Braking index of isolated pulsars. II. A novel two-dipole model of pulsar magnetism

Abstract

The magnetic dipole radiation (MDR) model is currently the best approach we have to explain pulsar radiation. However a most characteristic parameter of the observed radiation, the braking index n obs shows deviations for all the eight best studied isolated pulsars, from the simple model prediction n dip = 3. The index depends upon the rotational frequency and its first and second time derivatives, but also on the assumption of that the magnetic dipole moment and inclination angle, and the moment of inertia of the pulsar are constant in time. In a recent paper [Phys. Rev. D 91, 063007 (2015)] we showed conclusively that changes in the moment of inertia with frequency alone, cannot explain the observed braking indices.Possible observational evidence for the magnetic dipole moment migrating away from the rotational axis at a rateα ∼ 0.6 • per 100 years over the life time of the Crab pulsar has been recently suggested by Lyne et al. In this paper, we explore the MDR model with constant moment of inertia and magnetic dipole moment but variable inclination angle α. We first discuss the effect of the variation of α on the observed braking indices and show they all can be understood. However, no explanation for the origin of the change in α is provided.After discussion of the possible source(s) of magnetism in pulsars we propose a simple mechanism for the change in α based on a toy model in which the magnetic structure in pulsars consists of two interacting dipoles. We show that such a system can explain the Crab observation and the measured braking indices.

Explaining high braking indices of magnetarsSGR0501+4516 and1E2259+586 using the double magnetic‐dipole model

“…During the motion of the M 2 , its potential energy would convert into the kinetic energy. By taking C = 0 in Equation (10) of Hamil et al (2016), we can obtain the direction of M 2 when its potential energy is minimum, …”

“…The high braking indices of pulsars have been explained by different models (see Chen & Li 2016, Gao et al 2017 for brief reviews). We attribute the high braking indices n > 3 of SGR 0501+4516 and 1E 2259+586 to the decrease in their inclination angles and estimate their initial magnetic moments and initial inclination angles by using a novel double magnetic‐dipole model proposed by Hamil et al (2016) (hereafter the HSS model).…”

Refinement of the timing-based estimator of pulsar magnetic fields

“…Although the physics of the pulsar timing irregularities remains generally unclear, the proposed solutions of the 'anomalous braking indices' problem can be qualitatively divided into two categories. Type I models incorporate the relatively slow variability of NS parameters directly in the spin-down equation, assuming the variability of the surface magnetic field (Pons et al 2012;Zhang & Xie 2012;Ou et al 2016), obliquity (Melatos 2000;Lyne et al 2013;Arzamasskiy et al 2015) or effective moment of inertia (Tsang & Gourgouliatos 2013;Hamil et al 2015Hamil et al , 2016. Such models strictly keep the relationship between the observed P ,Ṗ and B in the form of the adopted spin-down law at any moment of time.…”

Application of a two dipole model to PSR J1640-4631, a pulsar with an anomalous braking index

“…Although the change of the inclination angle could yield a braking index that is different to three, the physical mechanisms causing α have not been fully understood. Recently, Hamil et al (2016) proposed a novel two-dipole model (hereafter HSS model) in which the magnetic structure of pulsars includes two interacting dipole fields. In this Letter, we apply the HSS model to explain the high braking index of PSR J1640-4631.…”

“…However, the physical mechanisms causing the change of the magnetic inclination angle have not been fully understood. In this Letter, we apply a two-dipole model given by Hamil et al (2016) to explain the decrease of the magnetic inclination angle of PSR J1640-4631. The rotation effect of a charged sphere and the magnetization of ferromagnetically ordered material produce magnetic moments M 1 and M 2 , respectively.…”