Timing and Evolution of PSR B0950+08

TL;DR

This paper analyzes 14 years of timing data of PSR B0950+08, proposing a magnetic field decay model with oscillations to explain its spin and thermal evolution, and highlights the importance of combined timing and thermal studies.

Contribution

It introduces a long-term magnetic field decay model with oscillations to explain timing variations and thermal evolution of PSR B0950+08, integrating spin and thermal data.

Findings

Braking index varies oscillatingly with large amplitude.

Three-component oscillation model fits spin-frequency derivative data.

Standard cooling and vortex creep heating explain surface temperature.

Abstract

We present timing solutions of PSR B0950+08, using 14 years of observations at Nanshan 26-m Radio Telescope of Xinjiang Astronomical Observatory. The braking index of PSR B0950+08 varies from --367 392 to 168 883, which shows an oscillation with large amplitude ($\sim 10^5$) and uncertainty. Considering the variation of braking indices and the most probable kinematic age of PSR B0950+08, a model withe long-term magnetic field decay modulated by short-term oscillations is proposed to explain the timing data. With this magnetic field decay model, we discuss the spin and thermal evolution of PSR B0950+08. The uncertainties of its age are also considered. The results show that three-component oscillations are the more reasonable for the spin-frequency derivative distributions of PSR B0950+08, and the initial spin period of PSR B0950+08 must be shorter than $97\rm\ ms$ when the age is equal to the lower bound of its kinematic age. The standard cooling model could explain the surface temperature of PSR B0950+08 with its most probable kinematic age. Vortex creep heating with a long-term magnetic field decay could maintain a relatively high temperature at the later stages of evolution and explain the thermal emission data of old and warm pulsars. Coupling with the long-term magnetic field decay, an explanation of the temperature of PSR B0950+08 with roto-chemical heating needs an implausibly short initial rotation period ($P_0 \lesssim 17\rm{ ms}$). The spin and thermal evolution of pulsars should be studied simultaneously. Future timing, ultraviolet or X-ray observations are essential for studying the evolution and interior properties of pulsars.