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In this Thesis we present the equilibrium magnetar model we have developed. The model is built in the framework of General Relativity, and follows a perturbative approach. It describes a non-rotating strongly magnetized neutron star surrounded by vacuum, with the assumption that the magnetic field acts as a stationary axisymmetric perturbation of a static and spherically symmetric unmagnetized star.
Inside the star we adopt ideal magnetohydrodynamics, i.e. we neglect finite electrical conductivity effects. The above assumptions are quite standard in the literature.
The magnetic field configurations we find reproduce the twisted-torus geometry. Moreover, we include the contribution from the higher (l > 1) multipolar components of the magnetic field and their couplings, in addition to the dipolar (l = 1) component usually considered. We use an argument of minimal energy to find, among the possible solutions, the energetically favoured configuration. This allows us to evaluate the ratio of toroidal and poloidal fields in terms of magnetic field energy. All these elements constitute an improvement with respect to previous models.
The equilibrium configurations we obtain can be used as input for studies on dynamical processes involving magnetars. In this Thesis we also consider one of the possible applications: the emission of gravitational waves from magnetically-deformed rotating neutron stars. We compute the quadrupolar deformation induced by the magnetic field on the star’s structure and the resulting gravitational wave emission spectrum. For completeness, we extend the analysis to other models. Finally, we estimate the stochastic gravitational wave background produced by the entire magnetar population, which results from the superposition of the single source emissions; we also evaluate the detectability of such background by third generation detectors such as the Einstein Telescope.