# Atmospheric Structure and Radiation Pattern for Neutron-Star Polar Caps Heated by Magnetospheric Return Currents

## TL;DR

This paper models how magnetospheric return currents heat neutron-star polar caps, affecting atmospheric temperature profiles and radiation beaming, which is crucial for interpreting NICER observations of pulsar radii.

## Contribution

It provides detailed calculations of particle stopping mechanisms, heat deposition, and radiation patterns, improving models of neutron-star polar cap emission for NICER data analysis.

## Key findings

- Low-energy particles deposit energy in upper atmosphere layers, altering beaming patterns.
- High-energy particles penetrate deeper, enabling deep-heating models.
- Beaming patterns differ significantly from radiative equilibrium models.

## Abstract

The Neutron-star Interior Composition ExploreR (NICER) is collecting data to measure the radii of neutron stars by observing the pulsed emission from their surfaces. The primary targets are isolated, rotation-powered pulsars, in which the surface polar caps are heated by bombardment from magnetospheric currents of electrons and positrons. We investigate various stopping mechanisms for the beams of particles that bombard the atmosphere and calculate the heat deposition, the atmospheric temperature profiles, and the energy spectra and beaming of the emerging radiation. We find that low-energy particles with {\gamma} $\sim 2-10$ deposit most of their energy in the upper regions of the atmosphere, at low optical depth, resulting in beaming patterns that are substantially different than those of deep-heated, radiative equilibrium models. Only particles with energies {\gamma} $\gtrsim 50$ penetrate to high optical depths and fulfill the conditions necessary for a deep-heating approximation. We discuss the implications of our work for modeling the pulse profiles from rotation-powered pulsars and for the inference of their radii with NICER observations.