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Lecture 21

Lecture 21. Neutron stars. Neutron stars. If a degenerate core (or white dwarf) exceeds the Chandrasekhar mass limit (1.4M Sun ) it must collapse until neutron degeneracy pressure takes over. Neutron stars. The force of gravity at the surface is very strong:.

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Lecture 21

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  1. Lecture 21 Neutron stars

  2. 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.

  3. Neutron stars The force of gravity at the surface is very strong: • 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

  4. 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: • This reduces the Coulomb repulsion between protons

  5. 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

  6. Superfluidity • Free neutrons pair up to form bosons • Degenerate bosons can flow without viscosity • A rotating container will form quantized vortices • At r~4x1015 kg/m3 neutron degeneracy pressure dominates • Nuclei dissolve and protons also form a superconducting superfluid

  7. Neutron stars: structure • Outer crust: heavy nuclei in a fluid ocean or solid lattice. • Inner crust: a mixture of neutron-rich nuclei, superfluid free neutrons and relativistic electrons. • Interior: primarily superfluid neutrons • 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).

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

  9. Cooling • Internal temperature drops to ~109 K within a few days • Surface temperature hovers around 106 K for about 10000 years Luminosity (ergs/s) Surface temperature (K)

  10. 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

  11. Break

  12. 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

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

  14. Pulsars • The shape of each pulse shows substantial variation, though the average pulse shape is very stable. Pulsar PSR1919+21 time

  15. Possible explanations • How to obtain very regular pulsations? • 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. • 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. • Rotating stars • How fast can a star rotate before it breaks up?

  16. 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.

  17. 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!

  18. 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)

  19. 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.

  20. 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

  21. 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

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