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We demonstrate that ab-initio calculations in QCD at high densities offer significant and nontrivial information about the equation of state of matter in the cores of neutron stars, going beyond that which is obtainable from current astrophysical observations. We do so by extrapolating the equation of state to neutron-star densities using a Gaussian process and conditioning it sequentially with astrophysical observations and QCD input. Using our recent work, imposing the latter does not require an extrapolation to asymptotically high density. We find the QCD input to be complementary to the astrophysical observations, offering strong additional constraints at the highest densities reached in the cores of neutron stars; with the QCD input, the equation of state is no longer prior dominated at any density. The QCD input reduces the pressure and speed of sound at high densities, and it predicts that binary collisions of equal-mass neutron stars will produce a black hole with greater than 95% (68%) credence for masses M ≥ 1.38M ⊙ (M ≥ 1.25M ⊙). We provide a Python implementation of the QCD likelihood function so that it can be conveniently used within other inference setups.

The equation of state of neutron-star cores can be constrained by requiring a consistent connection to the perturbative Quantum Chromodynamics (QCD) calculations at high densities. The constraining power of the QCD input depends on uncertainties from missing higher-order terms, the choice of the unphysical renormalization scale, and the reference density where QCD calculations are performed. Within a Bayesian approach, we discuss the convergence of the perturbative QCD series, quantify its uncertainties at high densities, and present a framework to systematically propagate the uncertainties down to neutron-star densities. We find that the effect of the QCD input on the neutron-star inference is insensitive to the various unphysical choices made in the uncertainty estimation.

I discuss why state-of-the art perturbative QCD calculations of the equation of state at large chemical potential that are reliable at asymptotically high densities constrain the same equation of state at neutron-star densities. I describe how these theoretical calculations affect the EOS at lower density. I argue that the ab-initio calculations in QCD offer significant information about the equation of state of the neutron-star matter, which is complementary to the current astrophysical observations.