One of the primary goals of Neutron Star Interior Composition Explorer (NICER)-like X-ray missions is to impose stringent constraints on the neutron star equation of state by precisely measuring their masses and radii. NICER has recently expanded the dataset of inferred mass-radius relations for neutron stars, including four rotation-powered millisecond pulsars PSR J0030+0451, PSR J0740+6620, PSR J0437-4715, and PSR J1231-1411. In this work, the mass-radius relation and X-ray emitting region properties of PSR J1231-1411 are inferred with an independent pulse profile modeling based on the spherical star Schwarzschild-spacetime and Doppler approximation. With one single-temperature elongated hot spot and one single-temperature crescent hot spot, the inferred gravitational mass is M=1.12±0.07M⊙ and the inferred equatorial radius is Req=9.91−0.86+0.88 km (68% credible intervals). It provides an alternative geometry configuration of the X-ray emitting region for PSR J1231-1411 to sufficiently explain the observation data of NICER and XMM-Newton. The inferred radius is smaller than that derived by \citet{salmi2024nicer} (M=1.04−0.03+0.05M⊙, Req=12.6±0.3 km), and the inferred mass is slightly higher in this work. The inferred geometry configurations of the X-ray emitting region in both works are non-antipodal, which is not consistent with a centered dipole magnetic field and suggests a complex magnetic field structure.
@article{arxiv.2502.09147,
title = {PSR J1231-1411 revisited: Pulse Profile Analysis of X-ray Observation},
author = {Liqiang Qi and Shijie Zheng and Juan Zhang and Mingyu Ge and Ang Li and Shuang-Nan Zhang and Fang-Jun Lu and Han-Long Peng and Liang Zhang and Hua Feng and Zhen Zhang and Yupeng Xu and Zheng-Wei Li and Li-Ming Song and Shu Zhang and Lian Tao and Wentao Ye},
journal= {arXiv preprint arXiv:2502.09147},
year = {2025}
}