Sensitivity of the Neutron Star Equation of State Inferences to Mass and Radius Measurements

Technical Summary: Sensitivity of the Neutron Star Equation of State Inferences to Mass and Radius Measurements

Problem Statement
Determining the Equation of State (EoS) of neutron star (NS) matter remains a primary challenge in nuclear physics and astrophysics, as the superdense matter in NS cores is inaccessible to laboratory experiments. While numerous observational constraints exist (masses, radii, tidal deformabilities), the extent to which specific classes of observations—particularly mass versus radius measurements—qualitatively versus quantitatively constrain the EoS is a subject of ongoing debate. Previous works have utilized various parameterization schemes, often facing systematic biases or debates regarding the necessity of non-parametric approaches versus phenomenological models. This work aims to update previous EoS inferences with recent observational data and theoretical constraints, and to systematically isolate the impact of different observation classes on the resulting EoS constraints.

Methodology
The authors employ an explicit Inverse Oppenheimer-Volkoff Mapping (IOVM) based on a universal three-parametric approximation for the EoS, as established in their previous work (Paper I). This approach relies on the finding that the EoS in the core density range $\rho_0 \dots \rho_{tov}$ can be described by a universal function dependent on three parameters: the central pressure ($P_{tov}$) and density ($\rho_{tov}$) of the maximum-mass NS, and the radius ratio $r_{1/2} = R(M_{tov}/2)/R_{tov}$.

The study updates the methodology and data sets from Paper I in the following ways:

1. Theoretical Constraints:
   • Chiral Effective Field Theory ($\chi$EFT): Imposed as a prior corridor for the low-density regime ($\rho < 1.5\rho_0$).
   • Perturbative Quantum Chromodynamics (pQCD): Used to set an upper limit on $P_{tov}$ as a function of $\rho_{tov}$ for high densities, ensuring causality without relying on EoS interpolation above $\rho_{tov}$.
   • Causality and Geometry: Retained the causality condition ($c_{s,tov} \leq c$) and the phenomenological constraint $r_{1/2} > 1$.
2. Observational Data Updates:
   • Revised mass measurements for PSR J1614–2230 and PSR J0952–0607.
   • Exclusion of PSR J0348+0432 and PSR J2215+5135 due to remeasured masses or lack of robustness against systematics.
   • Updated X-ray spectroscopy results for PSR J0740+6620 and PSR J0030+0451 based on recent NICER analyses.
   • Inclusion of two new NICER objects (PSR J0614–3329 and PSR J1231–1411).
   • Retention of the GW170817 event and its electromagnetic counterpart (AT2017gfo/GRB 170817A) as a constraint on the maximum mass ($M_{tov}$).

The authors perform Bayesian inference by fitting the three-parametric model to these updated constraints. They further decompose the analysis by creating distinct data subsets: a "minimal" set (only $M_{tov} \gtrsim 2 M_\odot$), a "min+masses" set (high-mass pulsars and GW170817 upper limit), and a "min+radii" set (objects with both mass and radius measurements). Finally, they simulate hypothetical future observations to test sensitivity.

Key Contributions and Results

1. Updated Constraints: The revised constraints on the EoS are consistent with, but tighter than, those in Paper I. The updates result from a combination of new observational data and refined theoretical inputs (specifically the $\chi$EFT corridor and pQCD limits). The most significant shift occurs at low densities ($\rho \lesssim 2\rho_0$) due to the implementation of the chiral corridor, which lowers the upper boundary of the EoS credibility band.
2. Dominance of Theoretical and Mass Constraints: The analysis reveals that theoretical constraints (causality, pQCD, $\chi$EFT) combined with the requirement that $M_{tov} > \sim 2 M_\odot$ dominate the EoS inference across most density ranges.
   • Mass Measurements: Observations of masses well above $2 M_\odot$ (e.g., spider pulsars) and upper limits on $M_{tov}$ improve constraints over a wide density range, effectively narrowing the credible region for the entire EoS curve.
   • Radius Measurements: Radius measurements primarily refine constraints in the low-density regime ($\rho \lesssim 2\rho_0$). They do not qualitatively alter the EoS inference at higher densities.
3. Quantitative vs. Qualitative Impact: The authors find that existing observations of NS radii improve the EoS inference quantitatively (narrowing error bars) but not qualitatively (shifting the central trend or excluding new physics regimes). The posterior distributions for NS properties settle around the "ultimate" results even with limited constraints, provided the fundamental theoretical limits and the $M_{tov} > 2 M_\odot$ condition are met.
4. Sensitivity to Future Observations:
   • Precise Radius of Canonical NS: A hypothetical precise measurement of a $1.4 M_\odot$ NS radius would shrink the $M-R$ credibility band by a factor of 2–3 for low/moderate masses but would not significantly alter high-density constraints or the uncertainty in $M_{tov}$.
   • Extremely Massive NS: The most impactful hypothetical observation would be the detection of an extremely massive NS (e.g., $M \approx 2.4 - 2.6 M_\odot$) or a significantly improved upper limit on $M_{tov}$. Such a measurement would tighten constraints across the entire density range. However, even a detection of a $2.5 - 2.6 M_\odot$ NS would not qualitatively change the current understanding of the EoS within the existing framework, though it would reduce the allowed parameter space significantly.
   • New Physics: Observations lying well outside the current allowed region (e.g., $R < 10$ km or $M > 2.7 M_\odot$) would point to new physics, such as strong first-order phase transitions or violations of current theoretical limits, necessitating a revision of the framework.

Significance and Claims
The paper claims that the current understanding of the NS EoS is robustly anchored by theoretical limits and the existence of massive neutron stars, rather than by precise radius measurements of canonical stars. The authors emphasize that while future radius measurements will continue to refine low-density constraints, the most effective path to improving EoS knowledge is tightening the constraints on the maximum neutron star mass ($M_{tov}$).

The study concludes that single observations, even with high precision, are unlikely to dramatically alter the current EoS constraints unless they reveal physics beyond the current theoretical manifold (e.g., phase transitions). The proposed semi-analytic three-parametric approach is presented as an efficient tool for analyzing the cumulative impact of numerous future observations, such as those expected from next-generation gravitational wave detectors. The authors caution that if future data strongly contradicts current constraints, it would signal new physics in NS cores, rendering the current parameterization inapplicable.