Braking index of isolated uniformly rotating magnetized pulsars

Oliver Hamil, Jirina Stone, Martin Urbanec, Gabriela Urbancova

Published 2015-03-31Version 1

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. Although the exact mechanism of the spin-down is a question of debate in detail, the commonly accepted view is that it arises through emission of magnetic dipole radiation (MDR) from a rotating magnetized body. Other processes, including the emission of gravitational radiation, and of relativistic particles (pulsar wind), are also being considered. 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 as yet. We employ four physically realistic equations of state, and two computational codes, to model the dynamical effects of rotation on the braking index in the MDR model. In addition to this we simulate an effect on moment of inertia where we assume a certain amount of superfluid matter has manifest between the crust and core region of the star thus essentially eliminating momentum transfer between the two regions. We find that the effects of rotation on braking index are significant at high frequencies, but have little effect at frequencies consistent with the most accurately measured pulsars to-date.