1. The Expanding Universe

2. Getting the Distances to Galaxies is a “Big Industry”
d = constant x (L/B)1/2
The Distance Ladder
Location Distance Method
solar system A.U radar ranging
Local Galaxy pc stellar parallax
Across Galaxy 10,000 pc spectroscopic
“parallax”
Nearby galaxies Mpc Variable stars
Distant galaxies 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 …

3. Distance Measurements to Other Galaxies (1)
Cepheid Method: Using Period – Luminosity relation for classical Cepheids:
Measure Cepheid’s 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.

4. Cepheid Distance Measurement
Repeated brightness measurements of a Cepheid allow the determination of the period and thus the absolute magnitude.
 Distance

5. Doppler velocity map of galaxy.
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.

6. 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

7. 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.)

8. Distance Measurements to Other Galaxies (2): The Hubble Law
Distant galaxies are moving away from our Milky Way, with a recession velocity, vr, proportional to their distance d:
vr = H0*d
H0 ≈ 70 km/s/Mpc is the Hubble constant
Measure vr through the Doppler effect  infer the distance

9. 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 Hubble’s constant.
It is designated as H0. Pronounced “H not”.
velocity = H0 x distance

10. 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.

11. Redshifted Spectral Lines

12. Increasing Distance

13. Recession Velocity (km/sec)
Hubble’s Data (1929)
Recession Velocity (km/sec)
1000
500 1 2
Distance (Mpc)

14. Added more data :Hubble & Humason (1931)
20,000
Recession Velocity (km/sec)
15,000
10,000
5000
1929 Data 10 20 30
Distance (Mpc)

15. v = H0 x d Hubble’s Law 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 lightyear=1 million ly

16. Interpretation
Hubble’s 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)

17. 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

18. The Hubble Time: T0 Hubble’s Law says So as in the analogy:
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

19. 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

20. Common Misconception of Universe Expansion
Milky Way

21. Common Misconception Description: Problems:
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 Hubble’s Law obeyed?
Should speed vs distance be linear?
Does the galaxy movement have to be uniform?

22. Space Itself is Expanding: Hubble Flow

23. Correct Explanation Description: Solutions:
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)
Hubble’s Law follows naturally.
Galaxy A is 1 Mly from MW : dA=1 Mly. Galaxy B has dB=3 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

24. Two Dimensional Analogy

25. Cosmological Redshift
Expansion of space stretches light:
Wavelengths get stretched into redder (longer) wavelengths
The greater the distance, the greater the stretching
Result:
The redshift of an object gets larger with distance.
Just what Hubble actually measured

26. Two Dimensional Analogy

27. 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!

29. 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

30. The Local Group
1 Megaparsec (Mpc)

31. 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

32. Rich Clusters Contain 1000’s 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 at X-ray wavelengths.

33. Rich Cluster
Abell 1689
(Hubble Space Telescope)