Unravelling the nature of transitional millisecond pulsars

Transitional millisecond pulsars (tMSPs) are binary systems in which there is a neutron star and a low-mass, likely non-degenerate companion star. These systems switch between states as: i) an observable radio millisecond pulsar ('RMSP state'), at which time there is no evidence for an accretion disc, and ii) a state similar to that of a low-mass X-ray binary (LMXB), in which there is an accretion disc and sometimes apparently active accretion into the neutron star magnetosphere, or even a luminous X-ray outburst ('LMXB state'). In this thesis we strive to understand the evolution and nature of the LMXB state of tMSPs; in particular, the persistent, low-luminosity, 'disc-dominated' state that they sometimes occupy. We have undertaken wide-ranging, multi-wavelength explorations of tMSPs by searching, monitoring, timing and imaging them with individual and simultaneous observations spanning the electromagnetic spectrum through Gamma-ray, X-ray, UV and radio wavelengths. This has required a wide diversity of instruments and techniques. These observations have led to significant insights into the nature of tMSPs, and in particular their persistent, low-level accretion state. Specifically, in case of the tMSP, PSR J1023+0038. We have successfully modelled its spin-down behaviour in the LMXB state and detected millisecond pulsations in its Hubble Space Telescope ultraviolet observations. To understand how representative PSR J1023+0038 is of the tMSP class, we studied the candidate tMSP 3FGL J1544-1125. We also tried to connect tMSPs and accreting millisecond X-ray pulsars by searching for radio pulsations from the prototype of this class, SAX J1808-3658.