1. Review for Test #4 on December 15
Topics:
Gamma Ray Bursts (GRB) and Black Holes
Our Milky Way Galaxy
Galaxies
Clusters of Galaxies and Large Scale Structure of the Universe
Cosmology, a past and future history of the Universe
Methods
Conceptual Review and Practice Problems Chapters
Review lectures (on-line) and know answers to clicker questions
Try practice quizzes on-line
Review (time Sunday, Nov 15 starting at 3pm) mainly Q&A format
Bring:
Two Number 2 pencils
Simple calculator (no electronic notes)
UNM Student ID

2. Test #3 Review How to take a multiple choice test 1) Before the Test:
Study hard (~2 hours/day Friday through Tuesday)
Get plenty of rest the night before
Bring at least 2 pencils, UNM student ID, and a calculator
2) During the Test:
Write out and bubble your last name, space, first name and Exam color in the name space of the scantron form. Write out and bubble your Banner ID in the ID space.
Draw simple sketches to help visualize problems
Solve numerical problems in the margin
Come up with your answer first, then look for it in the choices
If you can’t find the answer, try process of elimination
If you don’t know the answer, Go on to the next problem and come back to this one later
TAKE YOUR TIME, don’t hurry
If you don’t understand something, ask me.

3. Test #4 Possibly Useful Equations
Schwarschild Radius:
2 GM c2
R =
Lifetimes of stars (on the main sequence):
L = 1010/M2 years where M is the Mass in solar masses
and L is the Lifetime
Equivalence of Matter and Energy:
E = mc2

4. Gamma-Ray Bursts
Gamma-ray bursts also occur, and were first spotted by satellites looking for violations of nuclear test-ban treaties. This map of where the bursts have been observed shows no “clumping” of bursts anywhere, particularly not within the Milky Way. Therefore, the bursts must originate from outside our Galaxy.

5. Gamma-Ray Bursts
Distance measurements of some gamma bursts show them to be very far away – 2 billion parsecs for the first one measured.
Occasionally the spectrum of a burst can be measured, allowing distance determination.

6. Gamma-Ray Bursts
Two models – merging neutron stars or a hypernova – have been proposed as the source of gamma-ray bursts.

7. Black Holes and General Relativity
General Relativity: Einstein's (1915) description of gravity (extension of Newton's). It begins with:
The Equivalence Principle
Here’s a series of thought experiments and arguments:
1) Imagine you are far from any source of gravity, in free space, weightless. If you shine a light or throw a ball, it will move in a straight line.

8. 2. If you are in freefall, you are also weightless
2. If you are in freefall, you are also weightless. Einstein says these are equivalent. So in freefall, light and ball also travel in straight lines.
3. Now imagine two people in freefall on Earth, passing a ball back and forth. From their perspective, they pass it in a straight line. From a stationary perspective, it follows a curved path. So will a flashlight beam, but curvature of light path small because light is fast (but not infinitely so).
The different perspectives are called frames of reference.

9. 4. Gravity and acceleration are equivalent
4. Gravity and acceleration are equivalent. An apple falling in Earth's gravity is the same as one falling in an elevator accelerating upwards, in free space.
5. All effects you would observe by being in an accelerated frame of reference you would also observe when under the influence of gravity.

10. Examples:
1) Bending of light. If light travels in straight lines in free space, then gravity causes light to follow curved paths.

11. Observed! In 1919 eclipse.

12. Gravitational lensing
Gravitational lensing. The gravity of a foreground cluster of galaxies distorts the images of background galaxies into arc shapes.

13. 2. Gravitational Redshift
light received when elevator receding at some speed.
later, speed > 0
Consider accelerating elevator in free space (no gravity).
time zero, speed=0
light emitted when elevator at rest.
Received light has longer wavelength (or shorter frequency) because of Doppler Shift ("redshift"). Gravity must have same effect! Verified in Pound-Rebka experiment.

14. 3. Gravitational Time Dilation
A photon moving upwards in gravity is redshifted. Since 1 1 T

the photon's period gets longer. Observer 1
will measure a longer period than Observer 2. So they disagree on time intervals. Observer 1 would say that Observer 2's clock runs slow! 2
All these effects are unnoticeable in our daily experience!
They are tiny in Earth’s gravity, but large in a black hole’s.

15. Escape Velocity
Velocity needed to escape the gravitational pull of an object.
2GM R
vesc =
Escape velocity from Earth's surface is 11 km/sec.
If Earth were crushed down to 1 cm size, escape velocity would be speed of light. Then nothing, including light, could escape Earth.
This special radius, for a particular object, is called the Schwarzschild Radius, RS RS  M.

16. Black Holes
If core with about 3 MSun or more collapses, not even neutron pressure can stop it (total mass of star about 25 MSun ?).
Core collapses to a point, a "singularity".
Gravity is so strong that nothing can escape, not even light => black hole.
Schwarzschild radius for Earth is 1 cm. For a 3 MSun object, it’s 9 km.

17. Event horizon: imaginary sphere around object with radius equal to Schwarzschild radius.
Anything crossing over to inside the event horizon, including light, is trapped. We can know nothing more about it after it does so.

18. Black hole achieves this by severely curving space
Black hole achieves this by severely curving space. According to Einstein's General Relativity, all masses curve space. Gravity and space curvature are equivalent.
Like a rubber sheet, but in three dimensions, curvature dictates how all objects, including light, move when close to a mass.

19. Curvature at event horizon is so great that space "folds in on itself", i.e. anything crossing it is trapped.

20. Space Travel Near Black Holes
Matter encountering a black hole will experience
enormous tidal forces that will both heat it enough to radiate, and tear it apart.

21. Space Travel Near Black Holes
A probe nearing the event horizon of a black hole will be seen by observers as experiencing a dramatic redshift as it gets closer, so that time appears to be going more and more slowly as it approaches the event horizon.
This is called a gravitational redshift – it is not due to motion, but to the large gravitational fields present.
The probe itself, however, does not experience any such shifts; time would appear normal to anyone inside.

22. What’s inside a black hole?
No one knows, of course; present theory predicts that the mass collapses until its radius is zero and its density infinite; this is unlikely to be what actually happens.
Until we learn more about what happens in such extreme conditions, the interiors of black holes will remain a mystery.

23. Effects around Black Holes
1) Enormous tidal forces.
2) Gravitational redshift. Example, blue light emitted just outside event horizon may appear red to distant observer.
3) Time dilation. Clock just outside event horizon appears to run slow to a distant observer. At event horizon, clock appears to stop.

24. Do Black Holes Exist?  Observational Evidence for Black Holes
The existence of black hole binary partners for ordinary stars can be inferred by the effect the holes have on the star’s orbit, or by radiation from infalling matter.

25. Do Black Holes Really Exist?  Good Candidate: Cygnus X-1
- Binary system: 30 MSun star with unseen companion.
- Binary orbit => companion > 7 MSun.
- X-rays => million degree gas falling into black hole.

26. Final States of a Star 1. White Dwarf (WD)
No Explosive Event + Planetary Nebula (Possible Nova from Carbon Flash)
Supernova + ejecta
GRB + Hypernova + ejecta
1. White Dwarf (WD)
If initial star mass < 8 MSun or so (Max WD mass is 1.4 MSun , radius is about that of the Earth)
2. Neutron Star (NS)
8 MSun < initial star mass < 25 Msun (1.4 MSun < NS mass < 3? Msun radius is ~ 10 km - city sized)
3. Black Hole (BH)
If initial mass > 25 MSun
(For BH with mass = 3 Msun radius ~ 9 km)

27. Take a Giant Step Outside the Milky Way
Artist's Conception
Example (not to scale)

28. from above ("face-on")
see disk and bulge
Perseus arm
Orion arm
Sun
Cygnus arm
Carina arm
from the side ("edge-on")

29. The Three Main Structural Components of the Milky Way
1. Disk
- 30,000 pc diameter (or 30 kpc)
- contains young and old stars, gas, dust. Has spiral structure
- vertical thickness roughly 100 pc - 2 kpc (depending on component. Most gas and dust in thinner layer, most stars in thicker layer)
2. Halo
- at least 30 kpc across
- contains globular clusters, old stars, little gas and dust, much "dark matter"
- roughly spherical

30. 3. Bulge - About 4 kpc across - old stars, some gas, dust
- central black hole of 3 x 106 solar masses
- spherical

31. Shapley (1917) found that Sun was not at center of Milky Way
Shapley used distances to variable “RR Lyrae” stars (a kind of Horizontal Branch star) in Globular Clusters to determine that Sun was 16 kpc from center of Milky Way. Modern value 8 kpc.

32. Stellar Orbits
Halo: stars and globular clusters swarm around center of Milky Way. Very elliptical orbits with random orientations. They also cross the disk.
Bulge: similar to halo.
Disk: rotates.

33. Rotation of the Disk
Sun moves at 225 km/sec around center. An orbit takes 240 million years.
Stars closer to center take less time to orbit. Stars further from center take longer.
=> rotation not rigid like a phonograph record or a merry-go-round. Rather, "differential rotation".
Over most of disk, rotation velocity is roughly constant.
The "rotation curve" of the Milky Way

35. Spiral Structure of Disk
Spiral arms best traced by:
Young stars and clusters
Emission Nebulae HI
Molecular Clouds
(old stars to a lesser extent)
Disk not empty between arms, just less material there.

36. Problem: How do spiral arms survive?
Given differential rotation, arms should be stretched and smeared out after a few revolutions (Sun has made 20 already):
The Winding Dilemma

37. The spiral should end up like this:
Real structure of Milky Way (and other spiral galaxies) is more loosely wrapped.

38. A Spiral Density Wave Proposed solution:
Arms are not material moving together, but mark peak of a compressional wave circling the disk:
A Spiral Density Wave
Traffic-jam analogy:

39. Now replace cars by stars and gas clouds
Now replace cars by stars and gas clouds. The traffic jams are actually due to the stars' collective gravity. The higher gravity of the jams keeps stars in them for longer. Calculations and computer simulations show this situation can be maintained for a long time.
Traffic jam on a loop caused by merging

40. Molecular gas clouds pushed together in arms too => high density of clouds => high concentration of dust => dust lanes.
Also, squeezing of clouds initiates collapse within them => star formation. Bright young massive stars live and die in spiral arms. Emission nebulae mostly in spiral arms.
So arms always contain same types of objects, but individual objects come and go.

41. 90% of Matter in Milky Way is Dark Matter
Gives off no detectable radiation. Evidence is from rotation curve: 10
Rotation
Velocity
(AU/yr)
Solar System Rotation Curve: when almost all mass at center, velocity decreases with radius ("Keplerian") 5 1 1 10 20 30
R (AU)
Curve if Milky Way ended where visible matter pretty much runs out.
observed curve
Milky Way Rotation Curve

42. Not enough radiating matter at large R to explain rotation curve => "dark" matter!
Dark matter must be about 90% of the mass!
Composition unknown. Probably mostly exotic particles that don't interact with ordinary matter at all (except gravity). Some may be brown dwarfs, dead white dwarfs …
Most likely it's a dark halo surrounding the Milky Way.
Mass of Milky Way
6 x 1011 solar masses within 40 kpc of center.

43. Galaxy Classification
Spirals Ellipticals Irregulars
barred unbarred E0 - E Irr I Irr II
SBa-SBc Sa-Sc "misshapen truly
spirals" irregular
First classified by Hubble in => "tuning fork diagram"
bulge less prominent,
arms more loosely wrapped
Irr
disk and large bulge, but no spiral
increasing apparent flatness

44. Still used today. We talk of a galaxy's "Hubble type"
bulge less prominent,
arms more loosely wrapped
Irr
disk and large bulge, but no spiral
increasing apparent flatness
Still used today. We talk of a galaxy's "Hubble type"
Milky Way is an SBbc, between SBb and SBc.
Later shown to be related to other galaxy structural properties and galaxy evolution.
Ignores some notable features, e.g. viewing angle for ellipticals, number of spiral arms for spirals.

45. Irr I vs. Irr II Irr I (“misshapen spirals”) Irr II (truly irregular)
bar
poor beginnings
of spiral arms
Large Magellanic Cloud
Small Magellanic Cloud
These are both companion galaxies of the Milky Way.

46. Ellipticals are similar to halos of spirals, but generally larger, with many more stars. Stellar orbits are like halo star orbits in spirals.
Stars in ellipticals also very old, like halo stars.
An elliptical
Orbits in a spiral

47. A further distinction for ellipticals and irregulars:
Giant vs Dwarf
stars stars
10's of kpc across few kpc across
Dwarf Elliptical NGC 205
Spiral M31
Dwarf Elliptical M32

48. In giant galaxies, the average elliptical has more stars than the average spiral, which has more than the average irregular.
What kind of giant galaxy is most common?
Spirals - about 77%
Ellipticals %
Irregulars %
But dwarfs are much more common than giants.

49. "Star formation history" also related to Hubble type:
Ellipticals formed all their stars early on, no gas left. Stars are old, red, dim.
amount of star formation 1
14 (now)
time (billions of years)
Spirals still have star formation, and gas.
Luminous, massive, short-lived stars make spirals bluer than ellipticals
amount of star formation
time (billions of years) 1
14 (now)
Irregulars have a variety of star formation histories.

50. Distances to Galaxies
For "nearby" (out to 20 Mpc or so) galaxies, use a very bright class of variable star called a "Cepheid".
luminosity
time
Cepheid star in galaxy M100 with Hubble. Brightness varies over a few weeks.

51. From Cepheids in Milky Way star clusters (with known distances), it was found that period (days to weeks) is related to luminosity (averaged over period).
So measure period of Cepheid in nearby galaxy, this gives star's luminosity. Measure apparent brightness. Now can determine distance to star and galaxy.
Has been used to find distances to galaxies up to 25 Mpc.

52. Spectra of galaxies in clusters of increasing distance
prominent
pair of absorption
lines

53. In 1920's, Hubble used Cepheids to find distances to some of these receding galaxies. Showed that redshift or recessional velocity is proportional to distance:
V = H0 x D (Hubble's Law)
velocity (km / sec) Distance (Mpc)
Hubble's Constant (km / sec / Mpc)
Or graphically. . .
Current estimate:
H0 = 73 +/- 2 km/sec/Mpc
If H0 = 75 km/sec/Mpc, a galaxy at 1 Mpc moves away from us at 75 km/sec,
etc.

54. Get used to these huge distances!
Milky Way
30 kpc
Milky Way to Andromeda
700 kpc
Milky Way to Virgo Cluster
17 Mpc

55. Larger structures typically containing thousands of galaxies.
Clusters
Larger structures typically containing thousands of galaxies.
The Virgo Cluster of about 2500 galaxies (central part shown).
The center of the Hercules Cluster
Galaxies orbit in groups or clusters just like stars in a stellar cluster.
Most galaxies are in groups or clusters.

56. Galaxy Interactions and Mergers
Galaxies sometimes come near each other, especially in groups and clusters.
Large tidal force can draw stars and gas out of them => tidal tails.
Galaxy shapes can become badly distorted.

57. Galaxies may merge.
Some ellipticals may be mergers of two or more spirals. Since they have old stars, most mergers must have occurred long ago.

58. Interactions and mergers also lead to "starbursts": unusually high rates of star formation. Cause is the disruption of orbits of star forming clouds in the galaxies. They often sink to the center of each galaxy or the merged pair. Resulting high density of clouds => squeezed together, many start to collapse and form stars.
M82

59. Interactions and mergers can be simulated by computers.
Yellow = stars
Blue = gas
Mihos et al.

60. How do Galaxies Form?
Old idea: they form from a single large collapsing cloud of gas, like a star but on a much larger scale.
New idea: observations indicate that "sub-galactic" fragments of size several hundred parsecs were the first things to form. Hundreds might merge to form a galaxy.
Deep Hubble image of a region 600 kpc across. Small fragments are each a few hundred pc across, contain several billion stars each. May merge to form one large galaxy. This is 10 billion years ago.

61. Galaxy Formation and Evolution
This simulation shows how interaction with a smaller galaxy could turn a larger one into a spiral.

62. Active Galaxies
Seyfert Galaxies Between normal galaxies and most active galaxies
Radio Galaxies Gives off energy in radio part of spectrum not from nucleus but from lobes
Quasars (Quasi-stellar object) Brightest objects in the universe

63. Black Holes and Active Galaxies
This galaxy is viewed in the radio spectrum, mostly from 21-cm radiation. Doppler shifts of emissions from the core show enormous speeds very close to a massive object – a SUPER massive black hole.

64. Black Holes and Active Galaxies
Careful measurements show that the mass of the central black hole is correlated with the size of the galactic core.

65. Quasars - Quasi-stellar objects
The quasars we see are very distant, meaning they existed a long time ago. Therefore, they may represent an early stage in galaxy development. The quasars in this image are shown with their host galaxies.

66. Quasars - Quasi-stellar objects
The end of the quasar epoch seems to have been about 10 billion years ago; all the quasars we have seen are older than that.
The black holes powering the quasars do not go away; it is believed that many, if not most, galaxies have a supermassive black hole at their centers.

67. Evolution of Galaxies?
This figure shows how galaxies may have evolved, from early irregulars through active galaxies, to the normal ellipticals and spirals we see today.

68. Structures of Galaxies
Groups
A few to a few dozen galaxies bound together by their combined gravity.
No regular structure to them.
The Milky Way is part of the Local Group of about 30 galaxies, including Andromeda.

69. The Universe on Very Large Scales
Galaxy clusters join in larger groupings, called superclusters. This is a 3-D map of the superclusters nearest us; we are part of the Virgo Supercluster.

70. Classifying clusters:
1) “rich” clusters vs. “poor” clusters
Poor clusters include galaxy groups (few to a few dozen members) and
clusters with 100’s of members. Masses are 1012 to 1014 solar masses.
Rich clusters have 1000’s of members. Masses are 1015 to 1016 solar masses.
Higher density of galaxies.
2) “regular” vs. “irregular” clusters
Regular clusters have spherical shapes. Tend to be the rich clusters.
Irregular clusters have irregular shapes. Tend to be the poor clusters.

71. Spirals dominate isolated galaxies, groups, poor clusters.
Ellipticals and SO’s dominate rich clusters, especially dense central parts.
Fraction of giant galaxies

72. At cluster centers lie the largest ellipticals: “cD” galaxies. They
Why?
One explanation: denser environment => more mergers => more ellipticals made as bulges grew. Most mergers happened long ago when galaxies were closer together.
At cluster centers lie the largest ellipticals: “cD” galaxies. They
have digested many companions. Masses up to 1014 solar masses
(remember: Milky Way about 6 x 1011 solar masses)!
Are these cores of
swallowed companions
or galaxies seen in
projection? Opinion
differs.

73. There is more mass between galaxies in clusters than within them
Abell 2029: galaxies (blue), hot intracluster gas (red)
X-ray satellites (e.g. ROSAT, Chandra) have revealed massive amounts of
hot ( K!) gas in between galaxies in clusters (“intracluster gas”). A
few times more than in stars!

74. What is the origin of intracluster gas? Possibilities:
“Leftover” gas from the galaxy formation process
2) Gas lost from galaxies in tidal interactions, ram pressure stripping,
supernova explosions, and jets from active galactic nuclei
High density of galaxies in clusters means
that tidal interactions are common
How could you tell between 1) and 2) ?

75. Take a spectrum! Many lines of elements produced by nucleo-synthesis in stars. Can’t be mostly “leftover” gas.
X-ray brightness
X-ray frequency

76. √ 2 G Mobject Most mass in clusters is in Dark Matter
Recall Escape Velocity: needed to completely escape the gravity of a massive object.
2 G Mobject R √
vescape =
Example: Coma Cluster
Mass in visible matter (galaxies and intracluster gas) 2 x 1014 solar masses. Size 3 Mpc. Escape speed then 775 km/s.
But typical velocity of galaxy within cluster observed to be 1000 km/s, and many have km/s! Must be more mass than is visible (85% dark matter inferred).

77. Clusters of galaxies also bend the light of more distant galaxies
seen through them

78. From the lensed galaxy images, you can figure out the total mass
Arcs are galaxies seen through gravitational lens
Ellliptical galaxies are mainly red and dead
All the blue images are
of the same galaxy!
From the lensed galaxy images, you can figure out the total mass
of the cluster. Results: much greater than mass of stars and gas => further
evidence for dark matter!

79. Dark matter predicted not to interact with ordinary matter, or itself,
The Bullet Cluster
Dark matter predicted not to interact with ordinary matter, or itself,
except through gravity. Gas clouds, by contrast, can run into each other.
A collision of two clusters provides dramatic evidence for dark matter:
cluster
trajectory
cluster
trajectory
red shows hot gas from two clusters, seen with Chandra X-ray observatory.
The gas clouds have run into each other, slowing each one down
blue shows inferred
distribution of cluster
mass from gravitational
lensing of background
galaxies. The dark matter
has gone straight through
with no interaction, like
the galaxies have.
Gas clouds collide but galaxies don’t
Mostly galaxies pass through each other
Dark matter does not collide with itself - would see more blue stuff in the middle

80. In 1920's, Hubble used Cepheids to find distances to some of these receding galaxies. Showed that redshift or recessional velocity is proportional to distance:
V = H0 x D (Hubble's Law)
velocity (km / sec) Distance (Mpc)
Hubble's Constant (km / sec / Mpc)
Or graphically. . .
Current estimate:
H0 = ~75 km/sec/Mpc
If H0 = 75 km/sec/Mpc, a galaxy at 1 Mpc moves away from us at 75 km/sec,
etc.

81. Results from a mid 1980's survey.
So by getting the spectrum of a galaxy, can measure its redshift, convert it to a velocity, and determine distance.
Results from a mid 1980's survey.
Assumes H0 = 65 km/sec/Mpc. Note how scale of structure depends on this.
1980s Harvard Survey - looked at all the galaxy’s in a section of sky
Measured velocities from red shift and used this to measure distance
Great Wall was found from this survey
This study influenced current evolutionary simulations
Ask Greg about why H constant is smaller than current value
Hubble's Law now used to unveil Large Scale Structure of the universe. Result: empty voids surrounded by shells or filaments, each containing many galaxies and clusters. Like a froth.

82. The Study of the Universe as a Whole
Cosmology
The Study of the Universe as a Whole

83. Logistics

84. What is the largest kind of structure in the universe
What is the largest kind of structure in the universe? The ~100-Mpc filaments, shells and voids? On larger scales, things look more uniform.
600 Mpc

85. The Cosmological Principle
Given no evidence of further structure, assume:
The Cosmological Principle
On the largest scales, the universe is roughly homogeneous (same at all places) and isotropic (same in all directions). Laws of physics same.
Hubble's Law might suggest that everything is expanding away from us, putting us at center of expansion. Is this necessarily true?
(assumes H0 = 65 km/sec/Mpc)

86. If there is a center, there must be a boundary to define it => a finite universe. If we were at center, universe would be isotropic (but only from our location) but not homogeneous:
Finite volume of galaxies expanding away from us into...what, empty space? Us
But if we were not at center, universe would be neither isotropic nor homogeneous: Us

87. So if the CP is correct, there is no center, and no edge to the Universe!
Best evidence for CP comes from Cosmic Microwave Background Radiation (later).
The Big Bang
All galaxies moving away from each other. If twice as far away from us, moving twice as fast (Hubble's Law). So, reversing the Hubble expansion, everything must have been together once. How long ago?

88. H0 gives rate of expansion. Assume H0 = 75 km / sec / Mpc
H0 gives rate of expansion. Assume H0 = 75 km / sec / Mpc. So galaxy at 100 Mpc from us moves away at 7500 km/sec. How long did it take to move 100 Mpc from us?
time = =
= billion years
distance
velocity
100 Mpc
7500 km/sec 1 H0
(Experts note that this time is just ).
The faster the expansion (the greater H0), the shorter the time to get to the present separation.
Big Bang: we assume that at time zero, all separations were infinitely small. Universe then expanded in all directions. Galaxies formed as expansion continued.

89. But this is not galaxies expanding through a pre-existing, static space. That would be an explosion with a center and an expanding edge.
If CP is correct, space itself is expanding, and galaxies are taken along for the ride. There is no center or edge, but the distance between any two points is increasing.
A raisin bread analogy provides some insight:

90. But the cake has a center and edge
But the cake has a center and edge. Easier to imagine having no center or edge by analogy of universe as a 2-d expanding balloon surface:
Now take this analogy "up one dimension". The Big Bang occurred everywhere at once, but "everywhere" was a small place.
(To understand what it would be like in a 2-d universe, read Flatland by Edwin Abbott: )

91. If all distances increase, so do wavelengths of photons as they travel and time goes on.
When we record a photon from a distant source, its wavelength will be longer. This is like the Doppler Shift, but it is not due to relative motion of source and receiver. This is correct way to think of redshifts of galaxies.

92. The Cosmic Microwave Background Radiation (CMBR)
A prediction of Big Bang theory in 1940's. "Leftover" radiation from early, hot universe, uniformly filling space (i.e. isotropic, homogeneous). Predicted to have perfect black-body spectrum.
Photons stretched as they travel and universe expands, but spectrum always black-body. Wien's Law: temperature decreases as wavelength of brightest emission increases => was predicted to be ~ 3 K now.

93. Deviations are -0.25 milliKelvin (blue) to +0.25 milliKelvin
All-sky map of the CMBR temperature, constant everywhere to one part in 105 ! For blackbody radiation, this means intensity is very constant too (Stefan’s law).
(WMAP satellite)
Deviations are milliKelvin (blue) to milliKelvin
(red) from the average of Kelvin.

94. IF the Big Bang happened at one point in 3-d space:
That the CMBR comes to us from every direction is best evidence that Big Bang happened everywhere in the universe. That the temperature is so constant in every direction is best evidence for homogeneity on large scales.
IF the Big Bang happened at one point in 3-d space:
Later, galaxies form and fly apart. But radiation from Big Bang streams freely at speed of light! Wouldn't see it now.

95. The Expansion of the Universe Seems to be Accelerating
The gravity of matter should retard the expansion. But a new distance indicator shows that the expansion rate was slower in the past!
Type I supernovae: from ones in nearby galaxies, know luminosity. In distant galaxies, determine apparent brightness. Thus determine distance. Works for more
than 3000 Mpc. From redshifts, they are
not expanding as quickly from each
other as galaxies are now.
H0 was
smaller in
past (i.e.
for distant
galaxies)
Redshift (fractional shift in wavelength of spectral lines)
Taking this into account, best age estimate of Universe is 13.8 Gyrs.

96. The Cosmological Constant, 
Introduced by Einstein in 1917 to balance gravitational attraction and create static Universe (turned out to be wrong!). Can think of  as repulsive force that exists even in a vacuum. But accelerating universe indicates there is a . Also often called "dark energy". We have little idea of its physical nature.
The measured acceleration implies that there is more “dark energy” than the energy contained in matter.

97. The Early Universe The First Matter
At the earliest moments, the universe is thought to have been dominated by high-energy, high-temperature radiation. Photons had enough energy to form particle-antiparticle pairs. Why? E=mc2.
pair production
annihilation

98. At time < 0.0001 sec, and T > 1013 K, gamma rays could form proton-antiproton pairs.
At time < 15 sec, and T > 6 x 109 K, electron-positron pairs could form.
Annihilation occurred at same rate as formation, so particles coming in and out of existence all the time.
As T dropped, pair production ceased, only annihilation. A tiny imbalance (1 in 109) of matter over antimatter led to a matter universe
(cause of imbalance not clear, but other such imbalances are known to occur).

99. Primordial Nucleosynthesis
Hot and dense universe => fusion reactions.
At time sec (T = x 108 K), helium formed.
Stopped when universe too cool. Predicted end result: 75% hydrogen, 25% helium.
Oldest stars' atmospheres (unaffected by stellar nucleosynthesis) confirm Big Bang prediction of 25% helium.

100. Successes of the Big Bang Theory
1) It explains the expansion of the universe.
2) It predicted the cosmic microwave background radiation, its uniformity, its current temperature, and its black-body spectrum.
3) It predicted the correct helium abundance (and lack of other primordial elements).

101. Misconceptions about the Big Bang
“The universe was once small.” The observable universe, which is
finite, was once small. The nature of the entire universe at early times
is not yet understood. It is consistent with being infinite now.
“The Big Bang happened at some point in space.” The microwave
background showed that it happened everywhere in the universe.
3. “The universe must be expanding into something.” It is not expanding
into “empty space”. That would imply the Big Bang happened at some
location in space. It is a stretching of space itself.

102. 4. “There must have been something before the Big Bang.”
The Big Bang was a singularity in space and time (like the center of a black hole). Our laws of physics say the observable universe had infinitesimally small size, and infinite temperature and density.
In these conditions, we don’t have a physics theory to describe the nature of space and time. At the Big Bang, time took on the meaning that we know it to have.
"Before" is only a relevant concept given our everyday understanding of time. We must await a better understanding of the nature of space and time. Such theories are in their infancy.
Shouldn’t be surprising that these concepts are hard to grasp.
So was the heliocentric Solar System 400 years ago.

103. Plot of how the black-body temperature of the background radiation varies over the sky (the Galactic disk runs across the middle).
Our motion relative to this background causes a Doppler shift, so that the temperature varies by a few milliKelvin (blue-pink difference).

104. The Early Universe Inflation A problem with microwave background:
Microwave background reaches us from all directions.
Temperature of background in opposite directions nearly identical. Yet even light hasn't had time to travel from A to B (only A to Earth), so A can know nothing about conditions at B, and vice versa. So why are A and B almost identical? This is “horizon problem”.

105. Solution: Inflation. Theories of the early universe predict that it went through a phase of rapid expansion.
Separation between two points (m)
If true, would imply that points that are too far apart now were once much closer, and had time to communicate with each other and equalize their temperatures.

106. Inflation also predicts universe has flat geometry:
Microwave background observations seem to suggest that this is true.

107. State change of the Vacuum
What drove Inflation?
State change of the Vacuum
Vacuum has energy fluctuations, Heisenberg uncertainty principle states:
E t > h/2
Quantum fluctuations
They have mass

108. The End of the Universe
How will the Universe end? Is this the only Universe? What, if anything, will exist after the Universe ends?

109. The Five Ages of the Universe
1) The Primordial Era
2) The Stelliferous Era
3) The Degenerate Era
4) The Black Hole Era
5) The Dark Era
Stellifeous - the star era - lots of stars - where we are now
Degenerate - stars run out of gas - neutron stars and white dwarfs
Black holes dominate

110. The Geometry of the Universe determines its fate
Flat or negative curvature - universe ends in ice
Aka heat death
Measure hubble constant
We think the answer is the green line - universe will end in ice