The influence of deceleration and internal structure on the braking index of pulsars: Simplest model for the star

Pulsars are rotating neutron stars whose electromagnetic radiation is observed to pulsate and, despite the extremely stable rates, the frequencies of the pulses decay with time, as quantified by the braking index (n). It is extremely difficult to obtain this index from observations due to different factors. Theoretically, in the canonical model for neutron stars, one finds n = 3, but observational data shows that n is less than three. In this work, the canonical model is modified, incorporating the influence of the deceleration of the neutron star. As the star's rotation decelerates, the deformation of the star due to the centrifugal force decreases thereby reducing its moment of inertia. Consequently, the star decelerates less, reducing the braking index. In this work, the star is modeled as a very hard, compressible spherical shell filled with neutrons and protons superfluid that do not interacts with the shell. Using this toy model as a first approach, the braking index is found as a function of rotation, yielding a theoretical braking index closer to the one derived from observational data.