# Presentation: 318159

## The Expanding Universe:Evidence for Acceleration

- Review of Hubble’s Law
- Excel Activity: Hubble’s Law with recent data
- Modern interpretation of a Hubble diagram
- Brainstorm Activity: Hubble diagrams that account for a changing rate of expansion
- Excel Activity: Hubble diagrams with very distant galaxies

**Notes:**
A discovery was made in 1998 that has significantly changed our view of the cosmos. It was discovered that the expansion of the universe is accelerating. Why? We don’t know. But we’re calling it Dark Energy.

The idea of this activity is to use the 1998 data that led to this result to “discover” it for yourself. I’ve included on this CD a pdf of the 1998 paper from which all the data has been taken. (Specifically look at pages 18 & 19, columns 2 and 9.)

We’ll be making plots similar to those Edwin Hubble made when he first discovered the universe was expanding. I wasn’t sure how familiar everyone was with Hubble’s Law, so I have included a couple slides to review this.

Overview of five parts of the activity.

## Part 1: What is Hubble’s Law?

**In 1929 Edwin Hubble plotted the velocities of various galaxies vs. their distances**
**Interpretation: all galaxies are moving away from each other**

**Notes:**
Hubble found that on average galaxies are moving away from us and farther galaxies are moving faster. (Note: the graph does not imply that galaxies will begin moving faster as they get farther away. Instead, the galaxies that are far away got there precisely because they were moving faster.)

At first glance it appears we are at the center of a big explosion. But really we could be anywhere among the pieces that are exploding outward. From the perspective of any one piece, all the others would be moving away.

Demo galaxies on a rubber band as it stretches.

How did Hubble measure these velocities and distances?

## Measuring Velocity by Doppler Effect

- Light waves and sound waves spread outward in circles.
- If the source of waves is moving, then observer A will see these waves far apart (low frequency) while observer B sees them close together (high frequency).
- For sound waves, different frequencies are heard as different pitches. For light waves, different frequencies are seen as different colors in the rainbow.
- This change in frequency (Doppler Effect) can be used to measure the velocity of the source.

**Notes:**
Do demo of Doppler Effect with sound.

Mention terms “redshift” and “blueshift”

## Redshift as a measure of velocity

-  At low velocities

- z

- Definition of Redshift:

**Notes:**
The purple line shows the exact value of z, and the black one is v/c.

So for the galaxies Hubble was using, where all of the redshifts were less than 10%, z and v are essentially the same. So this is how Hubble measured velocity.

How do you measure the distance to other galaxies?

## Measuring Distance:Brightness of a Standard Candle

- Hubble used Cepheid variables and “typical” galaxies
- Newest standard is Type Ia supernovae
- As bright as an entire galaxy

## Measuring brightnessand finding distance

- Stellar brightness is quantified using “visual magnitude” scale
- Hipparchus ranked stars from 1 to 6: 1 being the brightest in the sky, 6 the dimmest (with unaided eye)
- Now we quantify magnitude:
- 	where m is apparent magnitude, d  is distance, and M is the absolute magnitude--the brightness of the object from a distance of 10 parsecs (pc)
- For Type Ia supernova,

**Notes:**
Why is the visual magnitude scale logarithmic? The human eye does not respond linearly to brightness. For example a 50W light bulb appears to have a brightness that is exactly in the middle of a 25W and a 100W.

10 parsecs is about 32 lightyears.

The value of M=-19.3 is not exact. Note: negative values of magnitude mean really bright.

So this gives us an exact way to determine distance based on apparent magnitude of an object if we know its absolute magnitude.

## Part II: Hubble’s Law with recent Data

- Open “Expanding Universe Data”
- Create a column of distances in megaparsecs. (Calculate these from visual magnitudes.)
- Create a column of velocities in km/s (calculated from redshifts.)
- Make a Hubble diagram. (Graph velocity vs. distance.)

**Notes:**
So the first thing we can do is improve on Hubble’s plot by using more recent data taken with better equipment and with an improved standard candle for measuring distance.

If you’re familiar with Excel, go to it. If you haven’t used Excel much for making graphs, I’ve written some more detailed instructions.

## Part 3: Interpretation of a Hubble Diagram

- Slope of graph is called the Hubble constant; it represents the rate of expansion:
- 			   from our graph
- Work backwards and calculate the time since the Big Bang: if a galaxy were 1 Mpc away, how long would it take to reach Earth moving at a speed of 56 km/s? Hint:

**Notes:**
Units of the Hubble constant are km/s per megaparsec. So if another galaxy is a million parsecs or 3.2 million light years away, you can expect it to be moving away from you at a rate of about 56 km/s. Andromeda galaxy is roughly that distance away, but it is moving towards us due to gravity. So this value really only works on larger distance scales.

A nice corollary is that if the universe is expanding at this constant rate, you can work backwards and figure out how long ago other galaxies would be where we are. In other words, how long does it take for an object moving at 56 km/s to cover a distance of 1000000 parsecs. That gives an estimate for the time since the Big Bang. (d=vt, so t=d/v = 3 x 10^19km / 56km/s  = 5.4 x 10^17 seconds = 17 billion years)

## Modern Interpretation of Hubble Diagram

- Re-interpreting redshift: Wavelengths are stretched by expansion of space (not Doppler shifted by velocity). So the y-axis shows the percent by which the universe expanded during the time that light traveled a distance, d.
- Example from our data: SN1990O
- 	z = 0.030; distance = 129 Mpc = 4.13 x 108 ly
- 	So the universe expanded by 3.0% during the 413 million years that light traveled to us from this supernova.

**Notes:**
Hubble viewed redshift as a Doppler effect from galaxies moving through space. Nowadays cosmologists say it is an expansion of space itself. One important difference between these is that objects can only move through space at speeds less than c, but there is no limit to how fast one object may move away from another due to the expansion of space in between them.

It is also easy to see how light waves traveling through this space would be stretched as it expands. Demo rubber band with stretching wavelengths.

When we look at distant galaxies we see light that left billions of years ago. While that light is travelng toward us its is getting stretched by the expansion of space. Because that light is traveling through space at c, the distance to these galaxies is also a measure of the amount of time that the light has been traveling and stretching.

## So how do we interpret the graph?

- Amount the universe has expanded as a function of time during which it has expanded.
- Careful: Large values of time represent times long ago (from galaxies far, far away), not times in the future.

**Notes:**
It’s tempting to look at this and say, “it shows how space is expanding as time goes on.” But data points farther to the right give information about what happened farther in the past.

## Part 4: Brainstorm 

- 	Before 1998, most people assumed that gravity was causing the expansion of the universe to slow down. If this assumption were correct, and the universe used to be expanding at a faster rate, what would our graph look like when we include galaxies that are very far away? Would it be straight or curved? If it curves, would it curve up or down?

**Notes:**
When I first began teaching physics I read about possible fates of the universe. Would it expand forever? Or would gravity slow the expansion to a halt, resulting in an eventual big crunch? I remember reading 10 or 15 years ago about how surveys of distant galaxies showed that they were not slowing down fast enough for the expansion to stop. Well now we know even more and that’s what we are going to explore.

## Part 5: Including Data for        Distant Galaxies

- Within the “Expanding Universe Data” there is a worksheet called “Distant Supernovae”. Copy this data and paste it immediately below the “Nearby” data.
- “Fill Down” the formula for distance.
- Make a graph of redshift vs. distance using both Nearby and Distant supernova data
- Is the graph linear or does it curve?
- How should we interpret this?

**Notes:**
Consensus: If the graph curves up, then the universe has expanded more than we would expect based on a constant rate of expansion. That implies that it used to be expanding at a faster rate than it is now. Thus the expansion is slowing down.

(Put differently: the slope is the rate of expansion. If the universe used to be expanding faster, then data points to the right (long ago) should have a steeper slope.)

Actual data curves down. That implies the universe is expanding faster now than it was several billion years ago. The expansion of the universe is accelerating. What could cause it to do this? Gravity is the only force we know of that acts over long distances. If all energy gravitates, there must be some other kind of energy that repels. Let’s call it “Dark Energy”.

Possible sources: vacuum energy. But computations of this say that there should be 10^120 times more than we can infer from our acceleration. That’s called the “fine tuning problem.”

We make the analogy of gravity as dimples in a flat sheet. Dark energy could be like bumps in this sheet. 

## Measuring Velocity from Redshift

- Doppler shift from receding source of light:
- Redshift (z) is defined by:
- Combining these:

**Notes:**
We’ve all experienced Doppler effect for sound. When the motorcycle drives by and you hear.... There is a change in frequency if the source is moving toward or away from you. The amount the frequency changes is related to the velocity of the source. The same applies for light, resulting in blue shifts and red shifts, corresponding to increases or decreases in frequency. Since there is no preferred reference frame for light, however, the formula for Doppler shift must account for relativity, and ends up looking like... where f0 is the frequency of the light in the frame of the source.

Redshift is measured as a percent change of the wavelength.

So we can see an exact relationship between redshift and velocity. Luckily, this relationship can be simplified for relatively low velocities...

## Approximating... 

- At low velocities

**Notes:**
The purple line shows the exact value of z, and the black one is v/c.

So for the galaxies Hubble was using, where all of the redshifts were less than 10%, z and v are essentially the same. So this is how Hubble measured velocity.

How do you measure the distance to other galaxies?