Visibility of pulsar emission: motion of the visible point

TL;DR

This paper analyzes the motion of the visible point in pulsar emission models, comparing the exact tangent model with the rotating vector model (RVM), and discusses implications for observational visibility and emission height estimates.

Contribution

It provides an exact solution for the visible point trajectory in pulsar models and evaluates the errors introduced by the RVM, highlighting the importance of emission height considerations.

Findings

The RVM underestimates the range of visible emission angles.

The visible point moves significantly as a function of pulsar phase.

Emission likely occurs at heights over ten percent of the light-cylinder distance.

Abstract

A standard model for the visibility of pulsar radio emission is based on the assumption that the emission is confined to a narrow cone about the tangent to a dipolar field line. The widely accepted rotating vector model (RVM) is an approximation in which the line of sight is fixed and the field line is not strictly tangent to it. We refer to an exact treatment (Gangadhara 2004) as the tangent model. In the tangent model (but not in the RVM) the visible point changes as a function of pulsar rotational phase, $\psi$, defining a trajectory on a sphere of radius $r$. We solve for the trajectory and for the angular velocity of the visible point around it. We note the recent claim that this motion is observable using interstellar holography (Pen et al. 2014). We estimate the error introduced by use of the RVM and find that it is significant for pulsars with emission over a wide range of $\psi$. The RVM tends to underestimate the range of $\psi$ over which emission is visible. We suggest that the geometry alone strongly favors the visible pulsar radio being emitted at a heights more than ten percent of the light-cylinder distance, where our neglect of retardation effects becomes significant.