Amorphous state in the mixed phase of quark-hadron phase transition in protoneutron stars

TL;DR

This paper investigates the hadron-quark mixed phase in protoneutron stars, revealing that high lepton-number fractions lead to an amorphous state without crystalline structures, affecting the star's equation of state and astrophysical phenomena.

Contribution

It demonstrates that in protoneutron stars, the mixed phase becomes amorphous due to charge screening, eliminating crystalline structures and density discontinuities.

Findings

No crystalline 'pasta' structures at high lepton fractions

The system forms an amorphous state with large, unstable pasta structures

The equation of state simplifies to a binary system approximation

Abstract

We study the hadron-quark mixed phase in protoneutron stars, where neutrinos are trapped and lepton number becomes a conserved quantity besides the baryon number and electric charge. Considering protoneutron-star matter as a ternary system, the Gibbs conditions are applied together with the Coulomb interaction. We find that there no crystalline ("pasta") structure appears in the regime of high lepton-number fraction; the size of pasta becomes very large and the geometrical structure becomes mechanically unstable due to the charge screening effect. Consequently the whole system is separated into two bulk regions like an amorphous state, where the surface effect is safely neglected. There, the local charge neutrality is approximately attained, so that the equation of state is effectively reduced to the one for a binary system. Hence, we conclude that there is no possibility for the density discontinuity to appear in protoneutron-star matter, which is a specific feature in a pure system. These features are important when considering astrophysical phenomena such as supernova explosions or radiation of the gravitational wave from protoneutron stars.