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The dense matter equation of state (EOS) determines neutron star (NS)structure but can be calculated reliably only up to one to two times thenuclear saturation density, using accurate many-body methods that employnuclear interactions from chiral effective field theory constrained byscattering data. In this work, we use physically motivated ansatzes for thespeed of sound $c_S$ at high density to extend microscopic calculations ofneutron-rich matter to the highest densities encountered in stable NS cores. Weshow how existing and expected astrophysical constraints on NS masses and radiifrom X-ray observations can constrain the speed of sound in the NS core. Weconfirm earlier expectations that $c_S$ is likely to violate the conformallimit of $c_S^2\leq c^2/3 $, possibly reaching values closer to the speed oflight $c$ at a few times the nuclear saturation density, independent of thenuclear Hamiltonian. If QCD obeys the conformal limit, we conclude that therapid increase of $c_S$ required to accommodate a $2 $ M$_\odot$ NS suggests aform of strongly interacting matter where a description in terms of nucleonswill be unwieldy, even between one and two times the nuclear saturationdensity. For typical NSs with masses in the range $1.2-1.4~$ M$_\odot$, we findradii between $10$ and $14$ km, and the smallest possible radius of a $1.4$M$_{\odot}$ NS consistent with constraints from nuclear physics andobservations is $8.4$ km. We also discuss how future observations couldconstrain the EOS and guide theoretical developments in nuclear physics.

Constraining the speed of sound inside neutron stars with chiral effective field theory interactions and observations