Braking Index of Isolated Pulsars

Isolated pulsars are rotating neutron stars with accurately measured angular velocities $\Omega$, and their time derivatives which show unambiguously that the pulsars are slowing down. The exact mechanism of the spin-down is a question of debate in detail, but the commonly accepted view is that it arises through emission of magnetic dipole radiation (MDR). The energy loss by a rotating pulsar is proportional to a model dependent power of $\Omega$. This relation leads to the power law $\dot{\Omega}$ = -K $\Omega^{\rm n}$ where $n$ is called the braking index, equal to the ratio ($\Omega \ddot{\Omega}$)/ ${\dot{\Omega}}^2$. The simple MDR model predicts the value of n = 3, but observations of isolated pulsars provide rather precise values of $n$, individually accurate to a few percent or better, in the range 1$ <$ n $ < $ 2.8, which is consistently less than the predictions of the MDR model. In this work, we study the dynamical limits of the MDR model as a function of angular velocity. The effects of variation in the rest mass, the moment of inertia, and the dependence on a realistic Equation of State of the rotating star are considered. Furthermore, we introduce a simulated superfluid effect by which the angular momentum of the core is eliminated from the calculation.