Connecting the coherent and stochastic X-ray variability of accreting millisecond pulsars

Accreting millisecond pulsars are rapidly rotating neutron stars with a dynamically important magnetic field. These objects are found in low-mass X-ray binary systems, where a small companion star acts as a mass donor, transferring material to the neutron star. As this plasma spirals toward the neutron star it heats up and radiates in the X-ray band, showing stochastic, quasi-periodic variations of the intensity. Close to the neutron star, the stellar magnetic field captures the inflowing plasma and guides it toward the magnetic poles on the surface. There, the impact of the flow causes a localized emission region that through periodic aspect variations gives rise to coherent pulsations at the neutron star millisecond rotation rate. In this thesis the variability of the X-ray emission is used to study these accreting millisecond pulsars. Through the quasi-periodic variability the nature of the accretion flow is investigated. The pulsations, on the other hand, originate from the stellar surface and are used to examine the properties of the pulsar and its evolution. Finally, both the coherent and stochastic variability signatures are brought together in order to study the magnetic coupling that connects the accretion flow and the millisecond pulsar.