I'm a mathematicians and I don't have a big knowledge of physics. I've heard that superfluidity can arise inside a neutron star and I've given to understand that this has to do with a hugh density that could bound neutron to have the same state.

I'm wondering how does it work. Can anybody give me a sketch of the phenomena or a simple reference to the argument?

Thank you in advance


The Kelvin (or Celsius) is an arbitrary temperature scale. What matters to Fermi liquids that may (or may not) undergo a transition to superfluidity is the dimensionless ratio $k_BT/E_F$, where $E_F$ is the Fermi energy. $E_F$ is a measure of the typical kinetic energy of a fermion. It is related to the density via $$ E_F=\frac{k_F^2}{2m}, \;\;\;\; n=\frac{k_F^3}{3\pi^2}. $$ In a neutron star the density is very large, and the Fermi energy of neutrons reaches 10s of MeV (M=$10^6$). Note that room temperature corresponds to about $1/40$ eV. In terms of $k_BT/E_F$ neutron stars are quite cold, with temperatures in the keV range. This means $k_BT/E_F<10^{-3}$, which is a typical regime for superfluidity to occur. Indeed, the Fermi energy of the electrons in a typical metal corresponds to a few 1000 K, and the critical temperature of conventional superconductors is at most a few 10s K.

The neutrons in a neutron star are more strongly coupled than the electrons in a metal, and neutron stars are indeed "high $T_c$" superconductors in the sense of a large critical $k_BT_c/E_F$. However, the main effect is the large $E_F$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.