Limiting masses and radii of neutron stars and their implications

Abstract

We combine the equation of state of dense matter up to twice nuclear saturation density ${n}_{\mathrm{sat}}$ obtained using chiral effective field theory $(\ensuremath{\chi}\mathrm{EFT})$ 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 $\ensuremath{\chi}\mathrm{EFT}$ 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 $\ensuremath{\sim}1.4\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\ensuremath{\bigodot}}$ and $\ensuremath{\sim}2.0\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\ensuremath{\bigodot}}$ stars. Including $\ensuremath{\chi}\mathrm{EFT}$ predictions from ${n}_{\mathrm{sat}}$ to $2\phantom{\rule{0.16em}{0ex}}{n}_{\mathrm{sat}}$ reduces the permitted ranges of the radius of a $1.4\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\ensuremath{\bigodot}}$ star, ${R}_{1.4}$, by $\ensuremath{\sim}3.5\phantom{\rule{0.16em}{0ex}}\text{km}$. If observations indicate ${R}_{1.4}<11.2\phantom{\rule{0.16em}{0ex}}\text{km}$, then our study implies that either the squared speed of sound ${c}_{s}^{2}>1/2$ for densities above $2\phantom{\rule{0.16em}{0ex}}{n}_{\mathrm{sat}}$ or that $\ensuremath{\chi}\mathrm{EFT}$ breaks down below $2\phantom{\rule{0.16em}{0ex}}{n}_{\mathrm{sat}}$. We also comment on the nature of the secondary compact object in GW190814 with mass $\ensuremath{\simeq}2.6\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\ensuremath{\bigodot}}$ and discuss the implications of massive neutron stars $>2.1\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\ensuremath{\bigodot}}\phantom{\rule{0.16em}{0ex}}(2.6\phantom{\rule{0.16em}{0ex}}{\mathrm{M}}_{\ensuremath{\bigodot}})$ in future radio and gravitational-wave searches. Some form of strongly interacting matter with ${c}_{s}^{2}>0.35\phantom{\rule{0.16em}{0ex}}(0.55)$ must be realized in the cores of such massive neutron stars. In the absence of phase transitions below $2\phantom{\rule{0.16em}{0ex}}{n}_{\mathrm{sat}}$, the small tidal deformability inferred from GW170817 lends support for the relatively small pressure predicted by $\ensuremath{\chi}\mathrm{EFT}$ for the baryon density ${n}_{\mathrm{B}}$ in the range $1\text{--}2\phantom{\rule{0.16em}{0ex}}{n}_{\mathrm{sat}}$. Together they imply that the rapid stiffening required to support a high maximum mass should occur only when ${n}_{\mathrm{B}}\ensuremath{\gtrsim}1.5\text{--}1.8\phantom{\rule{0.16em}{0ex}}{n}_{\mathrm{sat}}$.