From chiral EFT to perturbative QCD: a Bayesian Model Mixing approach to neutron-star matter

Constraining the equation of state (EOS) of strongly interacting, dense matter is the focus of intense experimental, observational, and theoretical effort. Chiral effective field theory (χEFT) can describe the EOS between the typical densities of nuclei and those in the outer cores of neutron stars while perturbative QCD (pQCD) can be applied to properties of deconfined quark matter, both with quantified theoretical uncertainties. However, describing the complete range of densities between nuclear saturation and an almost-free quark gas with a single EOS that has well-quantified uncertainties is a challenging problem. We argue that Bayesian multi-model inference from χEFT and pQCD can help bridge the gap between the two theories. We develop a correlated Bayesian model mixing approach that uses a Gaussian Process (GP) to assimilate different information into a single QCD EOS for charge-neutral, beta-equilibrated strongly interacting matter. In the present implementation, this mixed EOS is informed solely by those of χEFT and pQCD, together with the associated truncation errors. The GP is trained on the pressure as a function of number density in the low-density and high-density regions where χEFT and pQCD are, respectively, valid. A variety of GP kernels are examined, and sensitivity to the smoothness properties & correlation structure of the GP investigated. Draws from the GP representation of the EOS constrained by pQCD and ChiEFT are then used to solve for neutron-star structure. Finally, we discuss how measurements of neutron-star properties can be combined with the information in our GP equation of state to make inferences about strongly interacting matter at densities where neither pQCD or χEFT is directly applicable.