1. Neutron Stars

2. Gradual compression of a stellar iron core  trans. [g cm -3 ] CompositionDegen. pressure Remarks Iron nuclei; nonrel. free e - nonrel. e - ~ 10 6 Electrons become relativ.p F e ~ m e c Iron nuclei; relativ. free e - relativ. e - ~ 10 9 neutronization  F e ~ (m n – m p - m e ) c 2 p + e - → n + e Neutron-rich nuclei ( 62 28 Ni, 64 28 Ni, 66 28 Ni); rel. free e- relativ. e - ~ 4x10 11 neutron dripn become degen. and stable outside of nuclei Neutron-rich nuclei; free n; free rel. e - relativ. e - ~4x10 12 Neutron degen. pressure dominates Neutron-rich nuclei; superfluid free n; rel. free e - neutronn form bosonic pairs → superfluidity 2x10 14 Nuclei dissolve ~  at. nucl. Superfluid free n; superconducting free p; rel. free e - neutronp form bosonic pairs → superfl. & supercond. 4x10 14 pion production free n, p, e, other elem. particles ( , …) neutron

3. Radial Structure of a Neutron Star - Heavy Nuclei ( 56 Fe) - Heavy Nuclei ( 118 Kr); free neutrons; relativistic, degenerate e - - Superfluid neutrons

4. Properties of Neutron Stars Typical size: R ~ 10 km Mass: M ~ 1.4 – 3 M sun Density:  ~ 4x10 14 g/cm 3 → 1 teaspoon full of NS matter has a mass of ~ 2 billion tons!!! Rotation periods: ~ a few ms – a few s Magnetic fields: B ~ 10 8 – 10 15 G (Atoll sources; ms pulsars) (magnetars)

5. Neutron Star Cooling T c ~ 10 11 K T c ~ 10 9 K ~ 1 d URCA process: n → p + e - + e p + e- → n + e (non-degenerate n, p) T c ~ 10 8 K ~ 1,000 yrneutrino cooling T c ~ 10 8 K; T eff ~ 10 6 K for ~ 10,000 yr L ph ~ 7x10 32 erg/s max ~ 30 Å (soft X-rays)

6. The Lighthouse Model of Pulsars A Pulsar’s magnetic field has a dipole structure, just like Earth. Radiation is emitted mostly along the magnetic poles. Rapid rotation along axis not aligned with magnetic field axis → Light house model of pulsars Pulses are not perfectly regular → gradual build-up of average pulse profiles

7. Pulsar Emission Models: Polar Cap model Particle acceleration along magnetic field lines Synchrotron emission Curvature radiation Pair production Electromagnetic cascades

8.  Light Cylinder Pulsar Emission Models: Outer Gap model Electrons are bound to magnetic fields co-rotating with the pulsar At a radial distance r = c/  co-rotation at the speed of light → “light cylinder” → Particles ripped off magnetic fields Synchrotron emission Curvature radiation

9. Pulsar periods and derivatives Associated with supernova remnants Mostly in binary systems

10. Pulsar periods Over time, pulsars lose energy and angular momentum => Pulsar rotation is gradually slowing down. dP/dt ~ 10 -15 Pulsar Glitches:  P/P ~ 10 -7 – 10 -8

11. Energy Loss of Pulsars From the gradual spin-down of pulsars: dE/dt = (½ I  2 ) = I  = - (1/6)  ┴ 2  4 r 4 c -3 d dt  ┴ ~ B 0 r sin  One can estimate the magnetic field of a pulsar as B 0 ≈ 3 x 10 19 √ PP G

14. Images of Pulsars and other Neutron Stars The vela Pulsar moving through interstellar space The Crab nebula and pulsar

15. The Crab Pulsar Remnant of a supernova observed in A.D. 1054 Pulsar wind + jets

16. The Crab Pulsar Visual imageX-ray image

17. Dispersion of Pulsar Signals  t = (4  e 2 /m e c  1 3 )  DM DM = ∫ n e (s) ds 0 d DM = Dispersion Measure