Fast radio bursts and the radio counterparts of neutron star mergers

Many of the most energetic phenomena in the Universe can be seen by radio telescopes and are transient in nature. Recent scientific and technological advancements have enabled the breakthrough detections of two new types of exciting transient: fast radio bursts (FRBs) and neutron star mergers. This thesis focuses on devising new observational strategies for these two young topics, and exploring possible connections between them. What causes FRBs is not known. Some FRB sources repeat by emitting multiple times, whereas most are only observed to emit once. A highly debated question is whether there are multiple types of FRB, or whether they all have the same physical explanation. Part of this thesis explores this question, focusing on observations of the oldest known repeating FRB (Ch. 2) and comparing observations of other FRBs to models related to neutron star mergers (Ch. 3). We devise a new strategy using the Low-Frequency Array (LOFAR) to catch coherent radio emission, like FRBs, immediately following a gamma-ray burst/neutron star merger and provide the deepest limits yet (Ch. 4 & 5). We also look at the elusive longer lasting synchrotron radio afterglow known to follow binary neutron star mergers. We use LOFAR to study GW170817, the only merger radio afterglow ever to be associated with detected gravitational waves (Ch. 6). Such radio afterglows are encoded with rich high-energy physics but are difficult to find owing to their poorly constrained locations. We develop a LOFAR strategy in Ch. 7 that will enable us to probe the full location uncertainty region in the next gravitational wave observing run.