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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 strong: GM g 2 1.8 1012 m / s 2 R • 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 26 62 28 64 28 86 36 118 36 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 Superfluidity • 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). Rotation Conservation of angular momentum led to the prediction that neutron stars must be rotating very rapidly. Cooling 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 Break Pulsars • 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 Pulsars • The periods increase very gradually, with Characteristic lifetime of ~107 years. dP 10 15 dt Pulsars Pulsar PSR1919+21 • The shape of each pulse shows substantial variation, though the average pulse shape is very stable. 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 5x1031 W. M 1.4 M Sun R 10 4 m P 0.0333s P 4.2110 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