1. Neutron Stars and Black Holes
Chapter 11:
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 an M > 8 Msun star blows away its outer layers.
Pressure becomes so high that electrons and protons combine to form stable neutrons throughout the object.
The central core will collapse into a compact object of ~ a few Msun.
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!!!

3. Discovery of Pulsars Angular momentum conservation
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

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

5. The Crab Pulsar
Visual image
X-ray image

6. Light curves of the Crab Pulsar

7. 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.

8. Images of Pulsars and other Neutron Stars
The Vela pulsar moving through interstellar space
The Crab Nebula and pulsar

9. The Effects of Pulsar Winds
Pulsars blow off a constant stream (wind) of high-energy particles:
pulsar winds

10. 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.

11. 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.

12. 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

13. 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.

14. The X-Ray Burster 4U
Several bursting X-ray sources have been observed:
Rapid outburst followed by gradual decay
Optical
Ultraviolet

15. Some pulsars have planets orbiting around them.
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.

16. Neutron stars can not 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 can not 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!

17. 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
If you could compress Earth to a smaller radius => higher escape velocity from the surface.
vesc

18. The Schwarzschild Radius
=> There is a limiting radius where the escape velocity reaches the speed of light, c:
2GM
____
Vesc = c
Rs = c2
G = gravitational constant
M = mass
Rs is called the Schwarzschild radius.

19. 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 Have No Hair”
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)

22. The Gravitational Field of a Black Hole
Gravitational Potential
Distance from central mass
The gravitational potential (and gravitational attraction force) at the Schwarzschild radius of a black hole becomes infinite.

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

24. General Relativity Effects Near Black Holes (II)
Time dilation
Clocks starting at 12:00 at each point.
After 3 hours (for an observer far away from the black hole):
Clocks closer to the black hole run more slowly.
In a finite amount of time for an in falling clock to the events horizon and infinite amount of time will pass for an outside the event horizon observer.
Time dilation becomes infinite at the event horizon.
Event horizon

25. General Relativity Effects Near Black Holes (III)
gravitational redshift
All wavelengths of emissions from near the event horizon are stretched (redshifted).
 Frequencies are lowered.
Event horizon

26. Observing Black Holes Mass > 3 Msun => Black hole!
No light can escape a black hole
=> Black holes can not 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!

27. Compact object with > 3 Msun must be a black hole!
Compact object with > 3 Msun must be a black hole!

28. Jets of Energy from Compact Objects
Some X-ray binaries show jets perpendicular to the accretion disk

29. 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

30. 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.