A model for redistributing heat over the surface of irradiated spider companions

TL;DR

This paper develops a generalized heat redistribution model for irradiated spider companion stars, improving light curve fitting and understanding of binary system properties by incorporating diffusion and convection effects.

Contribution

It introduces a two-dimensional shell model for heat redistribution in irradiated stars, implemented in Icarus, and demonstrates its effectiveness over traditional direct heating models.

Findings

Redistribution effects concentrate near the irradiation terminator.

Models with heat redistribution are more likely than symmetric direct heating.

The best model involves diffusion with a uniformly rotating envelope.

Abstract

Spider pulsars are binary systems containing an energetic millisecond pulsar that intensely irradiates a closely orbiting low-mass companion. Modelling their companion's optical light curves is essential to the study of the orbital properties of the binary, including the determination of the pulsar mass, characterising the pulsar wind and the star itself. We aim to generalise the traditional direct heating model of irradiation, whereby energy deposited by the pulsar wind into the stellar envelope is locally re-emitted, by introducing heat redistribution via diffusion and convection within the outer stellar envelope. We approximate the irradiated stellar envelope as a two-dimensional shell. This allows us to propose an effective equation of energy conservation that can be solved at a reduced computational cost. We then implement this model in the \texttt{Icarus} software and use evidence sampling to determine the most likely convection and diffusion laws for the light curve of the redback companion of PSR J2215+5135. Redistribution effects concentrate near the terminator line of pulsar irradiation, and can create apparent hot and cold spots. Among the models tested for PSR J2215+5135, we find that all models with heat redistribution are more likely than symmetric direct heating. The best-fitting redistribution model involves diffusion together with a uniformly rotating envelope. However, we caution that all models still present serious systematic effects, and that prior knowledge from pulsar timing, spectroscopy and distance are key to determine with certainty the most accurate redistribution law. We propose an extension of the direct heating framework that allows for exploring a variety of heat redistribution effects. Future work is necessary to determine the relevant laws from first principles and empirically using complementary observations.