Superfluid models of neutron stars
The possibility that matter constituting neutron stars could be superfluid
and superconducting was raised a long time ago before the discovery
of pulsars by Jocelyn Bell and Anthony Hewish in 1967. Later, this prediction seemed to be confirmed by the observation of the
long relaxation time, on the order of months, following the first frequency glitch in the Vela pulsar.
What kinds of superfluid can be found in neutron stars?
Apart from a proton superconductor similar to conventional electron superconductors, two different kinds of
neutron superfluids are expected to be found in the interior of a neutron star. In the crust and in the
outer core, neutrons are expected to form an isotropic superfluid like helium-4, while in denser regions
they are expected to form a more exotic kind of (anisotropic) superfluid with
each member of a pair having parallel spins, as in superfluid helium-3. The central core of neutron stars might
contain various species like hyperons or even deconfined quarks which could also be superfluid.
What does superfluidity mean?
One of the striking consequences of superfluidity is the allowance for several distinct dynamic components. In 1938,
Tisza introduced a two-fluid model in order to explain the properties of the newly discovered superfluid phase of
liquid helium-4, which behaves either like a fluid with no viscosity in some experiments or like a classical fluid
in other experiments. Guided by the Fritz Londonā€™s idea that superfluidity is intimately related to Boseā€“Einstein
condensation (which is now widely accepted), Tisza proposed that liquid helium is a mixture of two components,
a superfluid component, which has no viscosity, and a normal component, which is viscous and conducts heat. These two
fluids are allowed to flow with different velocities. This two-fluid model has been very successful in explaining
many properties of superfluid helium.
The situation gets more complicated in superfluid mixtures, like mixtures of helium-3 and helium-4. The two
superfluids can flow without resistance but due to the interactions between the two kinds of atoms, the two
superfluids can exchange momentum. The end result is that the momentum and the velocity of each superfluid
are not aligned. This effect is known as mutual entrainment.
What does superfluidity imply for neutron stars?
A few years after the seminal work of Andreev & Bashkin on superfluid mixtures of helium-3 and helium-4,
it was realized that entrainment effects could play an important role in the dynamic evolution of neutron stars.
In particular, these effects are very important for studying the oscillations of superfluid neutron star cores.
Mutual entrainment not only affects the frequencies of the modes but, more surprisingly, (remembering that entrainment
is a nondissipative effect) also affects their damping.
The simplest model of cold superfluid neutron star cores is to consider two
components: a neutron superfluid and a plasma of charged particles. This model
is described in the following paper:
Chamel, MNRAS 388 (2008), 737-752. PDF
We have also developed a model of neutron-star
crusts with superfluid neutrons:
Carter, Chamel and Haensel, Int. J. Mod. Phys. D 15 (2006), 777-803. PDF
How strong are entrainment effects in neutron stars?
We have calculated the mutual entrainment parameters both in the core
Chamel and Haensel, Phys. Rev. C73 (2006),045802. PDF
in the pasta mantle
Carter, Chamel and Haensel, Nucl. Phys.A748 (2005),675-697. PDF
Carter, Chamel and Haensel, Nucl. Phys.A759 (2005),441-464. PDF
and in the inner crust of neutron stars
Chamel, Nucl. Phys.A747 (2005),109-128. PDF
Chamel, Nucl. Phys.A773 (2006),263-278. PDF
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