Inverse mapping of polarized optical emission from pulsars: basic formulation and determination of emission altitude

Abstract

We present an inverse mapping approach to determining the emission height of the optical photons from pulsars, which is directly constrained by empirical data. The model discussed is for the case of the Crab pulsar. Our method, using the optical Stokes parameters, determines the most likely geometry for emission including magnetic field inclination angle ($\alpha$), observers line of sight angle ($\chi$) and emission height. We discuss the computational implementation of the approach, along with any physical assumptions made. We find that the most likely emission altitude is at 20% of the light cylinder radius above the stellar surface, in the open field region. We also present a general treatment of the expected polarisation from synchrotron source with a truncated power law spectrum of particles.