# Effects of Compton scattering on the neutron star radius constraints in rotation-powered millisecond pulsars

## TL;DR

This study evaluates the impact of using the Thomson approximation versus exact Compton scattering in neutron star atmosphere models, finding minimal bias in radius constraints but some bias in hot spot size and temperature estimates.

## Contribution

It compares the effects of Compton and Thomson scattering models on neutron star parameter constraints, demonstrating the adequacy of the simpler Thomson model for radius measurements.

## Key findings

- Radius constraints are not significantly affected by the scattering model.
- Biases in hot spot size and temperature estimates occur when using the Thomson approximation.
- The Thomson model remains adequate for radius measurements with NICER data.

## Abstract

The aim of this work is to study the possible effects and biases on the radius constraints for rotation-powered millisecond pulsars when using Thomson approximation to describe electron scattering in the atmosphere models, instead of using exact formulation for Compton scattering. We compare the differences between the two models in the energy spectrum and angular distribution of the emitted radiation. We also analyse a self-generated synthetic phase-resolved energy spectrum, based on Compton atmosphere and the most X-ray luminous rotation-powered millisecond pulsars observed by the Neutron star Interior Composition ExploreR (NICER). We derive constraints for the neutron star parameters using both the Compton and Thomson models. The results show that the method works by reproducing the correct parameters with the Compton model. However, biases are found in size and the temperature of the emitting hot spot, when using the Thomson model. The constraints on the radius are still not significantly changed, and therefore the Thomson model seems to be adequate if we are interested only in the radius measurements using NICER.