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ItemDense matter and magnetic fields in neutron starsAnzuini, Filippo ( 2021)The life cycle of main sequence stars with masses in the range 8 - 25 solar masses ends in a supernova explosion, whose remnant is a dense compact object called neutron star. The huge gravitational field of neutron stars, counterbalanced by the pressure of strongly degenerate matter, combined with intense magnetic fields offer the opportunity to probe matter in extreme conditions, far beyond the reach of contemporary laboratory experiments. The wealth of observations of neutron stars gradually reveals more facets of their nature, although much is yet to be discovered. The aim of this work is to study the interplay of two ingredients of neutron star physics: dense matter and magnetic fields. The properties of ultra-dense matter can be inferred from the thermal radiation emitted by isolated neutron stars and magnetars. Detailed models of the atmosphere, surface, crust and core are required to determine how information about dense matter in the core is filtered out by the outer layers. Often, several key quantities that determine the thermal luminosity are unknown, such as the mass and radius, or the chemical composition and magnetic field configuration. The ionization state and emission model adopted for the stellar atmosphere and the chemical composition of the outer envelope (i.e. a layer with a typical thickness of ~ 100 m) affect the thermal radiation produced at the surface. Strong magnetic fields modify the heat transport in the atmosphere and in the crust and can decay, producing high Joule heating rates, complicating the interpretation of thermal luminosity observations in terms of the internal chemical composition and the neutrino emission processes active in the deeper regions of the core. Chapters 2 and 3 study the thermal radiation produced by neutron stars with cores hosting unconventional particles such as hyperons by performing state-of-the-art magneto-thermal evolution simulations. The influence of the magnetic field on the thermal evolution is examined for several plausible initial magnetic field configurations, and the thermal luminosity is compared with the data of thermally emitting, isolated neutron stars and magnetars. It is found that (i) internal heating is required by stars with and without hyperon cores, regardless of the composition of the outer envelope, if direct Urca processes activate in stars with masses ~ 1 solar mass and neutrons are superfluid in a large fraction of the core; and (ii) the thermal power produced by the dissipation of crustal electric currents sustaining the magnetic field can hide the effect of fast cooling processes related to the appearance of hyperons in the core, making hard to infer the chemical composition of neutron stars from thermal luminosity data. Although the intense magnetic field of neutron stars plays a central role in their phenomenology, the internal field is poorly known, and often one relies on simplistic magnetic topologies. Additionally, neutron stars may have internal velocity fields generated by differential rotation that affect the magnetic field configuration. One important question is whether in such conditions the magnetic field can force the fluid to rotate uniformly with the solid crust, or whether the fluid can be in a state of differential rotation on long, viscous time-scales. Due to computational limitations, performing detailed magneto-thermal simulations with the addition of evolving internal velocity fields of several fluid components is a nontrivial task. However, one can gain some insight into the magnetic configuration in the presence of internal flows by modeling the star as a spherical shell containing a single, idealized and electrically conducting fluid. In Chapter 4 we study the implications of internal fluid flows on the magnetic field configuration by applying a constant rotational shear between the inner and outer boundaries. It is found that differential rotation tangles the magnetic field lines and produces small-scale toroidal flux tubes containing bundles of closed toroidal field lines in proximity of the magnetic equator. In these toroidal flux tubes, the fluid velocity is set by viscosity rather than by the magnetic field, allowing differential rotation in neutron star interiors to persist on long, viscous time-scales. Hyperons are not the only unconventional particles that may appear in neutron star cores. Typical densities in massive stars may be sufficiently high for quarks to deconfine, and crystalline phases arising from inhomogeneous condensation of quarks may form. In Chapter 5 we develop an analytic approximation for the free energy of deconfined quark matter and study its ground state in the presence of strong magnetic fields and at high temperatures, which may be characteristic of neutron star binary mergers. It is shown that the magnetic field and temperature compete in enlarging and reducing respectively the region of the phase diagram where inhomogeneous phases of quark matter are favored, which correspond to the regions where the neutrino emissivity of quark matter increases due to the activation of direct Urca processes.