Competition between delta isobars and hyperons and properties of compact stars

Abstract

The $\Delta$-isobar degrees of freedom are included in the covariant density functional (CDF) theory to study the equation of state (EoS) and composition of dense matter in compact stars. In addition to $\Delta$'s we include the full octet of baryons, which allows us to study the interplay between the onset of delta isobars and hyperonic degrees of freedom. Using both the Hartree and Hartree-Fock approximation we find that $\Delta$'s appear already at densities slightly above the saturation density of nuclear matter for a wide range of the meson-$\Delta$ coupling constants. This delays the appearance of hyperons and significantly affects the gross properties of compact stars. Specifically, $\Delta$'s soften the EoS at low densities but stiffen it at high densities. This softening reduces the radius of a canonical $1.4 M_\odot$ star by up to 2~km for a reasonably attractive $\Delta$ potential in matter, while the stiffening results in larger maximum masses of compact stars. We conclude that the hypernuclear CDF parametrizations that satisfy the 2$M_\odot$ maximum mass constraint remain valid when $\Delta$ isobars are included, with the important consequence that the resulting stellar radii are shifted toward lower values, which is in agreement with the analysis of neutron star radii.