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Lecture 21
Neutron stars
Neutron stars
If a degenerate core (or white
dwarf) exceeds the Chandrasekhar
mass limit (1.4MSun) it must collapse
until neutron degeneracy pressure
takes over.
M  1.4M Sun
R  10km
  6.65 1017 kg / m3  2.9  nuclear
Neutron stars
M  1.4M Sun
R  10km
  6.65 1017 kg / m3  2.9  nuclear
The force of gravity at the surface is very
g  2  1.8 1012 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:
Fe, Ni, Ni, Kr,..., Kr
• 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
• Free neutrons pair up to form bosons
 Degenerate bosons can flow without viscosity
 A rotating container will form quantized vortices
• At ~4x1015 kg/m3 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 MSun (depending on
rotation rate).
Conservation of angular momentum led to the prediction that
neutron stars must be rotating very rapidly.
Luminosity (ergs/s)
Surface temperature (K)
• Internal temperature drops to ~109 K within a few days
• Surface temperature hovers around 106 K for about
10000 years
Neutron stars: luminosity
What is the blackbody luminosity of a 1.4 MSun neutron
star, with a surface temperature of 1 million K?
Chandra X-ray image of a
neutron star
• Variable stars with very well-defined periods (usually 0.252 s).
• Some are measured to ~15 significant figures and rival the
best atomic clocks on earth
• The periods increase very gradually, with
 Characteristic lifetime of ~107 years.
 10 15
Pulsar PSR1919+21
• The shape of
each pulse shows
variation, though
the average pulse
shape is very
Possible explanations
How to obtain very regular pulsations?
Binary stars: Such short periods would require very small
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
• The time-varying electric and magnetic fields form an EM wave
that carries energy away from the star as magnetic dipole
• 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
5x1031 W.
M  1.4 M Sun
R  10 4 m
P  0.0333s
P  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
 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