1. Galaxies – review Lecture 12, 13, 27 Upcoming classes
Phys 1830: Lecture 31
Comet ISON on APOD
Making images! Tuesday Dec 3!!! 7pm Allen 405
Download from
M82 by Remi Lacasse
SEEQ
Galactic wind i.e. fountain
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Previous Classes:
pulsars, gamma-ray bursts
This Class
Black holes
Galaxies – review Lecture 12, 13, 27
Upcoming classes
Death of massive stars, Light echos
Galaxies
Cosmology.
ALL NOTES COPYRIGHT JAYANNE ENGLISH

2. Announcements w.r.t. Exam
1 more Office Hour Mon 3:00pm Allen 514
Contact me to see other times.
e.g. go over missed classes, review images
Exam:
9-11 am Saturday Dec 14 – check Registrars’ website
about 70 questions
includes images
Pseudo-cummulative
like the other tests, doesn’t include lab

3. Review:
a) SN 1a progenitor
b) SN II progentior
b) is likely to become a gamma-ray burst due to a black hole forming in its core.

4. Discuss with your neighbour what you think a black hole is:
Black holes:
Discuss with your neighbour what you think a black hole is:
How do they form?
What is their structure?
How do we detect them?
Can anything escape from them?
What is gravity like near them? Are they a cosmic vacuum cleaner or not?
What are their sizes?
Puzzles?

5. What do you believe?
Nothing can escape from a black hole. No energy of any kind, no matter of any kind. Therefore once a black hole forms it can grow larger, by matter falling in, but it can never shrink.
True
False

6. What do you believe?
A black hole is like a cosmic vacuum cleaner, sucking things into it from exceedingly large distances away.
True
False

7. Black Holes: Definition
As an illustration, we collapse 4-D space-time to 2-D and embed it in 3-D space to show a shape; this is instead of using Einstein’s field equations equations which incorporate all dimensions and energy tensor (for energy + pressure).
Light needs to follow space-time, so it follows curved paths as well.
A region of space-time where the gravitation becomes overwhelming and the curvature of space-time is so great that space “folds” over on itself.

8. Black Holes: Definition:
Photon just outside a black hole.
These also lose energy.
Escape velocity is equal to or greater than the speed of light.
The escape velocity is the energy of motion required to overcome gravity and go into orbit.
 Matter and light cannot escape.
Even in the vicinity of a black hole, a photon moving away from it must give up energy. It does this, not by losing speed (that stays at 3 * 10**5 km/s), but by increasing its wavelength. (The energy of photon is E = h * frequency , where h is a constant. Contrast this with the energy of mass which is E= m c**2.)

9. Black Hole: components
Singularity: A point in the universe where the density of matter and the gravitational field are infinite.
Event Horizon: An imaginary spherical surface with a radius equal to the Schwarzschild radius, Rsch. Rsch is the distance from the centre of an object such that, if all the mass were compressed within that region, the escape speed would equal the speed of light.

10. Hold rubber sheet up high
Demo:
Hold rubber sheet up high
collapse 4D spacetime into 2D and embed in 3D space to represent mathematics
GR reduces to Newton’s laws
A tennis ball gives a curve that generates gravitational pull well-represented by Newton’s laws.
nice orbits
Ball bearing on a handle represents dense object
Event Horizon plus curves described by Newton’s laws.

11. Black Hole: Components
Consider friction experienced by gas moving at relativistic speeds (i.e. close to the speed of light). This generates heat that radiates at X-ray wavelengths.
Can also have:
Accretion disk
Jets
Magnetic field lines

12. Black Holes: Accretion Disk
Tidal forces stretch stars apart or a companion star’s outer layers flow towards the black hole.
The stellar material orbits in a disk.
Crashing into itself, the stellar gas loses energy and orbits closer and closer to the event horizon.
Some material falls through the Event Horizon while some particles travel along the magnetic field lines, creating bi-polar jets.
How does it acquire an accretion disk? Tidal stretching approaching objects.
W.r.t. loss of energy, consider friction experienced by gas moving at relativistic speeds (i.e. close to the speed of light). This generates heat that radiates at X-ray wavelengths.
Note that tidal forces occur even in regions of space with only Newtonian gravity effects. So the splitting up of the star happens because such tidal forces are strong even before the star encounters the curvature of spacetime near the event horizon.

13. Black Holes: The size of the Event Horizon
Only depends on mass!
M of Jupiter/ M of Sun
= 2 * 10**27 kg/2 * 10**30 kg
= 10**(27-30)
= 10 ** -3 solar masses.
Rsch of Jupiter ~ 3 km * 10**-3
= 3 * 10**3 m/km * 10**-3
= 3 m
i.e. roughly the height of a room.
G is the gravitational constant, c is the constant speed of light. M is the mass.
You have to be very close to fall through the event horizon! The tidal radius is somewhat larger so you’d have started to stretch before this (like Comet Shoemaker-Levy) - the stretching near a black hole is called the toothpaste effect, since it is like squeezing a tube of toothpaste.
DO THIS CALCULATION FOR THE SUN!

14. Black Holes:
If our Sun became a black hole right now, what would happen to the orbit of the Earth.
a) Earth would get sucked into the black hole because black holes act like Cosmic Vacuum Cleaners.
b) Nothing since the force of gravity doesn’t change until one is close to the event horizon.

15. Black Holes: Inside the Event Horizon
According to General Relativity, time isn’t a particularly special dimension. This means it can be swapped with another dimension.
Outside the event horizon you can move in any direction in space but only 1 direction in time (towards the future).
Inside the event horizon you can only move forward in space towards the singularity but you can move backwards and forwards in time!
Moving backwards in time won’t get you out of the black hole anymore than me going to my home tonight will move me back to this morning when I left.

16. Place a black hole between you and a star:
Alain Riazuelo, IAP/UPMC/CNRS
Note a very faint star in the middle of the image – place an intervening BH  2 images of the star.
Note the Milky Way and the Large Magellanic Cloud (LMC)

17. Black Holes: Can anything escape a black hole?
1. E.g. Roger Blandford: Mechanical energy can escape.
Threaded through the gas, in the accretion disk and falling into the black hole, are magnetic field lines.
The lines twist around the rotating black hole, slowing it down.
The energy of rotation travels out along the lines and is deposited in the disk  explains X-ray hot spots.
Use a scarf and tug on it. The energy of the tug travelling through the scarf is mechanical energy.

18. Black Holes: Can anything escape a black hole?
2. Hawking Radiation:
A Quantum Mechanical effect due to the Heisenberg Uncertainty Principle.
Even a vacuum has fluctuations:
Pairs of virtual particles appear to together at some position in spacetime, move apart, come back together and annihilate.
- If close to a black hole, one of the pair falls into it and the other member can escape to infinity, becoming a real particle.
Uncertainty Principle: both velocity and position cannot be well defined.
Although virtual particles appear and annihilate too quickly to be observed, their effects are observed. E.g. in particle accelerators. This is called the Casimir Effect
The infalling member deposits negative energy into the black hole. .

19. Black Holes: Can anything escape a black hole?
2. Hawking Radiation:
Radiation with a black body temperature inversely proportional to the black hole mass.
Small black holes have higher temperatures.
As the black hole radiates, it becomes smaller, temperature increases and it radiates faster.
Black holes evaporate!
A few solar mass black hole will has a temperature about 1 millionth of a degree above absolute zero.

20. What can escape from a black hole?
Light and matter.
Light and mechanical energy.
Matter and mechanical energy.
Hawking radiation and mechanical energy.
Hawking radiation and light.

21. Types of Black Holes Type Mass Rsch Location Detection Method Lifetime
Solar Masses
yrs
Supermassive
>3*10**6
1/2 light-min
Centre of Galaxies
Doppler shift of orbiting
10**97 to 10**106
gas or stars.
Period of orbit of stars in
images.
Mid-mass
smaller than
Globular Clusters
Doppler shift
(Intermediate)
the solar radius
X-rays from accretion.
Stellar Mass
1 to 10
3 to 30 km
Throughout disk
Doppler Shift of companion.
around 10**67
of galaxies
Gravitational lenses.
Primordial
less than 1
1 cm
Throughout universe
Gamma-rays if
around 10**10
evaporating but this is
the only type of black hole that has
not been observed
even indirectly.
got to here
Come in all sizes. (Note – a googol is 10**100 and 10**googol is called googolplex.)
Primordial BH form in fluctuations at the beginning of the Big Bang. Created by compression of matter by external forces (pressure) in the early universe.
All types of BH are rare.

22. Intermediate Black Holes. Formation by mergers of stars.
Types of Black Holes:
M 13 Danny Lee Russell
Intermediate Black Holes.
Formation by mergers of stars.
Globular cluster has about a 1 million stars within several pc.
Star density high in globular clusters so more opportunity for the merger of stars.

23. Types of Black Holes: Supermassive Black Holes
Measure the motion of stars or gas (using spectra) in the centre of galaxies.
Become an astronomer and figure this out!
Supermassive Black Holes
Centres of Galaxies (including Milky Way)
In both spirals and ellipticals.
If the bulge is small and featureless then there is no evidence that there is a black hole.
Do galaxies form around black holes? Or do galaxies form and in the centre black holes accumulate? This is a question of current research.