@@ -46,10 +46,45 @@ This equation is particularly useful if we want to know information about the ra
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{Redshift}
When dealing with cosmological objects, we need to take into account the contribution of the redshift: 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 $f_{em}$ by:
\begin{equation}
\centering
f_{obs} = f_{em}/(1+z).
\end{equation}
\noindent
The implication of this effect lies in a factor (1+z) multiplied to the masses involved.\\
An important consequence is that if the instrument could be able to detect in a broader range of lower frequencies, it could be possible to identify objects located at higher redshifts, i.e. more ancient, or apparent high masses increased by the cosmological distance \cite{yu}. Examples of these objects are Intermediate Mass Black Holes (IMBH) or stellar-mass BHs, whose nature and physics are still unknown.
\subsection{Multi-messenger astronomy}
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 to localize and study the source under several other points of view.\\
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 if the gravitational-wave detector is able to provide a location 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.
\subsection{Duty cycle of the detector}
The ground-based instruments are currently tuned to detect inspiraling binaries: the duty cycle of the detector is then very important for assessing its sensitivity. This quantity represents the number of cycles spent by the instrument in the frequency bandwidth of interest. As we will see in Chapter \ref{CPSdiff}, this depends on how much time the detector can maintain resonance, i.e. on its stability, and it is given by \cite{mag}:
\begin{equation}
\centering
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.
\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 the author 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.\\
The strategy investigated is based on noise subtraction: 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.\\
\section{The goals of the collaboration}
\noindent
The importance of the improvement of seismic motion 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.
@@ -190,13 +191,17 @@ There are three appendices useful to make the work more complete: appendix A ill
\bibitem{first} B. P. Abbott, \textit{Observation of Gravitational Waves from a Binary Black Hole Merger}, Phys. Rev. Lett. 116, 061102, 2016
\bibitem{yu} H. Yu et al, \textit{Prospects for Detecting Gravitational Waves at 5 Hz with Ground-Based Detectors}, Phys. Rev. Lett. 120, 141102, 2018
\bibitem{bird} S. Bird et al., \textit{Did LIGO detect dark matter?}, Phys. Rev. Lett. 116, 201301, 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
\bibitem{yu} H. Yu et al, \textit{Prospects for Detecting Gravitational Waves at 5 Hz with Ground-Based Detectors}, Phys. Rev. Lett. 120, 141102, 2018
\bibitem{lantztalk} B. Lantz, \textit{System-wide upgrades to improve the Seismic Isolation and control of detectors beyond A+}, talk, 2020
\bibitem{goulding} A. D. Goulding et al, \textit{Discovery of a Close-separation Binary Quasar at the Heart of a z$\sim$0.2 Merging Galaxy and Its Implications for Low-frequency Gravitational Waves}, The Astrophysical Journal Letters, 879:L21 (7pp), 2019
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@@ -274,8 +279,6 @@ Beginning of Gravitational Wave Astronomy}
\bibitem{technote3} C. Di Fronzo et al., \textit{Reducing differential motion of Advanced LIGO seismic platforms to improve interferometer control signals:analysis of feasibility}, technical note, 2020, DCC T2000365-v2
\bibitem{lantztalk} B. Lantz, \textit{System-wide upgrades to improve the Seismic Isolation and control of detectors beyond A+}, talk, 2020
\bibitem{jenne} J. Driggers, \textit{Noise Cancellation for Gravitational Wave Detectors}, PhD thesis, 2016
\bibitem{llo} A. Pele' et al., \textit{ECR: Differential CPS and cavity offload}, proposal, 2019, DCC E1900330-v1
