I. Background
Before the 20th century, it was believed that the universe was static and consisted only of the Milky Way. This is to say that it was believed that the Milky Way Galaxy was the universe and the universe was the Milky Way Galaxy. Therefore, the words “galaxy” and “universe” were used interchangeably. It was also believed that no other galaxies existed outside our own.
Strange spiral nebulae had been observed in telescopes, but it had not been discovered if these were objects within the Milky Way or if they could possibly be outside of it. Astronomers debated this in the beginning of the 20th century, with the most famous exchange occurring in 1920 when two well-known astronomers, Harlow Shapley and Heber Curtis, engaged in what today is often referred to as the “Great Debate.”
In 1912, Vesto Slipher, an American astronomer, observed the shift in the spectrum of galaxies. Thus, he was the first to observe the redshift of galaxies. Few other astronomers from different observatories understood the significance of this discovery.
Between 1922 and 1923, Edwin Hubble observed Cepheid variable stars in many of the known spiral nebulae and found that they could not be objects within the Milky Way as they were too far away. It was thus understood that they were other galaxies and became known as “island universes.” He published his results in 1924 and 1925.
Then in 1927, Georges Lemaître, a Belgian Catholic priest, astronomer, and professor, published a paper describing mathematically a universe that was expanding. “In that paper, he showed that the data collected by Hubble and two other astronomers up to that time was enough to derive a linear velocity-distance relation between the galaxies, and that this supported a model of an expanding universe based on Einstein’s equations for General Relativity.” [http://en.wikipedia.org/wiki/Edwin_Hubble] Unfortunately, the journal he published his article in was one read by few astronomers outside of Belgium. In the same year, he also proposed what today is called the Big Bang Theory.
Hubble applied Henrietta Swan Leavitt’s period-luminosity relationship for Cepheids to determine the distances to the spiral nebulae and combined his data with redshift data from Slipher and Milton L. Humason. From this larger data set of 46 galaxies, he noticed a linear relationship between the distance to the objects and their redshifts. This came to be known as “Hubble’s Law.” It supported the Big Bang theory.
II. Data Description
You will be using both spectral data and visual images of five galaxies. Calculations will be conducted on your recorded data. You will then try to determine an estimate for your Hubble constant, Ho by making a graph.
III. Procedures
You will be recording your data (measurements, calculations, and graph) and your answers to the questions on the “Hubble’s Law Lab Data Sheets.” You will need to type your answers and copy/paste your graph into the document, save it, and then upload it to eCampus.
You may want to review the definitions of “major axis” and “minor axes for an ellipse and the word “compare.” You will need a ruler with millimeters marked (the small lines between the 30 larger centimeter lines on a standard 12-inch ruler) and a calculator.
In Figure 1 below, you will find a column of images of 5 elliptical galaxies. Each image is to the same scale; thus their different angular sizes relate to their distances from Earth. The galaxies of the type shown all have approximately the same linear diameter of 0.02 megaparsec. Below the first column you will find a line whose length represents 150” (150 arcseconds). To the right of the first column, you will find a second column of the galaxies’ respective spectra. You will notice two dark, closely spaced lines within the bright band. These are the K and H absorption lines of ionized calcium, respectively. You will notice these two lines move towards the right as you move down the column. The horizontal arrow below each spectrum is there to help you find these two lines in each image. You will also notice that all the spectra are flanked along the top and bottom with white lines which are labeled in the bottom spectra as “a” through “g.” Their wavelengths are listed below, next to Figure 1.
You will find short directions listed on the “Hubble’s Law Data Sheets” document with more explanatory directions listed under Part III A through D below. Be sure to read all instructions carefully. Also, remember to show work for each individual question within its answer area, or for one ROW of the data tables in parts II and III below the table. The equation with the proper numbers placed in it will suffice. Make the final answers obvious by either highlighting them or placing a box around them for the individual questions.
A. Part I: Scale factor
Using the lines listed under the spectra for Hydra, measure the distance between the “a-line” and the “g-line” in millimeters. Measure to the nearest millimeter. Record this in #1.
Find the difference in their wavelengths in angstroms (Å) and record your answer in #2.
Then divide your answer from #2 by your answer in #1 and record your result in #3. The answer is your scale factor which will be used in Part II.
The labeled spectra have the following wavelengths:
Line Wavelength
a 3888.7 Å
b 3964.7 Å
c 4026.2 Å
d 4143.8 Å
e 4471.5 Å
f 4713.1 Å
g 5015.7 Å
B. Part II: Velocity Determinations
Measure the distance in millimeters between the “a” line and the K line on the spectrum for each galaxy and record in the second column in the data table. Then measure the distance in millimeters between the “a” line and the H line on the spectrum for each galaxy and record it in the third column in the data table. These values will be called “s” and will be used in the next double column.
Then take each of the “s” values and multiply them by your answer in question #3 in part I, and then add the rest wavelength for line “a” (listed above). Do this for both the K and H spectral lines for each galaxy. Record your answers in the double column with the equation “λ = λa + (#3) × (s)” at the top. These answers represent the observed wavelength for the K and H spectral lines.
If these galaxies were stationary, their H and K lines would be found within their spectra in the same places we find them in an Earth laboratory, which is referred to as the rest wavelength. The rest wavelength for the K line is 3933.7 Å; the rest wavelength for the H line is 3968.5 Å. In order to find the (amount of) redshift, subtract the rest wavelength from the observed wavelength for both the K and H lines for each galaxy and record the answers in the third double-column.
Next, the recessional velocity will be calculated. To do this, take the redshift and multiply it by c (use 3.0 × 105 km/s), then divide by the proper rest wavelength, either the K or H line. The result will have units of km/s. Record these values in the last double column.
Lastly, find the average for the recessional velocities for each galaxy using their K and H line velocities. This answer will be recorded in the last column. In reality, this number would need to be corrected for the motion of the Sun around the center of the Galaxy. However, that correction is very small, and thus may be ignored here.
C. Part III: Distance Determinations
The images can be measured in millimeters. A scale factor will be needed to convert from millimeters to a more appropriate unit. First, the line labeled 150” will need to be measured in millimeters. Record this measurement in question #4. To find the scale factor, divide your answer in #4 into 150” and record this in question #5. This value is your scale factor which will be used in the data table in this section.
All five images are of elliptical galaxies. Measure the length of the diameter in millimeters and enter that measurement in the proper cell of the first column. If the galaxy is not a perfect circle, measure both the major and minor axis and average the values. Place the average of the value in the proper cell of the first column.
Next, use the scale factor you calculated in question #5 to convert the diameter in millimeters to arc seconds by multiplying the two values. Insert the answer in the proper cell of the second column.
Then, convert arc seconds into radians by dividing your diameter in arc seconds by 206,265, the number of arc seconds per radian. Do this for each galaxy and record these values in the third column. This value will be called “d”.
Last, calculate the distance to each galaxy by dividing “d” into the value 0.02, their linear diameters as measured in megaparsecs. Record these calculated values in the last column for each galaxy.
D. Part IV: Final Results
In order to make it easier to graph, “copy-paste” the last columns of the two previous data tables into the small data table in part IV. (When using spreadsheet software, you may want to “copy-paste” these values into the worksheet, choosing the “transpose” option.) On the abscissa (horizontal or x-axis) should be the distances, and along the ordinate (vertical or y-axis) should be the average recessional velocity. After plotting the 5 given galaxies, have it show a trendline with the intercept set to 0 (zero) and display the equation on the graph. Remember to include labels on the axes and grid lines showing. This is YOUR Hubble diagram from which YOUR Hubble constant is found. Copy-paste your graph into the placeholder on page 3 (the placeholder is the graph grid image).
Next, answer question 6 by recording what YOUR Hubble constant, Ho, is. YOUR Hubble constant is the slope of the line, which is the number before the “x” variable in the displayed equation. The answer question 7 by comparing YOUR value to the currently accepted value of 72 (kilometers per second) per megaparsec. (Recall it does not matter which value is divided into the other, as long as it is clear in your answer what you did. e.g. “My value is twice as large as the accepted value” or “The accepted value is 50% of my value.”)
E. Part V: Age and size of the universe
Using the information, you have gathered, measured, and calculated, answer questions 8 through 11.
In question 8, re-arrange the given equation to solve for the estimated radius, “D”, for the observable universe, where c is the speed of light and H is YOUR Hubble constant found in question 6.
Using the answer from #8, convert megaparsecs into light years by multiplying your value by 3.3 × 106. This gives the size of the observable universe as measured in light years.
To find YOUR calculated age of the universe, divide YOUR Hubble constant from #6 by 1 × 1012 to change the units from (kilometers per second) per megaparsec into (kilometers per year) per kilometer. Then take the inverse of this value (divide it into 1). This value is YOUR age for the universe.
Compare YOUR universe age to the ages of three different objects: The Earth, the Sun, and the oldest stars.
Save your file using the class’ standard naming procedure and upload to eCampus.
