An analytic approach for the study of pulsar spindown

In this work we develop an analytic approach to study pulsar spindown. We use the monopolar spindown model by Alvarez and Carramiñana (2004 Astron. Astrophys. 414 651–8), which assumes an inverse linear law of magnetic field decay of the pulsar, to extract an all-order formula for the spindown parameters using the Taylor series representation of Jaranowski et al (1998 Phys. Rev. D 58 6300). 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 analytic solution for pulsar frequency spindown in the absence of glitches. We examine the different cases that arise in the analysis of the roots in the solution of the non-linear differential equation for pulsar period evolution. We provide expressions for the spin-down parameters and find that the spindown values are in reasonable agreement with observations. A detection of gravitational waves from pulsars will be the next landmark in the field of multi-messenger gravitational wave astronomy. (paper)