The Expanding Universe

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The Expanding Universe
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Getting the Distances to Galaxies is a Big
Industry
d constant x (L/B)1/2
The Distance Ladder
Location Distance Method
solar system 10 A.U. radar
ranging Local Galaxy 100 pc
stellar parallax Across Galaxy 10,000 pc
spectroscopic
parallax Nearby galaxies
15 Mpc Variable stars Distant galaxies
200 Mpc Standard candle
and
Tully-Fisher
1 Mpc 1 million parsecs
We have studied stellar parallax, and variable
stars.
Spectroscopic parallax is simply comparison of
brightness of identical stars. Standard candle is
comparison of brightness of identical supernovae
explosions. Tully-Fisher is a way to measure
galaxy luminosity from its rotations speed.
More
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Distance Measurements to Other Galaxies (1)

• Cepheid Method Using Period Luminosity
  relation for classical Cepheids
• Measure Cepheids Period ? Find its luminosity ?
  Compare to apparent magnitude ? Find its distance

b) Type Ia Supernovae (collapse of an accreting
white dwarf in a binary system) Type Ia
Supernovae have well known standard luminosities
? Compare to apparent magnitudes ? Find its
distances
Both are Standard-candle methods Know absolute
magnitude (luminosity) ? compare to apparent
magnitude ? find distance.
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Cepheid Distance Measurement
Repeated brightness measurements of a Cepheid
allow the determination of the period and thus
the absolute magnitude.
? Distance
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Tully-Fisher Distance Indicator
Recall, luminosity of stars scales with mass of
stars therefore, luminosity of galaxy scales
with number of stars (and thus, mass of stars).
Thus, luminosity of galaxy gives mass of
galaxy. Going backwards measure the velocity
to weigh the galaxy to obtain luminosity.
velocity
L constant x (velocity)4
d constant x (L/B)1/2
Doppler velocity map of galaxy.
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The Extragalactic Distance Scale

• Many galaxies are typically millions or billions
  of parsecs from our galaxy.

• Typical distance units
• Mpc Megaparsec 1 million parsec
• Gpc Gigaparsec 1 billion parsec

• Distances of Mpc or even Gpc ? The light we see
  left the galaxy millions or billions of years
  ago!!

• Look-back times of millions or billions of years

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The Hubble Law
The problem is that 200 Mpc is nothing! Well, it
turns out that there is another indicator for
extreme distances. The Hubble Law The further
away a galaxy is, the greater is its redshift.
Red Blue
(As you can see, it is not perfect.)
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Distance Measurements to Other Galaxies (2) The
Hubble Law
E. Hubble (1913) Distant galaxies are moving
away from our Milky Way, with a recession
velocity, vr, proportional to their distance d
vr H0d
H0 70 km/s/Mpc is the Hubble constant

• Measure vr through the Doppler effect ? infer
  the distance

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Hubble Law Takes us All the Way Out
Implies that Galaxies are flying away and that
the speed with which they are moving away is
proportional to there distance away.
The distance scale revisited.
The further away the galaxy, the faster it is
receding from us. (more on this later)
velocity constant x distance
The constant is called Hubbles constant. It is
designated as H0. Pronounced H not.
velocity H0 x distance
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Discovery of Expansion

• 1929 Edwin Hubble measured the
  distances to 25 galaxies
• Compared distances and recession velocities
• Calculated recession velocity by assuming the
  redshift of spectral lines is due to the Doppler
  Effect
• Discovered
• Recession velocity gets larger with distance.
• Systematic expansion of the Universe.

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Redshifted Spectral Lines
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Hubbles Data (1929)
Recession Velocity (km/sec)
1000
500
0
0
1
2
Distance (Mpc)
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Added more data Hubble Humason (1931)
20,000
Recession Velocity (km/sec)
15,000
10,000
5000
1929 Data
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Distance (Mpc)
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Hubbles Law
v H0 x d

• v recession velocity in km/sec
• d distance in Mpc
• H0 expansion rate today (Hubble Parameter)
• Measure Hubble Parameter by calculating slope of
  the linear relationship
• Best value H0 22 2 km/sec/Mly
• where Mly Mega lightyear1 million ly

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Interpretation

• Hubbles Law demonstrates that the Universe is
  expanding in a systematic way
• The more distant a galaxy is, the faster it
  appears to be moving away from us.
• Hubble Parameter Rate of expansion today.
• Comments
• Empirical result - based only on data
• Actual value of H0 is important. Allows us to get
  a rough idea of the Age of the Universe (time
  elapsed since the Big Bang)

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Age of the Universe (Analogy)

• You leave Columbus by car for Florida, but leave
  your watch behind.
• How long have you been on the road?
• Your speed 100 km/h
• Your trip meter reads distance 300 km
• Time since you left T distance ? speed
• T 300 km ? 100 km/h 3.00 hours

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The Hubble Time T0

• Hubbles Law says
• A galaxy at distance d away has a recession
  speed, v H0?d
• So as in the analogy
• T0 d / v
• but since, v H0?d, T0 d / H0?d 1 / H0
• Hubble Time T0 1 / H0
• Estimate of the Age of the Universe

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Best Estimate of the Age

• 14.0 ? 1.4 Gyr
• This age is consistent with the ages of the
  oldest stars seen in globular clusters.
• 1 Gyr 1 Gigayear 1 billion years

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Common Misconception of Universe Expansion
Milky Way
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Common Misconception

• Description
• Galaxies are all moving away from each other
  through space
• Explosion of the Big Bang sent them flying
• Big Bang sent all galaxies flying away from MW
  because that is what we observe
• Problems
• Why is the Milky Way the Center of the Universe?
• Why is Hubbles Law obeyed?
• Should speed vs distance be linear?
• Does the galaxy movement have to be uniform?

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Space Itself is Expanding Hubble Flow
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Correct Explanation

• Description
• Galaxies typically have small (compared to Hubble
  flow), gravitationally influenced motions in any
  direction in space. (More on this later)
• SPACE ITSELF IS EXPANDING
• Distance between galaxies is growing, they only
  appear to be moving away
• Solutions
• Nothing special about the Milky Way. Every galaxy
  would see the others receding from them (in the
  same manner)
• Hubbles Law follows naturally.
• Galaxy A is 1 Mly from MW dA1 Mly. Galaxy B
  has dB3 Mly
• Expansion of universe doubles the scale of the
  coordinate system
• Now A distance is 2 Mly B distance is 6 Mly
• VA (2-1)1 Mly dA VB (6-3)3 Mly dB V
  d

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Two Dimensional Analogy
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Cosmological Redshift

• Expansion of space stretches light
• Wavelengths get stretched intoredder (longer)
  wavelengths
• The greater the distance,the greater the
  stretching
• Result
• The redshift of an objectgets larger with
  distance.
• Just what Hubble actually measured

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Two Dimensional Analogy
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Time to be more precise

• Most galaxies are found in groups clusters
• Galaxies are held in them by gravity
• It is the distance between clusters of galaxies
  that is getting bigger due to the expansion of
  the universe
• Within a cluster, galaxies can have other motions
  due to the gravity produced by the total matter
  in the cluster. Gravitational Force is stronger
  on these small scales than the expansion.
• For example, the Andromeda Galaxy and the Milky
  Way are on a collision course!

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The Local Group

• Group of 39 galaxies including the Milky Way and
  Andromeda
• Size 1 Mpc
• 5 bright galaxies (M31, MW, M33, LMC, IC10)
• 3 Spirals (MW, M31, M33)
• 22 Ellipticals (4 small Es 18 dEs)
• 14 Irregulars of various sizes (LMC, SMC nearest
  neighbors)
• Total Mass 5x1012 Msun

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The Local Group
1 Megaparsec (Mpc)
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Virgo Cluster

• Nearest sizable cluster to the Local Group
• Relatively loose cluster, centered on two bright
  Ellipticals M87 M84
• Properties
• Distance 18 Mpc
• Size 2 Mpc
• 2500 galaxies (mostly dwarfs)
• Mass 1014 Msun

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Rich Clusters

• Contain 1000s of bright galaxies
• Extend for 5-10 Mpc
• Masses up to 1015 Msun
• One or more giant Elliptical Galaxies at center
• Ellipticals found near the center.
• Spirals found at the outskirts.
• 10-20 of their mass is in the form of a very hot
  (107-8K) intracluster gas seen only atX-ray
  wavelengths.

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Rich Cluster Abell 1689 (Hubble Space Telescope)