1. Neutron Stars and Black Holes

2. The central core will collapse into a compact object of ~ a few Msun.
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 Remnant of a supernova observed in A.D. 1054
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. Neutron stars cannot exist with masses > 3 Msun
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 vesc vesc vesc
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 Mass > 3 Msun => Black hole!
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 Optical
Ultraviolet

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

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.