Constraints on the internal physics of neutron stars from the observational data of several young pulsars: the role of a power-law decaying dipole magnetic field

TL;DR

This study investigates how a power-law decay of the magnetic field in young pulsars affects their internal physics, using observational data to test the model and suggesting alternative magnetic field evolution.

Contribution

It introduces a power-law decay model for pulsar magnetic fields and tests its consistency with observational data, particularly focusing on the Crab pulsar.

Findings

Power-law decay model is inconsistent with Crab pulsar observations.

Crab's magnetic field likely increases over time, not decays.

Further measurements of tilt angle change rates are needed for other pulsars.

Abstract

The observational data (e.g., the timing data and magnetic tilt angles $\chi$) of young pulsars can be used to probe some critical issues about the internal physics of neutron stars (NSs), for instance, the number of precession cycles $\xi$ and the internal magnetic field configuration (IMFC) of NSs. Evolution of the dipole magnetic field $B_{\rm d}$ of NSs may play an important role in determining the final results. In this work, a power-law form is adopted to describe the decay of $B_{\rm d}$. In such a scenario, the IMFC and $\xi$ of young pulsars with an ordinary $B_{\rm d}\sim10^{12}-\-10^{13}$ G and a steady braking index $n$ are investigated. Since the tilt angle change rates $\dot{\chi}$ of pulsars with $n<3$ can be theoretically predicted, a test on the power-law decay model can thus be made by comparing the theoretical values to that obtained from observations. However, such a comparison can only be made on the Crab pulsar currently, and the results show that the power-law decay model is inconsistent with the Crab's observations. We suggest that rather than decay, the Crab's $B_{\rm d}$ should increase with time at a rate $\sim12-14$ G/s. A definite conclusion on the validity of the power-law decay model for pulsars with ordinary $B_{\rm d}$ may be given if $\dot{\chi}$ of other pulsars could be measured.