Gravitational waves (GWs) are ripples in the spacetime emitted by sources such as black holes (BHs) and neutron stars (NSs). The detection of GW by the Laser Interferometer Gravitational Observatory (LIGO) not only has proven the existence of these waves but have also opened the era of gravitational wave astronomy. In fact, many astrophysical properties of the emitting sources can be extracted from the detected signals, such as the mass and the spin of the system, moreover constraints on the graviton mass can be set and more generally, studies of fundamental physics in strongly curved space-time can be done. All these kinds of study have been done on the three GW detections from binary BHs merger that the LIGO and Virgo Collaborations have achieved since September 2015, day of the first detection. Many other types of GWs sources are expected to exist. Among these, there are continuous gravitational waves signals (CWs), characterized by a semi-periodic waveform, with duration much longer than the usual span of experimental Runs (~1 yr). This type of signals have the unique properties to be self-coherent, allowing in the case that the phase evolution is known, the application of matched filter techniques in order to detect them and estimate their physical parameters with very high precision. CW signals cover a wide region in GW astronomy. In ground based interferometers CWs are expected from asymmetric spinning NSs while in the future spacecraft GW detectors (e.g. LISA), we expect to find these signals emitted by a large population of coalescing BHs. Matched filter techniques are highly computational expensive and the analysis is not possible if the source parameters are not accurately known, due to the presence of too many templates. For these reasons efficient algorithms in high dimensional spaces, such as machine learning and Bayesian Markov chains, are often employed. The aim of this project is set the basics to develop a new pipeline for CW detection.
Data analysis detection pipelines based on MCMC already exist within the GW collaborations LIGO and Virgo in which I am an active member. As stressed before, CW searches in ground-based interferometer consist in looking for CW from spinning NSs. Many pipelines exist devoted for this task but only few are based on MCMC algorithms. Some example of MCMC implementation for CW from NSs in LIGO/VIRGO data are given in [S. Suvorova, PRD (2016), 93, 123009] and in their latest application for a CW search over a large parameter space for the astrophysical source Sco-X1 [LIGO and Virgo Collaboration, arXiv:1704.03719] . These methods not only have the features to be able to extract a possible signal in a high and dense dimensional space, but can also be naturally extended for searching over different models of CWs emission. This possibility was explored in a recent work [M. Isi et al, arXiv:1703.07530] where CW where used to constraint the presence of non-GR polarizations in a possible GW from NSs. As it is possible to see in the last two references, no machine learning method for the analysis of ground-based interferometer data are employed to speed-up the MCMC. The task to implement machine learning in MCMC is not trivial and it is being studied since the birth of machine learning techniques, a complete review of this task can be found in [C. Andrieu, Machine Learning (2003), 50, 5]. Basically the main problem is that most of the machine learning algorithms do not preserve the Markov property of the system, thus meaning that the probability of a new state for the system depend on the entire history of the previous states. The convergence of MCMC to the posterior distribution of the parameters lie on this assumptions and the lack of this property can cause the MC to converge in a different distribution (NO SICURO). Empirically it can be shown that the break of this property does not change the outcome of the MCMC in some cases and some ¿soft¿ machine learning method can be implemented.
On the other hand machine learning techniques are currently being implement by the LIGO and Virgo collaboration for transient noise classification task s[Jade Powell et al 2017 Class. Quantum Grav. 34 034002]. Noise classification in ground based interferometer data it is a very important task, in fact the presence of non-vetoed noise transients can prevent a possible GW detection.
As can be deduced from the references above no one in the LIGO and VIRGO collaborations are trying to develop machine learning based algorithm for CW searches even though their potentiality. A successful implementation of such type of algorithms can bring in open in this way a new window to look for CW in ground based interferometer data.
Moreover, this type of methods are of large interest for CW search in future space GW detectors such as LISA. Their capabilities will allow to extract simultaneously together many different CW sources which should populate the LISA sensitivity band. The outcome of the project can simultaneously represent a further step in ground based interferometer data analysis and a new cornerstone in the development of data analysis pipeline for CW during the LISA epoch. Besides those promising results in the field of statistics and computer science, it is important to not forget all the possible physical information that is possible to infer from detection of CWs.
In the case of CW from NSs in ground based interferometer a detection can bring to improve our knowledge on the equation of state for dense neutron matter and possible to a better understand the energy balance of spinning NSs. On the LISA side instead many CWs astrophysical sources are expected to populate the LISA band with a high SNR. Binary BHs merger, which are expected to firstly be visible in the LISA band and then in the VIRGO/LIGO band, can be firstly detected in LISA with a good localization and then serve as prior for a follow-up in the LIGO band.