As above, so below: assessing extremeness of the neutron-star equation of state based on the unstable branch

Microscopic models of neutron-star matter have been widely used in astrophysical applications. The focus of attention has been on densities up to the maximal densities reached in stable neutron stars. The possibility that the underlying model assumptions may have important implications at higher densities has not been addressed. Here, we show that the behaviour at higher densities is strongly constrained by requiring a causal, stable, and thermodynamically consistent extension to the perturbative-QCD regime. We explicitly reveal what that behaviour must be and provide a tool for constructing and visualizing such extensions. We find that purely hadronic models trusted up to the maximal central density often require radically different behaviour at higher densities from that assumed in the original model, while models with additional degrees of freedom fare better. Our analysis disfavors purely nucleonic models for describing all stable neutron stars and supports the appearance of some type of additional degrees of freedom in stable massive neutron stars.