A Hidden Degeneracy in Two-Spot Models for Thermal X-Ray Pulse-Profile Fitting

TL;DR

This paper identifies an intrinsic degeneracy in two-spot models for thermal X-ray pulse-profile fitting, which can bias neutron star radius estimates and explain multi-modal posterior structures.

Contribution

The study reveals a fundamental degeneracy in simplified two-spot models affecting parameter inference in thermal X-ray pulse-profile analysis.

Findings

Degeneracy causes multi-modal likelihood surfaces in models with Doppler effects.

Inferred neutron star radius can be biased by up to 30%.

Degeneracy explains multi-modal structures in synthetic pulse-profile evaluations.

Abstract

We discover an intrinsic degeneracy in the semi-analytic two-spot model for parameter inference in thermal X-ray pulse-profile modeling. Although this degeneracy exists in our simplified model with two small circular hot spots and without Doppler effects, it causes the likelihood surface of parameter inference based on ST-U and more complex models with Doppler effects to have multi-modal structures. Consequently, the posterior surface may also exhibit multi-modal structures if there is insufficient prior knowledge of parameters. Because of this, the inferred value of the neutron star radius can be biased even by $30\%$. This finding also provides a promising way to explain the multi-modal structures discovered in the evaluation of recovery performance using synthetic pulse-profiles that mimic the PSR J0030+0451 pulse-profiles~\citep{Vinciguerra2023,Vinciguerra2024}. Our work may have profound implications for the reanalysis of NICER data and the analysis of upcoming eXTP data.