Superfluidity and Neutron stars: Thermal and dynamical aspects

Born from gravitational-core collapse supernovae, neutron stars are initially extremely hot (with temperatures ∼10¹² K) but cool down to temperatures ~10⁹ K within a few days. The very dense matter in their interior is expected to undergo various quantum phase transitions analogous to those observed in laboratories. Similarly to ultracold quantum gases, free neutrons in the inner crust are predicted to form a condensate of 1S0 pairs whereas an homogeneous neutron-proton superfluid mixture is contained in the outer core. Nuclear superfluidity has found strong support from the rapid cooling of the Cassiopeia A remnant, the thermal relaxation of the crust of neutron stars in accreting systems, and the observation of pulsar frequency glitches.

Despite the importance of the superfluid dynamics in interpreting these latter astrophysical phenomena, most microscopic calculations of the nuclear pairing properties have been carried out so far for static situations. We have recently studied the dynamics of hot neutron-proton superfluid mixtures within the time-dependent density functional theory [1]. Neutron and proton pairing gaps in the homogeneous neutron star core, as well as self-consistent microscopic inputs for macroscopic dynamical models of neutron stars, have been computed in the presence of arbitrary superfluid currents [2].

Within the same framework, we have also shown the existence of a dynamical "gapless" state in which nuclear superfluidity is not destroyed even though the energy spectrum of quasiparticle excitations exhibits no gap. The absence of an energy gap strongly alters the neutron specific heat which becomes very different from that in the classical BCS state (in the absence of superflows) [3]. Implications for the crust cooling of neutron stars, as well as the consequences of gapless superfluidity for neutron vortex dynamics will be discussed [4].

[1] N. Chamel & V. Allard, Phys. Rev. C 100, 065801 (2019).
[2] V. Allard & N. Chamel, Phys. Rev. C 103, 025804 (2021).
[3] V. Allard & N. Chamel, Phys. Rev. C 108, 045801 (2023).
[4] V. Allard & N. Chamel, Phys. Rev. Lett. 132, 181001 (2024)