Towards a Reformulation of the Hough Method for Continuous Gravitational Wave Searches

The recent detections of gravitational waves performed by the Advanced LIGO and Advanced Virgo interferometers have established an entirely new channel to probe information from the Universe. In a complementary fashion to electromagnetic waves, gravitational waves are perturbations of the spacetime, traveling through the Universe. So far, the detected gravitational waves were produced as a result of the coalescence of compact objects, such as black holes or neutron stars. They emit a highly concentrated burst of energy, following a wellunderstood propagation mechanism. However, there is more. It is theoretically described that some compact objects are able to sustain imperfections in its shape for a long period of time. The most common example is given by a neutron star, the crust of which may present a small bump which corresponds to a deviation from a perfectly symmetric object. Due to the persistence in time of such physical mechanisms, the emitted signal presents a remarkable property with respect with the previous situation: It may last for long periods of time, compared to the extremely short duration of the coalescence of compact binaries; thus, we label these signals as continuous waves. The detection of such continuous signals will open a new chapter in gravitational wave astronomy, extending the field from transient signals to the observation of persistent sources, which can be monitored with ever increasing precision, over very long periods of time, as is common in traditional electromagnetic astronomy. Due to the modulation of the signal resulting from the motion of the Earth, it will be possible to accurately measure both gravitational wave polarizations, and the accurate tracking of the gravitational wave phase over many years will yield information about the equation of state and possible transient events like seismic activity in the neutron star crust. The work presented here further develops the capabilities of the SkyHough pipeline, which is one of the main tools used by the LIGO and Virgo Collaboration to search for continuous wave signals. This search algorithm implements the Hough transform, which is a type of pattern recognition algorithm, first developed to recognize particle tracks in bubble chambers. One of the main advantages of this method has been its robustness against noise. As opposed to current searches for transients, like comparable mass compact objects, searches for continuous wave signals are limited by computational resources, and carrying out optimally sensitive searches is computationally prohibitive. All-sky searches are therefore typically carried out semicoherently: a stream of data is first split into different time segments, then a suitable quantity measuring significance is assigned to each segment. Finally, the results for each segment are combined into a single quantity, which can be used to state the presence of a signal within the analyzed dataset. Noise artifacts populate every step of the statistical procedure. Even though one can attempt to construct an analytical derivation of the noise statistical properties at each step, it is more reliable to work with numerical approaches, as they take into account the effects measured by the data analysis procedure. A good representation of the noise distribution is important to state the significance of a certain result. The main contribution of this work is the development of a new formulation which combines data from different detectors into a single analysis. This new method relies on a more accurate estimation of the noise, which replaces the assumption of some prescribed underlying noise distribution, as has been used in previous versions of the SkyHough pipeline. This noise estimation is based on the introduction of an efficient random sampling procedure in the large parameter space of signals. Working with this new accurate estimate of the background noise distribution, one is able to increase the sensitivity of the searches, as a better understanding of the background behavior translates to a better identification of signals in terms of its statistical significance. In addition, I have started to explore further improvements to the SkyHough pipeline: the use of the universal statistics approach of [26], the use of artificial neural networks for candidate classification, and the utilization of a method developed by [19] to deal with spectral leakage. These investigations are not yet concluded, but allow us to explore the directions in which data analysis pipelines for continuous wave searches may evolve in the near future. Together with the continuously increasing sensitivity of our detectors, it is expected that these improvements will contribute to keep the SkyHough pipeline at the forefront of data analysis of continuous waves, pointing us towards the correct way to a first detection. The document is structured as follows: Chapter 1 introduces the basic theory on gravitational waves and interferometric detectors; chapter 2 introduces neutron stars, discussing their relevance within the field of continuous gravitational waves; chapter 3 describes the SkyHough pipeline for the detection of continuous gravitational waves; chapter 4 introduces the S6 Mock Data Challenge, which is the data set that we used to test our improvements against previous implementations of the SkyHough pipeline; chapter 5 discusses the main results, implementing the sampling procedure to properly take into account the contribution of noise fluctuations into the data analysis pipeline; chapter 6 describes some minor developments, still on an experimental stage, which could yield relevant contributions to the data analysis procedure; chapter 7 concludes the work, summarizing the main results.