Limiting masses and radii of neutron stars and their implications

We combine equation of state of dense matter up to twice nuclear saturation density ($n_{\rm sat}=0.16\, \text{fm}^{-3}$) obtained using chiral effective field theory ($\chi$EFT), and recent observations of neutron stars to gain insights about the high-density matter encountered in their cores. A key element in our study is the recent Bayesian analysis of correlated EFT truncation errors based on order-by-order calculations up to next-to-next-to-next-to-leading order in the $\chi$EFT expansion. We refine the bounds on the maximum mass imposed by causality at high densities, and provide stringent limits on the maximum and minimum radii of $\sim1.4\,{\rm M}_{\odot}$ and $\sim2.0\,{\rm M}_{\odot}$ stars. Including $\chi$EFT predictions from $n_{\rm sat}$ to $2\,n_{\rm sat}$ reduces the permitted ranges of the radius of a $1.4\,{\rm M}_{\odot}$ star, $R_{1.4}$, by $\sim3.5\, \text{km}$. If observations indicate $R_{1.4}<11.2\, \text{km}$, our study implies that either the squared speed of sound $c^2_{s}>1/2$ for densities above $2\,n_{\rm sat}$, or that $\chi$EFT breaks down below $2\,n_{\rm sat}$. We also comment on the nature of the secondary compact object in GW190814 with mass $\simeq 2.6\,{\rm M}_{\odot}$, and discuss the implications of massive neutron stars $>2.1 \,{\rm M}_{\odot}\,(2.6\,{\rm M}_{\odot})$ in future radio and gravitational-wave searches. Some form of strongly interacting matter with $c^2_{s}>0.35\, (0.55)$ must be realized in the cores of such massive neutron stars. In the absence of phase transitions below $2\,n_{\rm sat}$, the small tidal deformability inferred from GW170817 lends support for the relatively small pressure predicted by $\chi$EFT for the baryon density $n_{\rm B}$ in the range $1-2\,n_{\rm sat}$. Together they imply that the rapid stiffening required to support a high maximum mass should occur only when $n_{\rm B} \gtrsim 1.5-1.8\,n_{\rm sat}$.