Combining the Mass--Radius Posteriors of J0030+0451 Allowing for Unknown Model Systematics

Abstract

The NASA Neutron star Interior Composition Explorer (\emph{NICER}) mission measures the X-ray pulse profiles of select millisecond pulsars and uses sophisticated pulse profile modeling (PPM) techniques to constrain their masses ($M$) and radii ($R$), in order to probe the state of matter in their interiors. One of the most studied pulsars, PSR J0030+0451, has been analyzed by multiple groups using different choices of hotspot models. The different choices of hotspot prescriptions to fit the same observational data led to different $M$--$R$ posteriors that do not completely agree with one another, resulting in a practical bottleneck for dense-matter equation-of-state (EoS) inference. In this paper, we adapt a robust Bayesian combination framework to the published $M$--$R$ posteriors of PSR J0030+0451 while allowing for unknown systematic uncertainties that might have led to the apparently divergent results. Using this technique, we combine eight existing $M$--$R$ posteriors into a single conservative and reproducible posterior that incorporates unknown model systematics across the currently available analyses and is suitable for direct use in EoS studies. The resulting constraint is $M = 1.46^{+0.09}_{-0.08}\,M_\odot$, $R = 12.69^{+0.64}_{-0.55}\,\mathrm{km}$, and compactness $C = 0.172^{+0.006}_{-0.007}$ (68\% credible interval). Incorporating this combined J0030+0451 constraint in an EoS-agnostic joint analysis with PSR~J0437--4715 and GW170817 yields $R_{1.4} = 11.98^{+0.58}_{-0.68}\,\mathrm{km}$ and $\Lambda_{1.4} = 320^{+216}_{-138}$. Our results provide a combined $M$--$R$ constraint for J0030+0451 and a practical framework for incorporating cross-model uncertainty into neutron star EoS inference pipelines.