Finite-size effects on the hadron-quark phase transition in neutron stars

Abstract

We study the finite-size effects, like the surface and Coulomb energies, on the hadron-quark mixed phase in neutron stars. The equilibrium conditions for coexisting hadronic and quark phases are derived by minimizing the total energy including the surface and Coulomb contributions, which are different from the Gibbs conditions without finite-size effects. We employ the relativistic mean-field model to describe the hadronic phase, while the Nambu-Jona-Lasinio model with vector interactions is used for the quark phase. It is found that finite-size effects can significantly reduce the region of the mixed phase, and the results lie between those of the Gibbs and Maxwell constructions.We show that a massive star may contain a mixed phase core and its size depends on the surface tension of the hadron-quark interface and the vector coupling between quarks. The repulsive vector interaction in the Nambu-Jona-Lasinio model can stiffen the equation of state of quark matter, and therefore, delay the phase transition and increase the maximum mass of neutron stars.

Chiral pasta: Mixed phases at the chiral phase transition

“…In order to compute the Coulomb energy density (27) in the steplike approximation one first needs to compute the electric field. Due to the symmetry of the problem in all three cases (bubbles, rods, and slabs in unit cells of corresponding shapes), this is best done with the method of Gaussian surfaces.…”

“…Piecewise integration over the radial coordinate then yields the Coulomb energy (27) per unit volume,…”

“…1 Various levels of approximations have been employed in the literature for mixed phases at the quark-hadron transition. Usually, nuclear and quark matter are treated with two different models [21][22][23][24][25][26][27][28][29][30]. In this approach, the profile of a quark-hadron interface cannot be calculated microscopically since this requires knowledge of an effective potential that connects the two phases.…”

Phase transitions in neutron stars and their links to gravitational waves

“…For intermediate values of σ HQ , the full Gibbs formalism, i.e. a full pasta phase calculation, must be used taking into account the formation of phase structures in the mixed phase [138]. Recently, several works have included finite-size effects at the hadron-quark phase transition in a phenomenological way, mimicking the mixed phase by a function which depends on the broadening of the phase transition [30,131,139].…”

Estimation of transport coefficients of dense hadronic and quark matter

“…However, recent observations of massive pulsars [1,2] and the data extracted from the detection of gravitational wave (GW170817) from binary NS merger (BNSM) [3] have put some constraints on the EoS of NSs. Theoretical research also suggest the possibility of hadron-quark phase transition in NS cores and the formation of hybrid stars (HSs) [4,5,6,7,8,9,10,11,12] and even existence of quark stars (QSs) [4,13,14]. For recent review on it, readers can go through the Refs.…”