Nuclear parameter inference with semi-agnostic priors

Radio pulsar timing, X-ray pulse profile modeling, and gravitational-wave detections of binary mergers involving at least one neutron star probe the properties of dense, neutron-rich matter in thermodynamic regimes inaccessible to nuclear laboratories. Such inference relies on building appropriate equation-of-state priors, such as the recently introduced semi-agnostic constructions that incorporate nuclear theory and experimental information available in low- to intermediate-density regimes, while offering the necessary flexibility at high density. In this paper, we assess how detections of mass, radius, and tidal deformability for low-mass or high-mass neutron stars contribute to constraining nuclear empirical parameters in an inference based on semi-agnostic equation-of-state priors. We first assessed the correlation factors between nuclear empirical parameters and the zero-temperature and beta-equilibrated pressure in different density regimes. We then simulated observations for three nucleonic equations of state to test the recovery of the corresponding nuclear empirical parameters. We show that not all nuclear empirical parameters significantly correlate with the pressure and find that they compete in the high-density regime, which challenges their inference. We also find that using semi-agnostic constructions instead of assuming a nucleonic content up to the highest densities in the neutron-star core can help recover the true nuclear empirical parameters with more accuracy. Parametrizing the high-density regime of the equation of state with the nucleonic meta-model can bias the inference of nuclear empirical parameters; semi-agnostic constructions provide a solution to this problem. However, many nuclear parameters contribute similarly to the construction of the baryonic pressure. We find that they are difficult to infer independently, even with extremely precise measurements.