Hubble's Law and the Expansion Rate of the Universe
PART I: Galaxy Distance
1. Use the provided worksheet to record your data and the results of your calculations. You will submit the completed worksheet to the Hubble Redshift Dropbox. You an either scan it for submission or take a picture of it. Make sure that the worksheet is legible in the scan/picture! Illegible work will not receive credit!
2. Measure all of the galaxies listed on the worksheet to find their angular sizes and thus their distances:
a. Choose a galaxy that is listed on your worksheet and click on the corresponding "Image" link on the Galaxy List website:
https://www.astro.washington.edu/courses/labs/clearinghouse/labs/HubbleLaw/galaxies.html
Note that not all of the galaxies listed on the website are listed on your worksheet - make sure to choose the correct galaxy.
b. Find the angular size of the galaxy using its image:
-The images used in this lab are negatives, so that bright objects, such as stars and galaxies, appear dark.
-There may be more than one galaxy in the image; the galaxy of interest is always the one closest to the center.
-To measure the size, click on opposite ends of the galaxy at either end of the longest diameter. Try to find the farthest extents of the
galaxy. If you make an error, make sure to click the "try again" link to reset the page.
-After you click the second point, the web page will report the angular size of the galaxy in milliradians. Record the stated angular
size in the appropriate space of the worksheet.
c. Calculate the distance to the galaxy by dividing the actual size of the galaxy (22 kpc) by the measured angular size of the galaxy (in
milliradians). Record this value in the appropriate space of the worksheet.
d. Repeat the above steps for all of the galaxies on your worksheet.
PART II: Galaxy Recessional Velocity
3. Find the recessional velocity of the galaxy using its spectrum:
a. Click on the "NGC XXXX Spectra" link for a galaxy. The spectra link will take you to a page containing a full optical spectrum and two magnified sections of the galaxy's spectrum. On the left side you will find the portion of the spectrum containing the Calcium K and H absorption lines. On the right side you will find the portion containing the H-alpha emission line. The absorption lines due to calcium will be some of the strongest features (deepest valleys) of the spectral lines. At the bottom of the left frame are two black labeled lines that show the rest wavelength positions of the two calcium lines. The wavelengths of these black lines are listed at the top of the left spectrum image. The emission line due to hydrogen will be the strongest feature (tallest peak) in the right-side spectrum. At the bottom of the right frame is a single labeled line that marks the position of the hydrogen-alpha rest wavelength. The value of this wavelength is given at the top of the image.
b. You will need to click on each of the red-shifted absorption lines in order to measure the wavelength at which these lines are observed in the galaxy. Measure the red-shifted wavelengths by clicking at the middle of the corresponding spectral line - i.e., click the bottom of the absorption line or the top of the emission line -- in each galaxy's spectrum. Measure the calcium K line, calcium H line, and H-alpha line for each of the galaxies.
c. Record these wavelengths in the appropriate spaces of the worksheet.
d. Repeat steps a-c for all of your selected galaxies.
4. Calculate the recessional velocity of each galaxy:
a. Calculate the redshift z for a galaxy and record the value in the appropriate spot in the worksheet.
b. Average the calculated redshifts of the three lines in each galaxy spectrum and record the average in the appropriate space of the worksheet. The three values should be relatively close to each other. If they aren't, then recheck your calculations.
c. Multiply the averaged redshift value by the speed of light (300,000 km/s) to get the recessional velocity of the galaxy.
d. Repeat steps a-c for each galaxy.
PART III: Create a Hubble Plot of Galaxy Distance vs. Velocity
5. Plot the recessional velocity of each galaxy as a function of its distance from us by using the graph paper on the last page of the worksheet. The points should all fit on the graph, although there may be one that is just off the top of the scale.
6. The Hubble Constant is equal to the slope of the line that runs through the data points you just plotted on your graph. Draw a "best fit" line through your data to estimate the Hubble Constant. Your line should go start at the origin (0,0). You may find that most of the points lie on a fairly straight line but a few are way off. It is OK to ignore those that are way off when determining what line is the "best fit". In a perfect world, your straight "best fit" line would run through every data point. However, you will find that you cannot get all of your data points to lie on a single straight line. Thus, you will want to draw a line that "runs through the center of the points" so that you have about as many points above the line as below it. The galaxies that are way off of the line may have a large proper motion that is
not associated with the expansion of the universe but is instead due to other motions. Alternately, those galaxies may not fit the "standard size" for a galaxy and will thus appear closer or farther away than they actually are. The slope of your line is your estimated value of the Hubble Constant. It will have units of km/s/Mpc (a very strange unit that consists of a velocity - km/s - divided by a distance - Mpc).
PART IV: Calculate the Age of the Universe
If the universe has been expanding at a constant speed since its beginning, then the Universe's age would simply be 1/H0.
• Find the inverse of your value of H0 (inverse = 1/H0).
• Multiply the inverse of H0 by 3.09 x 1019 km/Mpc (km/Mpc is read as "kilometers per megaparsec") to cancel the distance units.
• Since you now have the age of the Universe in seconds, divide this number by the number of seconds in a year: 3.16 x 107 sec/yr
Questions
1. What is your value for the Hubble Constant and the age of the Universe? Quantitatively (use ratios) compare your age for the Universe to the age of the Sun (5 billion years), and to the age of the oldest stars in the Milky Way (approximately 12.5 billion years). Comment on your findings.
2. What happens to the calculated age of the Universe if the Hubble Constant were larger than what you found here? How about for a smaller Hubble constant? (That is, would the age of the Universe increase or decrease if your constant were larger? What if your constant were smaller?)
Need the table, graph and all questions answered. I have attached all documents and example website-
https://drive.google.com/file/d/0B6D1QE2W34LsTEhVVGpzNWN4bGM/view?pref=2&pli=1
Attachment:- Assignment.rar