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A New Bayesian Framework with Natural Priors to Constrain the Neutron Star Equation of State

Boyang Sun, Tianqi Zhao, James M. Lattimer

Abstract

We propose a new Bayesian framework to infer the neutron star equation of state (EOS) from mass and radius observations and neutron matter theory by defining priors that directly parameterize mass-radius space instead of pressure-energy density space. We use direct and accurate inversion approximations to map mass-radius relations to the underlying EOS. We systematically compare its EOS inferences with those inferred from traditional EOS parameterizations, taking care to quantify the systematic prior uncertainties of both. Our results show that prior uncertainties should be included in all Bayesian approaches. The more natural alternative framework provides broader coverage of the physically allowed mass-radius space, especially small radius configurations, and yields enhanced computational efficiency and substantially reduced dependence on prior choices. Our results demonstrate that direct parameterization in observed space offers a robust and efficient alternative to traditional methods.

A New Bayesian Framework with Natural Priors to Constrain the Neutron Star Equation of State

Abstract

We propose a new Bayesian framework to infer the neutron star equation of state (EOS) from mass and radius observations and neutron matter theory by defining priors that directly parameterize mass-radius space instead of pressure-energy density space. We use direct and accurate inversion approximations to map mass-radius relations to the underlying EOS. We systematically compare its EOS inferences with those inferred from traditional EOS parameterizations, taking care to quantify the systematic prior uncertainties of both. Our results show that prior uncertainties should be included in all Bayesian approaches. The more natural alternative framework provides broader coverage of the physically allowed mass-radius space, especially small radius configurations, and yields enhanced computational efficiency and substantially reduced dependence on prior choices. Our results demonstrate that direct parameterization in observed space offers a robust and efficient alternative to traditional methods.
Paper Structure (10 equations, 2 figures)

This paper contains 10 equations, 2 figures.

Figures (2)

  • Figure 1: Left panel: An illustration of the PMR method, showing the adopted $M$-$R$ mesh (thin lines) as well as the allowed $M$-$R$ boundary (thick red line). Sample $M$-$R$ curves are indicated as purple lines. 95% confidence regions for the PMR$_u$ and PMR$_w$ priors are shown as the blue region and enclosed by the dotted dashed orange curve, respectively. Right panel: Together with the allowed $M$-$R$ bounds and the PMR mesh as a backdrop, the 95% confidence regions for the traditional Bayesian methods using the PP4 and spectral parameterized EOSs are shown. For both, parameters were sampled either uniformly (subscript "u”), log-uniformly (subscript "ulog”), or from a Gaussian distribution (subscript "g”).
  • Figure 2: Comparison of Bayesian results of PMR (left) and traditional methods (right). Left: the upper panel shows the 1-$\sigma$ and 2-$\sigma$ boundaries of three priors discussed in Methodology. The coral-colored shaded region in the left panel is a region our inversion formula may not reach, corresponding to masses less than $1/3M_{\rm max}$, below which the boundaries are obtained by linear interpolation. The first lower panel shows the ratios of $\sigma_{prior}$ and $\sigma_{model}$ to $\sigma_{tot}$ for $300-1400$ MeV fm$^{-3}$ for 1-$\sigma$ (dashed lines) and 2-$\sigma$ (solid lines), respectively. The second lower panel shows the ratio of $\sigma_{tot}$ of the PMR to the traditional methods. Right: similar to the left panel, but for traditional Bayesian methods, with the second lower panel showing the ratios of $\sigma_{prior}$ of the two approaches.