Superfluid Heat Conduction and the Cooling of Magnetized Neutron Stars

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We report on a new mechanism for heat conduction in the neutron star crust.

• We find that collective modes of superfluid neutron matter, called superfluid phonons (sPhs), can influence heat conduction in magnetized neutron stars.
• They can dominate the heat conduction transverse to magnetic field when the magnetic field $B \gsim 10^{13}$ G.
• At density $\rho \simeq 10^{12}-10^{14} $ g/cm$^3$ the conductivity due to sPhs is significantly larger than that due to lattice phonons and is comparable to electron conductivity when temperature $\simeq 10^8$ K.