15.2 Distances of Galaxies
• Our Goals for Learning
• How do we measure the distances to galaxies?
• What is Hubble’s Law?
• How do distance measurements tell us the age of the universe?
How do we measure the distances to galaxies?
Step 1
Determine size of solar system using radar
Step 2
Determine distances of stars out to a few hundred light­years using parallax
Brightness alone does not provide enough information to measure distance
The relationship between apparent brightness and luminosity depends on distance:
Luminosity
Brightness = 4 pi x (distance)2
We can determine a star’s distance if we know its luminosity and can measure its apparent brightness:
Luminosity
Distance = 4 pi x Brightness
A standard candle is an object whose luminosity we can determine without measuring its distance.
We can use standard candles to measure distances.
Step 3
Apparent brightness of star cluster’s main sequence tells us its distance
Which kind of stars are best for measuring large distances?
1. High­luminosity stars
82%
2. Medium­luminosity stars
8%
3. Low­luminosity stars
10%
:00
Cepheid variable stars are very luminous
Cepheid variable stars with longer periods have greater luminosities
Step 4
The period of a Cepheid variable star tells us its luminosity.
Its luminosity plus its apparent brightness tells us its distance. So we can use Cepheid variable stars as standard candles to measure distances.
Edwin Hubble, using Cepheids as standard candles, was the first to measure distances to other galaxies
Measuring distances using Cepheids has been a key mission of the Hubble Space Telescope
Hubble’s extra­sharp vision allows us to observe individual Cepheid variable stars in galaxies up to 100 million light­
years away
Galaxy M100
Clicker Question: You’ve found a Cepheid variable star in Galaxy A with a period of 100 days. You've also found a Cepheid variable star in Galaxy B with a period of 10 days. Both Cepheids have the same brightness as seen from Earth. Which galaxy is farther away from us?
• GET YOUR ANSWER READY:
• A) Galaxy A
• B) Galaxy B
• C) Both are the same distance
Which galaxy is farther away?
1. Galaxy A
2. Galaxy B
81%
9%
3. Both are the same distance
10%
:00
White­dwarf supernovae can also be used as standard candles
Step 5
Supernova
Apparent brightness of white­dwarf supernova (another kind of standard candle) tells us the distance to its galaxy
(up to 10 billion light­
years)
In summary, we measure galaxy distances using a chain of techniques known as the distance ladder
What is Hubble’s Law?
By measuring velocities and distances of galaxies, Hubble found that a galaxy’s velocity and distance are related in a special way
The spectral features of virtually all galaxies are redshifted ⇒ They’re all moving away from us
Hubble’s Law: velocity = H0 x distance
Redshift of a galaxy tells us its distance through Hubble’s Law:
velocity
distance = H
0
Distances of farthest galaxies are measured from redshifts
What have we learned?
• How do we measure the distances to galaxies?
• Our measurements of galaxy distances depend on a chain of methods. The chain begins with radar ranging in our own solar system and parallax measurements of distances What have we learned?
• What is Hubble’s law?
• Hubble’s law tells us that more distant galaxies are moving away faster. It allows us to determine a galaxy’s distance from the speed at which it is moving away from us, which we can measure from its Doppler shift. Activity #49, page 185­188
• Page 186 has 3 photos of a flat (2­dimensional) universe of galaxies, taken at 3 different times.
• Use it to answer the questions in Part I on page 185.
• We’ll do those as clicker questions, then do the same for Part II.
2. If you were in one of the other galaxies, would the MW (Milky Way) galaxy appear to be moving away from you?
88%
1. Yes
2. No
3. It depends
o
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3%
It
de
p
N
Y
es
9%
:00
4. Are any of the galaxies moving closer to each other?
80%
1. Yes
2. No
3. Maybe
16%
M
ay
be
o
N
Y
e
s
4%
:00
5. If we measured radial velocities of other galaxies, what would we see?
88%
10%
.
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2%
A
1. All galaxies redshifted
2. All galaxies blueshifted
3. Some galaxies redshifted, some galaxies blueshifted
:00
6. If someone in another galaxy measured radial velocities of galaxies besides their own, what would they see?
84%
12%
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4%
A
1. All other galaxies redshifted
2. All other galaxies blueshifted
3. Some galaxies redshifted, some galaxies blueshifted
:00
Part II, page 187 (instructions on page 186)
• Using Figure 2, fill in the blank entries in the lower right of Table 1: you’re measuring how far galaxies A and B moved between images II and III, divided by the time elapsed between images II and III.
• Then, using the bottom row of Table 1 (which you’ve just filled in), in Figure 3 plot the velocities of galaxies A and B as a function of their distance.
• Then answer questions 8D, 9, 10.
8D. Figure 3 shows that the farther away a galaxy is, the ___ it is moving away from the reference galaxy.
88%
4%
ee
d is
in
...
er
ow
–
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p
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th
er
N
st
er
8%
F
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1. Faster
2. Slower
3. Neither – speed is independent of distance
:00
9. How long has galaxy B been travelling if it started at the origin in Fig. 2, moved at constant speed, and ended up at its position in Image III?
1. 2 billion years
55%
2. 4 billion years
39%
3. 8 billion years
6%
:00
10. Who do you think is correct?
1. Sam
10%
2. Samantha
90%
:00