Torque Decay in the Pulsar (P,P_dot) Diagram. Effects of Crustal Ohmic Dissipation and Alignment

TL;DR

This paper models pulsar evolution in the (P,P-dot) diagram considering crustal ohmic dissipation and alignment, revealing how magnetic field decay influences pulsar spin-down and age estimates.

Contribution

It introduces analytical and detailed models of pulsar evolution incorporating crustal magnetic field decay and alignment effects, enhancing understanding of pulsar spin-down behavior.

Findings

Pulsars exhibit enhanced torque decay (~n>>3) after initial phase.

Long-term evolution depends on crust impurity levels.

Characteristic age approximates true age if crust impurities are negligible.

Abstract

We investigate the evolution of pulsars in the (P,P-dot) diagram. We first present analytical formulae to follow the evolution of a pulsar using simple exponential models for magnetic field decay and alignment. We then compare these evolutionary tracks with detailed model calculations using ohmic decay of crustal neutron star magnetic fields. We find that, after an initial phase with a small braking index, n, pulsars evolve with enhanced torque decay (n >> 3) for about 1 Myr. The long term evolution depends on the impurity parameter of the crust. If impurities are negligible in older isolated pulsars we expect their true age to be approximately equal to their observed characteristic age, tau = P/(2*P-dot). It is not possible from data to constrain model parameters of the neutron star crust.