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Equation-of-state-informed pulse profile modeling

Mariska Hoogkamer1, Nathan Rutherford2, Daniela Huppenkothen1, Benjamin Ricketts1,3, Anna L. Watts1, Melissa Mendes4,5,6, Isak Svensson4,5,6, Achim Schwenk4,5,6, Michael Kramer7 et al.

Kai Hebeler4,5,6, Tuomo Salmi8, and Devarshi Choudhury1

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Phys. Rev. D 113, 063049 – Published 24 March, 2026

DOI: https://doi.org/10.1103/z2hd-w9sy

Abstract

NICER has enabled mass-radius inferences for pulsars using pulse profile modeling (PPM), providing constraints on the equation of state (EOS) of cold, dense matter. To date, PPM and EOS inference have been carried out as two separate steps, with the former using EOS-agnostic priors. This approach has several drawbacks. Ideally, one would perform a fully hierarchical Bayesian inference where the pulse profile and EOS model parameters are jointly fit, but implementing such a framework is complex and computationally demanding. Here, we present an intermediate solution introducing an EOS-informed prior on mass radius into the existing PPM pipeline using normalizing flows. By focusing on the parameter space consistent with certain EOSs, this approach both tightens constraints on neutron star parameters while reducing computational costs and requiring minimal additional implementation effort. We test this approach on two pulsars, PSR J0740+6620 and PSR J0437-4715, and with two EOS model families: a model based on the speed of sound inside the neutron star interior (CS) and a piecewise-polytropic (PP) model. Both EOS models implement constraints from chiral effective field theory calculations of dense matter. For both pulsar datasets, the inferred radius credible intervals are narrower than in the EOS-agnostic case, with CS favoring smaller radii and PP favoring larger radii. For PSR J0437-4715, the EOS-informed priors reveal a new, more extreme geometric mode that is statistically favored but physically questionable. Including the PPM posteriors in the subsequent EOS inference further tightens the mass-radius posteriors through the chiral effective field theory constraints. However, there is also a sensitivity to the high-density extensions, where the PP (CS) model produces a shift toward larger (smaller) radii and corresponding stiffening (softening) of the pressure-energy density relation.

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Corrections

1 April, 2026

Correction: An incorrect version of Fig. 8 was used for publication and has now been replaced with the correct version.

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Phys. Rev. D 113, 063049– Published 24 March, 2026
  • Received 31 October 2025
  • Accepted 2 December 2025
  • Corrected 1 April 2026
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