2026/07/20 by Bao-An Li, Xavier Grundler
#astro-ph.HE #astro-ph.GA #astro-ph.SR #nucl-ex #nucl-th
Twin neutron stars (NSs), characterized by identical gravitational masses but different radii, are among the most promising astrophysical signatures of a strong first-order hadron--quark phase transition in supradense matter. We investigate how increasingly precise NS radius measurements improve the Bayesian inference of twin-star observability using mock radius data for a canonical 1.4 M_\odot NS. Radius uncertainties are varied from the current level of about 0.9 km to the ≈ 0.1 km precision anticipated from future X-ray and gravitational-wave observations. We quantify the information gained using the posterior distribution of the maximum twin-star radius separation ΔR together with an analytical model of branch distinguishability and complementary information-theoretic measures based on the branch observational efficiency and the Shannon entropy. The combined analyses reveal three inference regimes: a prior-dominated regime for σR \gtrsim 0.6 km, a rapid information-gain regime for 0.2 \lesssim σR \lesssim 0.6 km, and an information-saturation regime for σR \lesssim 0.2 km. These complementary analyses consistently indicate that radius measurements with a precision of about 0.2 km already extract most of the information available for identifying twin NSs within the present Bayesian framework. Beyond establishing a quantitative observational benchmark for future high-precision radius measurements, this work provides a general Bayesian framework for quantifying the information gain from progressively more precise observations and identifying the point of diminishing scientific returns.