Neutron Star

BEC and Neutron Star Xiaoguang Li Physics 599 11/30/2005

some properties of neutron star High density, temperature Lighthouse effect, strong magnetic field Superfluidity, Superconductor

BEC and Neutron Star BEC

neutron star

Boson

Fermion

10−6 gcm −3

1015 gcm −3

< 3K

106 K ( at surface )

Both are superfluids -- that is, liquids that flow without friction or viscosity.

The Condition inside a Neutron Star the basic nuclear interaction is attractive at large distances. The ratio nn n p is high, we need only consider n-n and p-p pairing. Superfluidity may occur whenever

∆ > kT The gap parameter ∆ depends on the strength of the pairing interaction and, in turn, on the density.

Cooling of Neutron Stars It is generally believed that neutron stars are formed at very high interior temperatures (T ≥ 1011 K ) in the core of a supernova explosion. the predominant cooling mechanism after formation is neutrino emission, with an initial cooling timescale of seconds. After about a day, the internal temperature drops to 109 −1010 K The gap parameter ∆ 1 − 2MeV

Evidence of Superfluidity superfluid vortices pulsars glitches

Vortices in the superfluidity For the normal liquid, for example a glass of water that is placed on a rotating turntable. After some initial slowness, the water starts to rotate uniformly with the glass. By definition, vorticity is also present in the uniform rotation because the flow velocity at the edges is larger than in the center. In contrast to the example of a glass of water above, the rotation in superfluids is always inhomogeneous (figure). The fluid circulates around quantized vortex lines. The vortex lines are shown as yellow in the figure, and the circulating flow around them is indicated by arrows. There is no vorticity outside of the lines because the velocity near each line is larger than further away. (In mathematical terms curl v = 0, where v(r) is the velocity field.)

Pulsars if there are charged particles trapped by the strong magnetic field of the neutron stars near the magnetic poles, the strong magnetic field directs the radiation field along the magnetic axis of the neutron stars. If the axis of the magnetic dipole is not aligned with the rotation axis of the neutron stars, then the radiation field would be sweeping through space, just like the light beam from a lighthouse. If the beam sweeps across the Earth, we would see an intermittent radiation ⇒ Pulsar.

Crab Pulsar From Chandra X-ray Observatory

Crab Nebula in X-ray.

Glitches These neutron stars usually rotate with such precision that they are known as the best timekeepers in the universe, but every so often their rotation rate suddenly increases. It is thought that these glitches are related to superfluidity inside the star, which allows the neutrons to flow without friction.

Supernova and neutron star Degenerate pressure „ „

Pauli’s Exclusion Principle Heisenberg’s Uncertainty Principle

Collapse Shock wave Supernova Neutron star

“Bosenova” Carl Wieman and colleagues at NIST have discovered that atoms inside a BEC can be made to attract or repel one another by "tuning" the magnetic field. They tried both: „

„

Like tiny supernova „ „ „

Collapse Explosion Small remnant

„

First, they made a selfrepelling BEC. It expanded gently, as expected. Then, they made a mildly selfattracting BEC. It began to shrink -- again as expected -but then it did something wholly unexpected. It exploded!

Black hole

If a fish gets too near, and enters an area where the water speed is faster than the fish can move, it will be sucked inwards.

In principle, black holes could be simulated by passing light close to a whirlpool of gas. If the centre of the whirlpool was moving faster than light, the light would be sucked inwards like the unfortunate fish. physicists have managed to do that using BECs.