Lecture 21

Neutron stars

Neutron stars

If a degenerate core (or white dwarf) exceeds the Chandrasekhar mass limit (1.4M

takes over.

Sun ) it must collapse until neutron degeneracy pressure

M R

 1 .

4

M Sun

 10

km

  6 .

65  10 17

kg

/

m

3  2 .

9 

nuclear

Neutron stars

M R

 1 .

4

M Sun

 10

km

  6 .

65  10 17

kg

/

m

3  2 .

9 

nuclear

The force of gravity at the surface is very strong:

g



GM R

2  1 .

8  10 12

m

/

s

2 • An object dropped from a height of 1 m would hit the surface at a velocity 0.6% the speed of light. • Must use general relativity to model correctly

Creation of Neutrons

• Neutronization: At high densities, neutrons are created rather than destroyed  The most stable arrangement of nucleons is one where neutrons and protons are found in a lattice of increasingly neutron rich nuclei: 56

Fe

,

26 62

Ni

28

,

64

Ni

28

,

86

Kr

36

,...,

118

Kr

36 • This reduces the Coulomb repulsion between protons

Neutron Drip

• Nuclei with too many neutrons are unstable; beyond the 'neutron drip-line', nuclei become unbound.  These neutrons form a nuclear halo: the neutron density extends to greater distances than is the case in a well-bound, stable nucleus

Superfluidity

• Free neutrons pair up to form bosons   Degenerate bosons can flow without viscosity A rotating container will form quantized vortices • At  ~4x10 15  kg/m 3 neutron degeneracy pressure dominates Nuclei dissolve and protons also form a superconducting superfluid

Neutron stars: structure

1. Outer crust: heavy nuclei in a fluid ocean or solid lattice. 2. Inner crust: a mixture of neutron-rich nuclei, superfluid free neutrons and relativistic electrons. 3. Interior: primarily superfluid neutrons 4. Core: uncertain conditions; likely consist of pions and other elementary particles.

• The maximum mass that can be supported by neutron degeneracy is uncertain, but can be no more than 2.2-2.9 M Sun (depending on rotation rate).

Rotation

Conservation of angular momentum led to the prediction that neutron stars must be rotating very rapidly.

Cooling

• Internal temperature drops to ~10 9 K within a few days • Surface temperature hovers around 10 6 K for about 10000 years

Neutron stars: luminosity

What is the blackbody luminosity of a 1.4 M Sun neutron Chandra X-ray image of a neutron star

Break

Pulsars

• Variable stars with very well-defined periods (usually 0.25 2 s). • Some are measured to ~15 significant figures and rival the best atomic clocks on earth

Pulsars

• The periods increase very gradually, with  Characteristic lifetime of ~10 7 years.

dP

 10  15

dt

• The shape of each pulse shows substantial variation, though the average pulse shape is very stable.

Pulsars

Pulsar PSR1919+21 time

Possible explanations

How to obtain very regular pulsations?

1. Binary stars: Such short periods would require very small separations. • Could only be neutron stars. However, their periods would decrease as gravitational waves carry their orbital energy away.

2. Pulsating stars • White dwarf oscillations are 100-1000s, much longer than observed for pulsars • Neutron star pulsations are predicted to be more rapid than the longest-period pulsars.

3. Rotating stars • How fast can a star rotate before it breaks up?

Pulsars: rapidly rotating neutron stars

• Discovery of the pulsar in the Crab nebula in 1968 (P=0.0333s) confirmed that it must be due to a neutron star.

• Many pulsars are known to have high velocities (1000 km/s) as expected if they were ejected from a SN explosion.

Pulsar model

• The model is a strong dipole magnetic field, inclined to the rotation axis.

• The time-varying electric and magnetic fields form an EM wave that carries energy away from the star as magnetic dipole radiation.

• Electrons or ions are propelled from the strong gravitational field. As they spiral around B-field lines, they emit radio radiation.

• Details are still very much uncertain!

The Crab Pulsar

• This movie shows dynamic rings, wisps and jets of matter and antimatter around the pulsar in the Crab Nebula 1 light year X-ray light (Chandra) Optical light (HST)

Crab nebula: energy source

• We saw that the Crab nebula is expanding at an accelerating rate. What drives this acceleration?

• To power the acceleration of the nebula, plus provide the observed relativistic electrons and magnetic field requires an energy source of 5x10 31 W.

M

 1 .

4

M Sun R

 10 4

m P

 0 .

0333

s

 4 .

21  10  13

Tests of General Relativity

• PSR1913+16: an eccentric binary pulsar system    Can observe time delay as the gravitational field increases and decreases Curvature of space-time causes the orbit to precess Loss of energy due to gravitational waves

Shapiro Delay

• When the orbital plane is along the line of sight, there is a delay in the pulses due to the warping of space