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

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 leptonnumber 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.Recently there have been many works about the hadronquark (HQ) phase transition in compact stars [1], where signatures of the phase transition are explored during supernova explosions [2,3] in the spectrum of the gravitational wave [4] and so on. The deconfinement transition might be of the first order at finite density although uncertainties remain, e.g., the equation of state (EOS) of quark matter or deconfinement mechanism [5]. In this case, the HQ-mixed phase appears and the phase equilibrium in the mixed phase must be carefully treated by applying the Gibbs conditions [6]. A simple treatment of the mixed phase may be the bulk Gibbs calculation, where phase equilibrium of two pieces of bulk matter is considered without the electromagnetic interaction. The EOS then looks like the second-order phase transition in the sense of Ehrenfest; there appears no constant-pressure region as in the van der Waals liquid. A realistic treatment of the mixed phase takes into account the finite-size effects, the electromagnetic interaction, and the surface tension. Generally, the properties of the mixed phase strongly depend on the finite-size effects to lead to the inhomogeneous crystalline (pasta) structures [7,8]. The EOS resembles the one given by the bulk Gibbs calculation for the weak surface tension, and close to the one given by the Maxwell construction for the strong surface tension [9,10]. These differences are mainly brought about by the charge-screening effect and rearrangement of the charge distribution in the presence of the Coulomb interaction [11].Here we consider the HQ-phase transition in protoneutron stars (PNSs), where neutrinos are trapped and lepton number is conserved. Consequently there are three conserved quantities-baryon number, electric charge, and lepton number. Thus, PNS matter should be treated as a ternary system, different from the usual neutron star mat...

Interface effects of strange quark matter with density dependent quark masses

“…For a vanishing surface tension, the MP consists of point-like HM and SQM, which is in accordance with the Glendenning construction [38]. For larger σ, due to the relocation of charged particles on the quark-hadron interface, the geometrical structures such as droplet, slab, tube, and bubble become stable [16,[39][40][41][42][43][44]. Those geometrical structures get larger as we increase σ and eventually the quark-hadron interface becomes planar, which is consistent with those obtained with Maxwell construction.…”

Contraction of cold neutron star due to in the presence a quark core

“…i j < i j|ν (12)|i j − ji >. In this relation, the operator ν(12) is the effective nuclear potential.…”

“…Accordingly, a mixed hadronquark phase exists in the neutron star, so that its energy is lower than that of the quark matter and nucleonic matter. Phase transition between quark matter core and hadronic external layers (hadron-quark phase) in neutron star is an interesting subject which has been investigated by many authors [6][7][8][9][10][11][12][13][14][15][16][17][18]. For example, the effects of quark-hadron matter in the center of neutron stars have been studied in Refs.…”

Structure of the hadron-quark mixed phase in protoneutron stars

“…One could consider more realistic profiles (Burgio et al 2011a), but we focus in this work on the difference between phase transition constructions. A fully microscopic treatment of the HQ mixed phase involving finite-size (pasta) structures can only be performed numerically Endo et al 2005Endo et al , 2006Maruyama et al 2007;Yasutake et al 2009Yasutake et al , 2012a. One introduces Coulomb energies and surface energies via a HQ surface tension and then minimizes the (free) energy of a Wigner-Seitz (WS) cell, allowing for different geometrical structures of the quark phase embedded in the hadron phase and vice versa.…”