational-wave detectors, and the development of new devices for sensing and reducing seismic motion.
