An analytic approach for the study of pulsar spindown

TL;DR

This paper develops an analytic model for pulsar spindown, incorporating magnetic field decay and gravitational radiation, providing formulas for pulsar parameters and validating with known pulsar data.

Contribution

It introduces a novel all-order analytic formula for pulsar spindown parameters, extending previous models to include gravitational wave emission effects.

Findings

First three spindown parameters match observed bounds.

Derived formulas for pulsar period and frequency.

Extended model includes gravitational radiation effects.

Abstract

In this work we develop an analytic approach to study pulsar spindown. We use the monopolar spindown model by Alvarez and Carrami\~{n}ana (2004), which assumes an inverse linear law of magnetic field decay of the pulsar, to extract an all-order formula for the spindown parameters which are expressed in terms of modified Bessel functions. We further extend the analytic model to incorporate the quadrupole term that accounts for the emission of gravitational radiation, and obtain expressions for the period $P$ and frequency $f$ in terms of transcendental equations. We derive the period of the pulsar evolution as an approximate first order solution in the small parameter present in the full solution. We find that the first three spindown parameters of the Crab, PSR B1509-58, PSR B0540-69 and Vela pulsars are within their known bounds providing a consistency check on our approach. After the four detections of gravitational waves from binary black hole coalescence and a binary neutron merger 170814, which was a novel joint gravitational and electromagnetic detection, a detection of gravitational waves from pulsars will be the next landmark in the field of multi-messenger gravitational wave astronomy.