Multipole moments and universal relations for scalarized neutron stars

In recent years there has been a surge of interest in what has come to be known as the `universal relations' between various global properties of neutron stars. These universal relations are equation of state independent relations between quantities such as the moment of inertia $I$, the tidal deformability or Love number $\lambda$, and the quadrupole $Q$ (I-Love-Q relations), or the relativistic multipole moments (3-hair relations). While I-Love-Q relations have been studied extensively in both general relativity and various alternatives, 3-hair relations have been studied only in general relativity. Recent progress on the definition of the multipole moments of a compact object in the case of scalar-tensor theories allows for the study of 3-hair relations in modified theories of gravity. Specifically, the aim of this work is to study them for scalarized stars in scalar-tensor theories with a massless scalar field that admit spontaneous scalarization. We find that the 3-hair relations between the mass and angular momentum moments that hold in general relativity hold for scalarized stars as well. The scalar moments also exhibit a universal behaviour, which is equation of state independent within one specific theory, but differs between different theories. Combining astrophysical observations one can in principle measure the different properties of scalarized neutron star and tell different theories apart.