# The effective magnetic field decay of radio pulsars: insights from the statistical properties of their spin frequency's second derivatives

## TL;DR

This study introduces a new statistical method to analyze the decay of magnetic fields in radio pulsars, revealing that the decay timescale exceeds several million years and is independent of specific theoretical models.

## Contribution

The paper presents a novel approach using the distribution of second derivatives of pulsar spin frequencies to estimate magnetic field decay timescales without relying on specific evolution theories.

## Key findings

- Magnetic field decay timescale exceeds ~5 Myr for young pulsars.
- Decay timescale exceeds ~100 Myr for older pulsars.
- The extent of the closed magnetic line region is close to the light cylinder radius.

## Abstract

We present a new method to investigate the effective magnetic field decay of isolated neutron stars, from the analysis of the long-term timing data of a large sample of radio pulsars \citep{2010MNRAS.402.1027H}. There are some differences between the distributions of frequency's second derivatives of the pulsar spins with different effective field decay timescales. Kolmogorov-Smirnov tests are performed to reexamine the consistency of distributions of the simulated and reported data for a series values of decay timescales. \textbf{We show that the timescale of the effective field decay exceeds $\sim 5~\rm {Myr}$ for pulsars with spin-down age $\tau_{\rm C}< 10^{7}~{\rm yr}$ or $\sim 100~\rm {Myr}$ for pulsars with $10^{7}<\tau_{\rm C}< 10^{9}~{\rm yr}$ in the sample. The result does not depend on any specific theories of the field evolution, the inclination decay or the variation in the moment of inertia. It is also found that the extent of the closed line region of the magnetic field is close to the light cylinder $r_{\rm lc}$, i.e., the corotating radius $r_{\rm c}\approx r_{\rm lc}$ is a good approximation for the observed pulsar population.