This work aims at studying how magnetic fields affect the observational properties and the long-term evolution of isolated neutron stars, which are the strongest magnets in the universe. The extreme physical conditions met inside these astronomical sources complicate their theoretical study, but, thanks to the increasing wealth of radio and X-ray data, great advances have been made over the last years.
A neutron star is surrounded by magnetized plasma, the so-called magnetosphere. Modeling its global configuration is important to understand the observational properties of the most magnetized neutron stars, magnetars. On the other hand, magnetic fields in the interior are thought to evolve on long time-scales, from thousands to millions of years. The magnetic evolution is coupled to the thermal one, which has been the subject of study in the last decades. An important part of this thesis presents the state-of-the-art of the magneto-thermal evolution models of neutron stars during the first million of years, studied by means of detailed simulations. The numerical code here described is the first one to consistently consider the coupling of magnetic field and temperature, with the inclusion of both the Ohmic dissipation and the Hall drift in the crust.
The thesis is organized as follows. In chapter 1, we give a general introduction to neutron stars. In chapter 2, we focus on the magnetosphere, describing the analytical and numerical search for force-free configurations. We also discuss its imprint on the X-ray spectra. Chapter 3 describes the numerical method used for the magnetic field evolution. Chapter 4 reviews the microphysical processes and ingredients entering in the full magneto-thermal evolution code, the results of which are presented in chapter 5. In chapter 6, we analyse observational X-ray data of isolated neutron stars, showing how their apparent diversity can be understood in the light of our theoretical results. In chapter 7, we quantitatively discuss how the magnetic field evolution can contribute to explain the peculiar rotational properties observed in some neutron stars. In chapter 8 we summarize the main findings of this thesis.
Most of the original parts of our research (mostly contained in the second part of chapter 2, and in chapters 3, 5, 6, 7 and 8 have been published in international refereed papers. We have extended and merged their contents in order to write a self-contained work including, when needed, overviews before entering into details of specific problems (e.g., chapters 1 and 4).
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