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We explore contribution of phonon to the thermal conductivity coefficient (κ) in the core of neutron stars. We formulate phonon contribution with the help of the effective field theory which furnishes phonon scattering rates in terms of equation of state. We also compute phonon dispersion relation beyond leading order which is function of the gap. With phonon scattering rates and next-to leading order dispersion relation we evaluate the coefficient solving Boltzmann equation. It is seen that κ is dominated by small-large angle combined collisions and at low temperature can be written as κ ∝ 1/∆. We show that thermal conductivity in the core is dominated by phonon-phonon collisions when phonon physics is governed by pure hydrodynamics.

Phonon contribution to the thermal conductivity in neutron star core.