Evolution of Spin Period and Magnetic Field of the Crab Pulsar: Decay of the Braking Index by the Particle Wind Flow Torque

TL;DR

This paper models the Crab pulsar's spin-down and magnetic field evolution considering both magnetic dipole radiation and particle wind flow, revealing insights into its braking index, age, and magnetic field behavior over time.

Contribution

It provides an exact analytic solution for the pulsar's rotation evolution incorporating wind torque, highlighting the non-constancy of the magnetic field and the evolution of the braking index.

Findings

Crab pulsar's real magnetic field remains unchanged despite the characteristic B-field increase.

The braking index decreases from ~3 to 1 over long-term evolution.

Characteristic age has an upper limit of ~10 kyr, not always reflecting true age.

Abstract

The evolutions of a neutron star's rotation and magnetic field (B-field) have remained unsolved puzzles for over half a century. We ascribe the rotational braking torques of pulsar to both components, the standard magnetic dipole radiation (MDR) and particle wind flow ( MDR + Wind, hereafter named MDRW), which we apply to the Crab pulsar (B0531 + 21), the only source with a known age and long-term continuous monitoring by radio telescope. Based on the above presumed simple spin-down torques, we obtain the exact analytic solution on the rotation evolution of the Crab pulsar, together with the related outcomes as described below: (1) unlike the constant characteristic B-field suggested by the MDR model, this value for the Crab pulsar increases by a hundred times in 50~kyr while its real B-field has no change; (2) the rotational braking index evolves from $\sim$3 to 1 in the long-term, however, it drops from 2.51 to 2.50 in $\sim$45 years at the present stage, while the particle flow contributes approximately 25% of the total rotational energy loss rate; (3) strikingly, the characteristic age has the maximum limit of $\sim$10 kyr, meaning that it is not always a good indicator of real age. Furthermore, we discussed the evolutionary path of the Crab pulsar from the MDR to the wind domination by comparing it with the possible wind braking candidate pulsar PSR J1734-3333.