Transcript Document
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