The Tully-Fisher Relation

1
The Tully-Fisher Relation

• A relation between the rotation speed of a spiral
  galaxy and its luminosity
• The more mass a galaxy has ?the brighter it is ?
  the faster it rotates ? the wider the spectral
  lines are
• Measuring rotation speed allows us to estimate
  luminosity comparing to observed (apparent)
  brightness then tells us the distance

2
Beyond the Galactic Scale Clusters of Galaxies

• The Local Group The Virgo Cluster

3
Superclusters
4
Beyond Superclusters

• Strings, filaments, voids
• Reflect structure of the universe close to the
  Big Bang
• Largest known structure the Great Wall (70 Mpc ?
  200 Mpc!)

5
Cosmology

• The part of astronomy (and astrophysics) that
  deals with the greatest structures in the
  universe and the evolution of the universe
  itself!

6
Cosmologically relevant Questions

• What is in the universe?
• How do these things interact?
• How does the universe change in time?
• Is there a beginning?
• Is there an end?

7
Whats in the Universe?

• Answers come from observations
• ? Lets observe

8
Whats in the Universe?
Big ..small
9
So, why is the night sky dark?(Olbers Paradox)

• Conclusion either
• Universe is not infinite or
• Universe changes in time

10
Everything is moving away from us!

• Measure spectrum of galaxies and compare to
  laboratory measurement
• lines are shifted towards red
• This is the Doppler effect Red-shifted objects
  are moving away from us

11
Hubbles Law

• The final rung on the cosmic distance ladder
• Hubbles observations (1920s)
• Light from distant galaxies is red-shifted
• The more distant the galaxy, the greater the
  red-shift
• Interpretation
• Galaxies are moving away from us
• More distant galaxies are moving faster
• The universe is expanding, carrying the galaxies
  with it!

12
Doppler Shifts of Galaxies
Hubble, 1929
13
Hubbles Law
Velocity H0 ? Distance Distance Velocity
/H0

• H0 (65 15) km/sec/Mpc is Hubbles constant
• Compare to distance velocity ? time
• Appears the universe exploded from a single
  point in the past the Big Bang
• Age of the universe is 1/H0 or about 14 billion
  years

14
The Expanding Universe

• Except for a few nearby galaxies (like
  Andromeda), all the galaxies are seen to be
  moving away from us
• Generally, the recession speed of a galaxy is
  proportional to its distance from us that is, a
  galaxy thats twice as far away is moving twice
  as fast (aside from local motions within galaxy
  clusters)

15
The Expanding Universe

• This expansion pattern (speed proportional to
  distance) actually implies that galaxies are all
  moving away from each other

Milky Way
Expansion
16
The Expanding Universe

• This expansion pattern (speed proportional to
  distance) actually implies that galaxies are all
  moving away from each other

Milky Way
Expansion
Twice as far away, so moves twice as fast
17
The Expanding Universe

• This expansion pattern (speed proportional to
  distance) actually implies that galaxies are all
  moving away from each other

Start
A while later
2d
d
18
The Expanding Universe

• Each galaxy sees the others moving away with the
  same pattern (further ? faster)
• As though the galaxies ride on a rubber band that
  is being stretched!

Start
A while later
19
The Expanding Universe

• In three dimensions, imagine the galaxies are
  raisins in an expanding loaf of bread

20
The Expanding Universe

• Appears the universe exploded from a state in
  which matter was extremely dense and hot the
  Big Bang
• Where did the expansion begin? Everywhere!
• Every galaxy sees the others receding from it
  there is no special point (center)

21
Cosmological Red-Shift

• Not really a Doppler effect
• Space itself is being stretched between galaxies

22
Conclusions from our Observations

• The Universe has a finite age, so light from very
  distant galaxies has not had time to reach us,
  therefore the night sky is dark.
• The universe expands now, so looking back in time
  it actually shrinks until?
• ?Big Bang model The universe is born out of a
  hot dense medium
• 13.7 billion years ago.

23
Big Bang

• The start of the universe, a primordial
  fireball
• ? the early universe was very hot and dense
• ? intimate connection between
• cosmology and nuclear/particle
• physics
• To understand the very big
• we have to understand the
• very small

24
How does the expansion work?

• Like an explosion (hot, dense matter in the
  beginning), but space itself expands!
• Slowed down by gravitational attraction
• Attraction is the stronger, the more mass there
  is in the universe
• Scientifically described by Einsteins
• General theory of Relativity (1915)

25
More General

• General Relativity is more general in the sense
  that we drop the restriction that an observer not
  be accelerated
• The claim is that you cannot decide whether you
  are in a gravitational field, or just an
  accelerated observer
• The Einstein field equations describe the
  geometric properties of spacetime

26
The Idea behind General Relativity

• We view space and time as a whole, we call it
  four-dimensional space-time.
• It has an unusual geometry, as we have seen
• Space-time is warped by the presence of masses
  like the sun, so Mass tells space how to bend
• Objects (like planets) travel in straight lines
  through this curved space (we see this as
  orbits), so
• Space tells matter how to move

27
Effects of General Relativity

• Bending of starlight by the Sun's gravitational
  field (and other gravitational lensing effects)

28
Assumption Cosmological Principle

• The Cosmological Principle on very large scales
  (1000 Mpc and up) the universe is homogeneous and
  isotropic
• Reasonably well-supported by observation
• Means the universe has no edge and no center
  the ultimate Copernican principle!

29
What General Relativity tells us

• The more mass there is in the universe, the more
  braking of expansion there is
• So the game is
• Mass vs. Expansion
• And we can even calculate who wins!

30
The Fate of the Universe determined by a single
number!

• Critical density is the density required to just
  barely stop the expansion
• Well use ?0 actual density/critical density
• ?0 1 means its a tie
• ?0 gt 1 means the universe will recollapse (Big
  Crunch) ? Mass wins!
• ?0 lt 1 means gravity not strong enough to halt
  the expansion ? Expansion wins!
• And the number is ?0 lt 1 (probably)

31
The size of the Universe depends on time!
Expansion wins!
Its a tie!
Mass wins!
Time
32
The Shape of the Universe

• In the basic scenario there is a simple relation
  between the density and the shape of space-time
• Density Curvature 2-D example Universe
  Time Space
• ?0gt1 positive sphere closed,
  bound finite
• ?01 zero (flat) plane open, marginal
  infinite
• ?0lt1 negative saddle open, unbound
  infinite