Modelling the braking "index'' of isolated pulsars

TL;DR

This paper proposes a model incorporating wobbling and internal damping effects in isolated pulsars to better explain observed deviations in their braking index from the standard magnetic dipole radiation theory.

Contribution

It introduces a new approach considering wobbling and damping effects to explain the lower observed braking indices in young pulsars.

Findings

Numerical results match observed braking indices.

Wobbling and damping effects can account for deviations.

Model extends traditional magnetic dipole radiation theory.

Abstract

An isolated pulsar is a rotating neutron star possessing a high magnetic dipole moment that generally makes a finite angle with its rotation axis. As a consequence, the emission of magnetic dipole radiation (MDR) continuously takes away its rotational energy. This process leads to a time decreasing angular velocity of the star that is usually quantified in terms of its braking index. While this simple mechanism is indeed the main reason for the spin evolution of isolated pulsars, it may not be the only cause of this effect. Most of young isolated pulsars present braking index values that are consistently lower than that given by the MDR model. Working in the weak field (Newtonian) limit, we take in the present work a step forward in describing the evolution of such a system by allowing the star's shape to wobble around an ellipsoidal configuration as a backreaction effect produced by the MDR emission. It is assumed that an internal damping of the oscillations occurs, thus introducing another form of energy loss in the system, and this phenomenon may be related to the deviation of the braking index from the pure MDR model predictions. Numerical calculations suggest that the average braking index for typical isolated pulsars can be thus simply explained.