Impact of symmetry energy on sound speed and spinodal decomposition in dense neutron-rich matter

Using a meta model for nuclear Equation of State (EOS) with its parameters constrained by astrophysical observations and terrestrial nuclear experiments, we examine effects of nuclear EOS especially its symmetry energy E${}_{sym}$(ρ) term on the speed of sound squared C${}_s^2$(ρ) and the critical density ρ${}_t$ where C${}_s^2$(ρ${}_t$) vanishes (indicating the onset of spinodal decomposition) in both dense neutron-rich nucleonic matter relevant for relativistic heavy-ion collisions and the cold n+p+e+µ matter in neutron stars at β-equilibrium. Unlike in nucleonic matter with fixed values of the isospin asymmetry δ, in neutron stars with a density dependent isospin profile δ(ρ) determined consistently by the β-equilibrium and charge neutrality conditions, the C${}_s^2$(ρ) almost always show a peak and then vanishes at ρ${}_t$. The latter strongly depends on the high-density behavior of E${}_{sym}$(ρ) if the skewness parameter J${}_0$ characterizing the stiffness of high-density symmetric nuclear matter (SNM) EOS is not too far above its currently known most probable value of about -190 MeV inferred from recent Bayesian analyses of neutron star observables. Moreover, in the case of having a super-soft E${}_{sym}$(ρ) that is decreasing with increasing density above about twice the saturation density of nuclear matter, the ρ${}_t$ is significantly lower than the density where the E${}_{sym}$(ρ) vanishes (indicating the onset of isospin-separation instability and pure neutron matter formation) in neutron star cores.