Inverse Mapping of Polarised Optical Emission from Pulsars : Basic Formulation and Determination of Emission Altitude

TL;DR

This paper introduces an inverse mapping method using optical polarization data to determine the emission height and geometry of pulsar emissions, specifically applied to the Crab pulsar, revealing an altitude at 20% of the light cylinder radius.

Contribution

The paper presents a novel inverse mapping approach utilizing optical Stokes parameters to estimate pulsar emission altitude and geometry from empirical data.

Findings

Emission altitude is approximately 20% of the light cylinder radius.

The method determines magnetic inclination and line of sight angles.

A general polarization model for synchrotron sources is also discussed.

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.