Shear modulus of the hadron-quark mixed phase

TL;DR

This paper calculates the shear modulus of the hadron-quark mixed phase in neutron stars, revealing it can be significantly higher than previous estimates, which impacts gravitational wave emission predictions.

Contribution

It provides the first detailed calculation of the shear modulus of the mixed phase using advanced models and a novel method for lattice sums with charge screening effects.

Findings

Shear modulus can reach a few times 10^33 erg/cm^3.

Shear modulus is two orders of magnitude higher than earlier estimates.

The results depend on the equation of state and surface tension parameters.

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.