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Neutron Stars and Black Holes

Discover the formation, properties, and fascinating phenomena of neutron stars and black holes. Learn about pulsars, X-ray binaries, and the mysteries surrounding black holes. Explore gravitational effects, event horizons, and more.

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Neutron Stars and Black Holes

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  1. Neutron Stars and Black Holes

  2. Neutron Stars A supernova explosion of a M > 8 Msun star blows away its outer layers. The central core will collapse into a compact object of ~ a few Msun.

  3. Formation of Neutron Stars Compact objects more massive than the Chandrasekhar Limit (1.4 Msun) collapse further. Pressure becomes so high that electrons and protons combine to form stable neutrons throughout the object: p + e-n + ne Neutron Star

  4. Properties of Neutron Stars Typical size: R ~ 10 km Mass: M ~ 1.4 – 3 Msun Density: r ~ 1014 g/cm3 Piece of neutron star matter of the size of a sugar cube has a mass of ~ 100 million tons!!!

  5. Discovery of Pulsars Angular momentum conservation => Collapsing stellar core spins up to periods of ~ a few milliseconds. Magnetic fields are amplified up to B ~ 109 – 1015 G. (up to 1012 times the average magnetic field of the sun) => Rapidly pulsed (optical and radio) emission from some objects interpreted as spin period of neutron stars

  6. Pulsars / Neutron Stars Neutron star surface has a temperature of~ 1 million K. Cas A in X-rays Wien’s displacement law, lmax = 3,000,000 nm / T[K] gives a maximum wavelength of lmax = 3 nm, which corresponds to X-rays.

  7. Pulsar Periods Over time, pulsars lose energy and angular momentum => Pulsar rotation is gradually slowing down.

  8. Lighthouse Model of Pulsars A Pulsar’s magnetic field has a dipole structure, just like Earth. Radiation is emitted mostly along the magnetic poles.

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

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

  11. The Crab Pulsar (2) Visual image X-ray image

  12. Light Curves of the Crab Pulsar

  13. Proper Motion of Neutron Stars Some neutron stars are moving rapidly through interstellar space. This might be a result of anisotropies during the supernova explosion forming the neutron star

  14. Binary Pulsars Some pulsars form binaries with other neutron stars (or black holes). Radial velocities resulting from the orbital motion lengthen the pulsar period when the pulsar is moving away from Earth... …and shorten the pulsar period when it is approaching Earth.

  15. Neutron Stars in Binary Systems: X-ray Binaries Example: Her X-1 Star eclipses neutron star and accretion disk periodically 2 Msun (F-type) star Neutron star Orbital period = 1.7 days Accretion disk material heats to several million K => X-ray emission

  16. Pulsar Planets Some pulsars have planets orbiting around them. Just like in binary pulsars, this can be discovered through variations of the pulsar period. As the planets orbit around the pulsar, they cause it to wobble around, resulting in slight changes of the observed pulsar period.

  17. Black Holes Just like white dwarfs (Chandrasekhar limit: 1.4 Msun), there is a mass limit for neutron stars: Neutron stars cannot exist with masses > 3 Msun We know of no mechanism to halt the collapse of a compact object with > 3 Msun. It will collapse into a single point – a singularity: => A Black Hole!

  18. Escape Velocity Velocity needed to escape Earth’s gravity from the surface: vesc≈ 11.6 km/s. vesc Now, gravitational force decreases with distance (~ 1/d2) => Starting out high above the surface => lower escape velocity. vesc vesc If you could compress Earth to a smaller radius => higher escape velocity from the surface.

  19. The Schwarzschild Radius => There is a limiting radius where the escape velocity reaches the speed of light, c: 2GM ____ Rs = Vesc = c c2 G = Universal const. of gravity M = Mass Rs is called the Schwarzschild Radius.

  20. Schwarzschild Radius and Event Horizon No object can travel faster than the speed of light => nothing (not even light) can escape from inside the Schwarzschild radius • We have no way of finding out what’s happening inside the Schwarzschild radius. • “Event horizon”

  21. Black Holes in Supernova Remnants Some supernova remnants with no pulsar / neutron star in the center may contain black holes.

  22. Schwarzschild Radii

  23. “Black Holes Continued” Matter forming a black hole is losing almost all of its properties. Black Holes are completely determined by 3 quantities: Mass Angular Momentum (Electric Charge)

  24. General Relativity Effects Near Black Holes An astronaut descending down towards the event horizon of the BH will be stretched vertically (tidal effects) and squeezed laterally.

  25. General Relativity Effects Near Black Holes (2) Time dilation Clocks starting at 12:00 at each point. After 3 hours (for an observer far away from the BH): Clocks closer to the BH run more slowly. Time dilation becomes infinite at the event horizon. Event Horizon

  26. General Relativity Effects Near Black Holes (3) Gravitational Red Shift All wavelengths of emissions from near the event horizon are stretched (red shifted).  Frequencies are lowered. Event Horizon

  27. Observing Black Holes No light can escape a black hole => Black holes cannot be observed directly. If an invisible compact object is part of a binary, we can estimate its mass from the orbital period and radial velocity. Mass > 3 Msun => Black hole!

  28. Candidates for Black Hole Compact object with > 3 Msun must be a black hole!

  29. Compact Objects with Disks and Jets Black holes and neutron stars can be part of a binary system. Matter gets pulled off from the companion star, forming an accretion disk. => Strong X-ray source! Heats up to a few million K.

  30. X-Ray Bursters Several bursting X-ray sources have been observed: Rapid outburst followed by gradual decay Repeated outbursts: The longer the interval, the stronger the burst

  31. The X-Ray Burster 4U 1820-30 In the cluster NGC 6624 Ultraviolet Optical

  32. Black-Hole vs. Neutron-Star Binaries Black Holes: Accreted matter disappears beyond the event horizon without a trace. Neutron Stars: Accreted matter produces an X-ray flash as it impacts on the neutron star surface.

  33. Black Hole X-Ray Binaries Accretion disks around black holes Strong X-ray sources Rapidly, erratically variable (with flickering on time scales of less than a second) Sometimes: Quasi-periodic oscillations (QPOs) Sometimes: Radio-emitting jets

  34. Radio Jet Signatures The radio jets of the Galactic black-hole candidate GRS 1915+105

  35. Model of the X-Ray Binary SS 433 Optical spectrum shows spectral lines from material in the jet. Two sets of lines: one blue-shifted, one red-shifted Line systems shift back and forth across each other due to jet precession

  36. Gamma-Ray Bursts (GRBs) Short (~ a few s), bright bursts of gamma-rays GRB of May 10, 1999: 1 day after the GRB 2 days after the GRB Later discovered with X-ray and optical afterglows lasting several hours – a few days Many have now been associated with host galaxies at large (cosmological) distances. Probably related to the deaths of very massive (> 25 Msun) stars.

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