Download Hubble Redshift

Lab 11: Hubble Redshift: The Expansion of the Universe
Name: _________________________________
Lab Partner(s): _________________________________
Section: _________________________________
In the 1920s, Hubble and Humanson obtained many pictures of galaxies. Hubble paid particular
attention to Cepheid Variable stars within galaxies. These stars pulsate in a characteristic
fashion, which depends upon their absolute magnitude. The apparent magnitude of those stars
can be measured directly. The difference between the absolute and apparent magnitude provides
a method of determining the distances to these stars. Hubble also obtained spectra of the galaxies
containing the Cepheid Variables, and from the positions of the absorption lines of those
galaxies, he was able to determine the recessional velocity of the galaxies in his sample.
When Hubble plotted these distances against the velocities for each galaxy, he noted that the
further a galaxy was from the Milky Way, the faster it was moving away. Was there something
special about our place in the universe that made us a center of cosmic repulsion?
Astrophysicists readily interpreted Hubble’s relation as evidence of a universal expansion. The
distance between all galaxies in the universe was getting bigger with time, like the distance
between raisins in a rising loaf of bread. An observer on ANY galaxy, not just our own, would
see all the other galaxies traveling away, with the furthest galaxies traveling the fastest.
This was a remarkable discovery. The expansion is believed today to be a result of a “Big Bang,”
which occurred between 10 and 20 billion years ago, a date which we can calculate by making
measurements like those of Hubble. The rate of expansion of the universe tells us how long it has
been expanding. We determine the rate by plotting the velocities of galaxies against their
distances, and determining the slope
of the graph. This slope is called the Hubble Parameter, H0, and it tells us how fast a galaxy at a
given distance is receding from us.
In this exercise, you will follow in Hubble’s footsteps and determine the velocities of galaxies in
a similar manner. (More specifically, you will measure the redshift.) Following that, you will
correlate the distance of each galaxy to its recessional velocity, and you will discover for
yourself that the universe is indeed expanding!
Procedure
1. Select File…Run from the menu bar to begin the exercise. Open the dome by clicking on the
dome button, and turn the tracking on. You are currently in the “finder scope” view, which
allows you to see a large portion of the sky.
2. Choose a galaxy to take the spectrum of., and then center the galaxy in the red box on your
screen using the N, S, E, and W buttons.
3. Cick on the ‘monitor’/‘change view’ button to change to the instrument/spectrometer mode.
The view will now show the slit of a spectrometer. Fine-tune your centering to put the brightest
part of the galaxy in the slit. (The more light you get into your spectrometer, the stronger the
signal it will detect, and the shorter the time required to get a usable spectrum. If you position it
on the fainter parts of the galaxy, you are still able to obtain a good spectrum but the time
required will be much longer.)
4. Press the ‘take reading’ button at the upper right. Press ‘start/resume count’ to start recording a
spectrum. To check the progress of the spectrum, click the stop count button. The computer will
plot the spectrum with the available data. If the “Signal/Noise” is less than 20, resume the count.
When you the “Signal/Noise” is at least 20, stop the measurement. At this time, you should see
that there are two major absorption features in the spectrum. These features are approximately 40
Å apart.
5. Click the left mouse button exactly at the bottom of the K line (the left line) and the H line (the
right line). Record the measured wavelengths of the K and H lines, as well as the apparent
magnitude of the galaxy, in Table 1. You should also record the field your chosen galaxy is in.
(There will be some blank columns that you will fill in later, when you do your calculations.)
6. Click ‘return’ to get back to the telescope view. Switch the mode to ‘finder.’ Press ‘change
field’ at the top of the screen, and select a different field.
7. Select a different field and then repeat steps 2-6 until you have collected data on at least one
galaxy from EACH of the five fields. This means that you’ll have data on at least 5 galaxies
when you are done. Note that the galaxies in the field Ursa Major II are very faint. You might
have to wait until you are in spectrometer/instrument mode to see them.
Calculations
1. Once you have recorded the apparent magnitude, observed H wavelength, and observed K
wavelength for all 5 galaxies, you can begin your calculations and fill out the table. First,
calculate the distance using the following formula:
d  10 ( m  M 5) / 5
This should be familiar to you from doing the Pleiades lab. For this lab, we will assume all
galaxies have M=-22. Remember, m is apparent magnitude, M is absolute magnitude, and d is in
units of parsecs. PLEASE NOTE that Table 1 asks for the distance in mega-parsecs (Mpc).
There are 1,000,000 parsecs in a mega-parsec.
2. Next, calculate  for each line:
The actual wavelength of the H line (H) is equal to 397.0 nanometers, and the actual wavelength
of the K line (K) is 393.3 nanometers.
3. Now use this information to calculate the recessional velocity (v):
H
K
vH=c*-------and
vK=c*-------H
K
The speed of light (c) is equal to 300,000 km/s.
.
.
4. Take the average of the two measured velocities.
5. Make a Hubble diagram on the graph provided. Plot the average velocity of a galaxy (in
km/sec) on the y-axis, and the distance (in Mpc) on the x-axis. Draw a straight line that goes
through the origin and best fits all the data points. The slope of the line is the Hubble Parameter
(H). To calculate the slope, mark a data point near the upper right end of the line you drew. Use
the D and v of this point in the following equation:
v
H = ------D
This equation is the Hubble Law. Record your value for the Hubble Parameter below the graph.
Table 1
Galaxy Field
Name
m
D (Mpc)
1.
2.
3.
4.
5.
K line (left line)
measured
1.
2.
3.
4.
5.

H line (right line)
vK
measured

avg. velocity
vH
(km/s)
The Hubble Parameter H = _________________________ km/s/Mpc
Determining the Age of the Universe
The Hubble Law can be used to determine the age of the universe. Using the average value of H
you calculated above, determine the recessional velocity of a galaxy of a galaxy which is 800
Mpc away. (show your work)
Velocity of a galaxy 800 Mpc away: _______________________________km/sec
Verify your velocity by looking it up on your Hubble diagram. You now have two important
pieces of information:
1. How far away the galaxy is.
2. How fast it is moving away from us.
Think about a trip in your car. If you tell a friend that you are 120 miles away from your starting
point and that you traveled 60 miles per hour, your friend would know you started your trip two
hours ago. You know this from the following relationship:
D
D = V * T or T = ----V
Where D is distance, V is velocity, and T is time. Now let’s determine when the universe “started
its trip”. The distance is 800 Mpc; first convert Mpc into km because the velocity is in km/sec. (1
Mpc = 3.09  1019 km) (show your work)
800 Mpc = _____________________ km
How many seconds ago did the universe start? (show your work)
_____________________ seconds
There are about 3.15  107 seconds in one year. Convert your answer into years.
The age of the universe is ____________________ years.
References:
http://cosmos.phy.tufts.edu/%7Ezirbel/phys611/Hubble.pdf
ftp://io.cc.gettysburg.edu/pub/clea_products/manuals/Hubbl_sm.pdf