Pulsars are rotating neutron stars that are observed to be slowing down, implying a loss of their rotational energy. There can be several different physical mechanisms involved in their spin-down process. The properties of fast-rotating pulsars depend on the nature of the neutron star matter, which can also affect the spin-down mechanisms. In this work, we examine three different physical phenomena contributing to the spin-down: magnetic dipole radiation, gravitational mass quadrupole radiation due to the “mountain” formation, and gravitational mass current quadrupole radiation—or the r-modes—and calculate the expressions for the braking indices due to all of them. We have also considered the implications of the uncertainties of the equation of the state of neutron star matter and rapid rotation on the braking indices corresponding to the aforementioned processes and their combinations. In all cases, the rapid rotation results in a departure of the braking index from the standard values when the rotational effects are ignored. If generated with a saturation amplitude within the range of ${10}^{-4}–{10}^{-1}$, the r-mode oscillations dominate the spin-down of millisecond pulsars. Moreover, we explore the braking index in the context of millisecond magnetars. We also study the effects of different choices of baryon mass on the braking indices.

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• Nuclear matter in neutron stars
• Neutron stars & pulsars