Modelling the deformability of magnetized neutron stars in the light of future continuous gravitational waves detection

Neutron stars are known to host extremely powerful magnetic fields. Among other effects, one of the consequences of harboring such fields is the deformation of the neutron star structure, leading, together with rotation, to the emission of continuous gravitational waves (CGWs). We present an extensive numerical study of magnetized neutron stars in GR with a large variety of different Equations of State (EoSs) and show that it is possible to find simple relations between the magnetic deformation of a neutron star, its mass and radius, that are mostly independent on the EoS or magnetic configuration. We discuss how these relations can be used in conjunction with possible future CGWs detection to set constrains on the EoS and magnetic configurations of NSs (e.g. the presence of a superconducting phase). By carrying out a population synthesis, we estimate the possible CGWs detectability of galactic millisecond pulsars, with third generation GW detectors.