Detection of gravitational waves: from nanohertz to the audio band

The existence of gravitational waves was first predicted by Einstein's general theory of relativity a century ago. However gravitational waves have not yet been directly detected¹. Their direct detection will open a new observational window allowing one to listen to the Universe for the first time. Einstein's gravitational spectrum spans from extremely low frequencies, with wave periods comparable to the age of the Universe, to the audio band, with frequencies roughly between 10 Hz and several kilohertz. The subject of this thesis is the direct detection of gravitational waves in two different frequency bands: a) the audio band observed by terrestrial laser interferometers; b) the nanohertz band surveyed by pulsar timing arrays.

Ground-based interferometers, such as the Laser Interferometer Gravitational-wave Observatory (LIGO), are primarily searching for signals from binary coalescences of neutron stars and black holes. As the two objects orbit around each other, they lose energy through the emission of gravitational waves. As the orbital period decreases, the gravitational wave frequency and amplitude increase until the binary merges, emitting copious amounts of gravitational waves. Advanced LIGO detectors, which came online in September 2015, are expected to detect tens of such events each year after they reach design sensitivity in around 2019.

In addition to those individually detectable events, a gravitational wave background exists as a result of the combined emission of numerous sources throughout the Universe. This provides another promising target for advanced detectors. Modelling such a background signal and predicting its detection prospects is the subject of the first part of this thesis. We present a comprehensive study on the gravitational wave background from compact binary coalescences throughout the Universe. It improves on previous work by using observation-based source distributions and realistic gravitational waveforms. We show that advanced detectors are likely to detect this signal assuming a realistic coalescence rate. We also investigate if subtracting the contribution of individually detectable events can potentially unmask the highly sought primordial signals.

Pulsar timing arrays target gravitational waves at the lower nanohertz band. This is achieved through performing long-term radio timing observations of a spatial array of millisecond pulsars. In the second part of this thesis we focus on detection and sky localization of single sources by pulsar timing arrays, in particular signals expected from individual supermassive binary black holes. We have developed two independent coherent methods for this purpose.

The first technique is fast and robust, which is adapted from network analysis methods used by ground-based detectors. We demonstrate its effectiveness for three types of sources: circular binaries, eccentric binaries and bursts. To test its robustness, we apply it to realistic synthetic data sets that include effects such as uneven sampling, heterogeneous data spans and measurement precision. With the second technique, we perform an all-sky search for continuous waves in the recent Parkes Pulsar Timing Array data set. Although no statistically significant signals were detected, the quality of the data allows us to set the best limit on the gravitational wave amplitude in the nanohertz regime. With this data set we could detect gravitational waves from supermassive binary black holes with masses higher than one billion solar mass out to a luminosity distance of about 100 Mpc.

¹Note added - It was announced on 11 February 2016 that a signal from the coalescence of two black holes was detected by two LIGO detectors on 14 September 2015 (Abbott et al. 2016).