Braking index of isolated pulsars

Abstract

Isolated pulsars are rotating neutron stars with accurately measured angular velocities $\Omega$, and their time derivatives that show unambiguously that the pulsars are slowing down. The commonly accepted view is that it arises through emission of magnetic dipole radiation (MDR) from a rotating magnetized body. The calculated energy loss by a rotating pulsar with a constant moment of inertia is assumed 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. The MDR model predicts $n$ exactly equal to 3. Selected 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 spite of an extensive investigation of various modifications of the MDR model, no satisfactory explanation of observation has been found yet. The aim of this work is to determine the deviation of the value of $n$ from the canonical $n = 3$ for a star with a frequency dependent moment of inertia in the region of frequencies from zero to the Kepler velocity (onset of mass shedding by a rotating deformed star), in the macroscopic MDR model. For the first time, we use microscopic realistic equations of state (EoS) of the star to determine its behavior and structure. In addition, we examine the effects of the baryonic mass M$_{\rm B}$ of the star, and possible core superfluidity, on the value of the braking index within the MDR model.