Probing the extreme radio universe Insights into pulsar emission beams and fast radio burst populations

Two kinds of time-domain signals in radio astronomy, fast radio bursts (FRBs), one of the most energetic phenomena in the universe, and pulses from highly relativistic binary pulsars, contain rich information of extreme astrophysical processes. Both are also strongly linked with the physics of neutron stars. In this thesis, I investigated the properties of the one-off FRB population and I carried out detailed studies of a precessing pulsar system. First, I studied the intrinsic population of one-off FRBs with CHIME/FRB Catalog 1, using the updated Python package frbpoppy, which now includes multi-dimensional MCMC simulations and sped-up code, to find the best-fit model (Ch. 2). We find strong evidence that FRB birth rates evolve with the star formation rate of the universe, even with a short delay time. Next, I presented new data and analysis on the extremely relativistic binary PSR J1906+0746, a pulsar that shows geodetic precession (Ch. 3). I extended the reconstructed beam maps of this pulsar using FAST and Arecibo data based on polarization information. Finally, I searched the same data for the pulsar companion (Ch. 4), as the binary is very likely to be a double pulsar system. The non-detection provides stringent limit for the flux of the potential pulsar and also leaves space for future detection. In a summary, the result of this thesis deepens our understanding of the FRB population and of pulsar emission.