Shear modulus of the hadron-quark mixed phase

Abstract

Robust arguments predict that a hadron-quark mixed phase may exist in the cores of some "neutron" stars. Such a phase forms a crystalline lattice with a shear modulus higher than that of the crust due to the high density and charge separation, even allowing for the effects of charge screening. This may lead to strong continuous gravitational-wave emission from rapidly rotating neutron stars and gravitational-wave bursts associated with magnetar flares and pulsar glitches. We present the first detailed calculation of the shear modulus of the mixed phase. We describe the quark phase using the bag model plus first-order quantum chromodynamics corrections and the hadronic phase using relativistic mean-field models with parameters allowed by the most massive pulsar. Most of the calculation involves treating the "pasta phases" of the lattice via dimensional continuation, and we give a general method for computing dimensionally continued lattice sums including the Debye model of charge screening. We compute all the shear components of the elastic modulus tensor and angle average them to obtain the effective (scalar) shear modulus for the case where the mixed phase is a polycrystal. We include the contributions from changing the cell size, which are necessary for the stability of the lower-dimensional portions of the lattice. Stability also requires a minimum surface tension, generally tens of MeV/fm^2 depending on the equation of state. We find that the shear modulus can be a few times 10^33 erg/cm^3, two orders of magnitude higher than the first estimate, over a significant fraction of the maximum mass stable star for certain parameter choices.

22 pages, 12 figures, version accepted by Phys. Rev. D, with the corrections to the shear modulus computation and Table I given in the erratum

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Cited by in corpus (11)

• Maximum elastic deformations of relativistic stars
• Elastic properties of polycrystalline dense matter
• Elastic properties of phases with nonspherical nuclei in dense matter
• Chiral pasta
• Shear oscillations in the hadron-quark mixed phase
• Gravitational wave constraints on the shape of neutron stars
• Amorphous state in the mixed phase of quark-hadron phase transition in protoneutron stars
• Crustal failure as a tool to probe hybrid stars
• New modeling for hybrid stars with an elastic quark core
• Thermodynamical description of hadron-quark phase transition and its implications on compact-star phenomena
• Surface creasing of soft elastic continua as a Kosterlitz-Thouless transition