2025ApJ...981...99Q

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 data set 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 ± 0.07 M_⊙ and the inferred equatorial radius is ${R}_{{\rm{eq}}}=9.9{1}_{-0.86}^{+0.88}$ 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 T. Salmi et al. ($M=1.0{4}_{-0.03}^{+0.05}$M_⊙, R_eq = 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 nonantipodal, which is not consistent with a centered dipole magnetic field and suggests a complex magnetic field structure.