Neutron star matter with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="normal">Δ</mml:mi></mml:math> isobars in a relativistic quark model

Abstract

The possibility of the appearance of $\mathrm{\ensuremath{\Delta}}$(1232) isobars in neutron star matter and the so-called $\mathrm{\ensuremath{\Delta}}$ puzzle is investigated in a relativistic quark model where the confining interaction for quarks inside a baryon is represented by a phenomenological average potential in an equally mixed scalar-vector harmonic form. The hadron-hadron interaction in nuclear matter is then realized by introducing additional quark couplings to $\ensuremath{\sigma}$, $\ensuremath{\omega}$, and $\ensuremath{\rho}$ mesons through mean-field approximations. The hyperon couplings are fixed from the hyperon optical potentials at saturation density. Effects of moderate variations in the $\mathrm{\ensuremath{\Delta}}\text{\ensuremath{-}}\ensuremath{\omega}$ and $\mathrm{\ensuremath{\Delta}}\text{\ensuremath{-}}\ensuremath{\rho}$ coupling strengths on the critical density of forming $\mathrm{\ensuremath{\Delta}}$ resonances and on the mass-radius relation of neutron stars is studied. We have also made an attempt to study the impact of in-medium mass variations of the $\mathrm{\ensuremath{\Delta}}$ baryon on the structure of neutron stars. It is observed that, within the constraints of the masses of the precisely measured massive pulsars PSR J0348+0432 and PSR $\mathrm{J}1614\ensuremath{-}2230$, neutron stars with a composition of both $\mathrm{\ensuremath{\Delta}}$ isobars and hyperons are possible in the present model.