Lecture 21Lecture 21

Neutron stars

Neutron starsNeutron stars

If a degenerate core (or white dwarf) exceeds the Chandrasekhar mass limit (1.4MSun) it must collapse until neutron degeneracy pressure takes over.

nuclear

Sun

mkg

kmR

MM

9.2/1065.6

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317

Neutron starsNeutron stars

nuclear

Sun

mkg

kmR

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The force of gravity at the surface is very strong:

2122

/108.1 smR

GMg

• 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 NeutronsCreation 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:

KrKrNiNiFe 11836

8636

6428

6228

5626 ,...,,,,

• This reduces the Coulomb repulsion between protons

Neutron DripNeutron 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

SuperfluiditySuperfluidity

• 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: structureNeutron 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 neutrons4. 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).

RotationRotation

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

CoolingCooling

•Internal temperature drops to ~109 K within a few days

•Surface temperature hovers around 106 K for about 10000 years

Sur

face

tem

pera

ture

(K

)

Lum

inos

ity

(erg

s/s)

Neutron stars: luminosityNeutron 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

BreakBreak

PulsarsPulsars

•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

PulsarsPulsars

•The periods increase very gradually, with Characteristic lifetime of ~107 years.

1510dt

dP

PulsarsPulsars

time

Pulsar PSR1919+21

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

Possible explanationsPossible 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 starsPulsars: 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 modelPulsar 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 PulsarThe Crab Pulsar•This movie shows dynamic rings, wisps and jets of matter and antimatter around the pulsar in the Crab Nebula

X-ray light (Chandra) Optical light (HST)

1 light year

Crab nebula: energy sourceCrab 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.

13

4

1021.4

0333.0

10

4.1

P

sP

mR

MM Sun

Tests of General RelativityTests 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 DelayShapiro Delay

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