A novel approach for the analysis of the geometry involved in determining light curves of pulsars

TL;DR

This paper introduces a differential geometry-based method using Frenet-Serret equations to model magnetic lines in pulsar magnetospheres, enabling detailed simulations of light curves and spectra.

Contribution

It presents a novel numerical framework combining magnetic line geometry with emission modeling to produce multi-frequency pulsar light curves.

Findings

Provides a step-by-step numerical recipe for emission map computation.

Offers benchmark tests demonstrating the method's effectiveness.

Enables simultaneous analysis of geometry and radiation spectrum.

Abstract

In this work, we introduce the use of the differential geometry Frenet-Serret equations to describe a magnetic line in a pulsar magnetosphere. These equations, which need to be solved numerically, fix the magnetic line in terms of their tangent, normal, and binormal vectors at each position, given assumptions on the radius of curvature and torsion. Once the representation of the magnetic line is defined, we provide the relevant set of transformations between reference frames; the ultimate aim is to express the map of the emission directions in the star co-rotating frame. In this frame, an emission map can be directly read as a light curve seen by observers located at a certain fixed angle with respect to the rotational axis. We provide a detailed step-by-step numerical recipe to obtain the emission map for a given emission process, and give a set of simplified benchmark tests. Key to our approach is that it offers a setting to achieve an effective description of the system's geometry {\it together} with the radiation spectrum. This allows to compute multi-frequency light curves produced by a specific radiation process (and not just geometry) in the pulsar magnetosphere, and intimately relates with averaged observables such as the spectral energy distribution.