Quantum Nucleation of Two-Flavor Quark Matter in Neutron Stars

Rates for nucleation of two-flavor quark matter in a neutron star core, originally composed of nuclear matter in β equilibrium, are calculated at zero temperature by a quantum tunneling analysis incorporating the electrostatic energy. We find that a nucleated droplet would develop into bulk matter due to electron screening effects. ∗) E-mail address: [email protected] ∗∗) E-mail address: [email protected] 1 typeset using PTPTEX.sty The possibility that quark matter could exist in neutron stars and the astrophysical consequences have been considered for the past two decades. (See, e.g., Refs. 1)-3).) Usually, the main question was at what pressure the free energy per baryon for electrically neutral quark matter becomes less than that for nuclear matter. Recently, Glendenning discovered that, by relaxing the constraint of local charge neutrality, a phase where quark and nuclear matter in β equilibrium coexist in a uniform sea of electrons could appear for a finite range of pressures. This is because the presence of strange and down quarks plays a role in reducing the electron Fermi energy and in increasing the proton fraction of nuclear matter. His work and the subsequent work by Heiselberg et al. claimed that such a mixed phase could exhibit spatial structure such as quark matter droplets embedded in nuclear matter due to surface and Coulomb effects. As the star whose core consists of nuclear matter in β equilibrium spins down or accretes matter from its companion star, the central density could become sufficiently large for the mixed phase to be stable. Whether the mixed phase actually nucleates, however, depends on the occurrence of the dynamical processes leading to its nucleation. The first of these processes should be the conversion of nuclear matter to two-flavor quark matter, since the conversion to three-flavor quark matter, which requires many simultaneous weak interactions, is unlikely to occur. In this paper, therefore, we consider at what pressure a droplet of two-flavor quark matter forms in nuclear matter and whether it develops into bulk matter or remains finite. We begin by describing the bulk properties of the various components for densities well above the nuclear saturation density. For nucleons, we write the simple formula for the energy density adopted by Heiselberg et al.: