Title: The Expanding Universe: Evidence for Acceleration
1The Expanding UniverseEvidence for Acceleration
- Review of Hubbles Law
- Excel Activity Hubbles 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
2Part 1 What is Hubbles Law?
- In 1929 Edwin Hubble plotted the velocities of
various galaxies vs. their distances - Interpretation all galaxies are moving away from
each other
3Measuring 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.
4Redshift as a measure of velocity
Definition of Redshift
z
5Measuring DistanceBrightness of a Standard
Candle
- Hubble used Cepheid variables and typical
galaxies - Newest standard is Type Ia supernovae
- As bright as an entire galaxy
6Measuring brightnessand 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,
7Part II Hubbles 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.)
8Part 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 -
9Modern 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.
10So 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.
11Part 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?
12Part 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?
13Measuring Velocity from Redshift
- Doppler shift from receding source of light
- Redshift (z) is defined by
- Combining these
14Approximating