Our Expanding Universe

Description:

In the early 20th century, astronomers made an amazing discovery that changed everything they thought they understood about the universe. The discovery made was that almost every galaxy is moving away from us. Before this discovery, astronomers knew that the universe was full of stars and nebulae, but they had no idea that some of the nebulae were actually other galaxies, or that these galaxies were moving away from us.

When Hubble and Humason first made this discovery, they plotted the distance to the galaxies on one axis versus the recessional speed of the galaxies on the other axis and found that they were correlated. The tight correlation implied a fundamental relationship, which led to the calculation of what is now known as the Hubble constant. The relationship is known as Hubble’s Law. As any law in science, it merely describes the way the data behave and does not explain why. The explanation for why galaxies appear to be moving away from us at faster rates the farther they are away from us comes from the Big Bang theory. Theories seek to explain why, while laws simply describe repeated observable behavior.

According to the Big Bang theory, the Hubble constant describes the rate at which the universe is expanding. Hubble first determined the value of this constant to be 500 km/s/Mpc. This value means that for each Megaparsec of distance from us an object is, its distance from us is increasing by 500 km every second (or, conversely, a Megaparsec (3.086 x 1019 km) of space is increasing in size by 500 km every second). This exercise will give students a chance to understand how these measurements are made. In addition, students will calculate the value of the Hubble constant based on real data.

Introduction:

Determining the rate of expansion of the universe is an endeavor that astronomers have undertaken for almost a century. For decades, there were two conflicting values for this number. Only recently have astronomers begun to come to agreement about the value of the Hubble constant, but it is not through the measurements of recessional speeds of galaxies. As will be evident with this experiment, there is good reason to be skeptical of the determination of Hubble’s constant through a correlation of recessional speeds with distance.

First, you will acquire a galaxy spectrum, identify an absorption line and measure the redshift of the galaxy. Next, you will use a simple equation to determine the recessional speed of the galaxy and then compare your answer with the accepted value for recessional speed for that galaxy.

Finally, you will use NED (the NASA/IPAC Extragalactic Database) to acquire recessional speeds and distances for several (at least 10) galaxies of your choice. Using these data, you will determine the value for the Hubble constant and compare this value with Hubble’s original value (500 km/s/Mpc) and the current accepted value (72 km/s/Mpc).

1. Get the spectrum of a galaxy. Go to http://nedwww.ipac.caltech.edu/ and select “Spectra” under the heading “Data”. Once there, enter “NGC1050” for the “object name” and click on the “submit query” button. The second spectrum that appears is one for the galaxy NGC 1050 and shows data for the wavelengths from 5445 to 7899 Angstroms. (This information appears in the far right column of the table.)

2. Determine the wavelength of the tallest peak in the spectrum. Launch the Specview Applet by clicking on the word “Specview” below the spectrum for NGC 1050. This applet will allow you to display the data using any units, to display reference lines and to measure the wavelength of the emission lines shown. You may have to change the units.

3. Calculate the redshift of the galaxy. Usually the laboratory wavelength of the tallest peak in the spectrum is 6562.8 Angstroms. The redshift of the galaxy is equal to the observed wavelength (what you measure) minus the laboratory wavelength, divided by the laboratory wavelength. The number you get should be a number between zero and 1, closer to zero. Round off your answer to the nearest 1000th.

4. Calculate the recessional speed of the galaxy. The recessional speed of the galaxy is the redshift, times the speed of light. Use the speed of light in km/s, so that your answer will be in km/s. Check the answer you get against the value on NED. To check the value on NED, go to the website above and click on “Redshift” under the heading of “Data”. Once there, enter “NGC 1050” for the “object name” and click on the “redshift” button. Scroll down to find the recessional speed, which will be labeled “Velocity” or “Helio. Radial Velocity”. Ask your instructor which value you should use if the values are very different from one another.

5. Look up the luminosity distance for the galaxy. Go back to the website and look up the galaxy using the “by name” option under the “objects” heading. At the very bottom of the page, there is a section called “Cosmology-Corrected Quantities”. There should be at least three different distances listed. Use the “Luminosity Distance”. This distance is calculated using the luminosity and apparent brightness of the galaxy. This distance does not depend on the motion of the galaxy, so it is what we will use as an independent measure of distance.

6. Determine the value of the Hubble constant. Repeat steps 1 through 5 to get the heliocentric radial velocities and luminosity distances for at least nine other galaxies from the list found in Appendix A. Make sure the velocities are all greater than 1000 km/s. (This is because the motions of galaxies that are moving at slower speeds is not dominated by the expansion of the universe.) To determine the value of the Hubble constant, plot the data you collected on a graph using Excel. Put the speed on the y-axis and the distance on the x-axis. Make sure speed is in units of km/s and distance is in Mpc. The slope of the line that fits these data points is the Hubble constant.

7. Compare the value of the Hubble constant you determined to the current accepted value (72 km/s/Mpc) and to Hubble’s original value (500 km/s/Mpc). Determine the percent difference between your value and the other two values. (The formula for percent difference can be found in Appendix B.) The Hubble constant can also be used to calculate the age of the universe, assuming a constant rate of expansion. To perform this calculation, all you have to do is divide the number of km in a Mpc by the Hubble constant value, then divide it by the number of seconds in a year. That will give you the age of the universe in years. Use your textbook or the internet to find these conversion values.

OPTIONAL STEP 8. For the final product of this exercise, write a report in the style of a scientific publication. You should have an abstract explaining the goal of the experiment and a brief description of the experiment and the results. The introduction should describe the history behind the experiment and methodology. Use your textbook and reliable internet resources (like NASA websites) as resources for this part. Be sure to address why one should be skeptical of the determination of Hubble’s constant through a correlation of recessional speeds with distance. The next section would be the Data and Observations section where you describe how you acquired the data for this experiment and what methods you used to acquire it. Here, you should explain what types of spectra you used to get your recessional speeds; also, you should describe the process you used to extract the data for NGC 1050. The next section is the Analysis section. Here you present the graph you made of the data you collected and describe the analysis you did to extract the Hubble constant. Your comparison to the currently accepted and original values should be included in this section, as well as your calculations of the age of the universe. Finally, the Conclusions section will summarize the experiment and list the conclusions you drew from your data and your analysis. Don’t forget to include a References section and list all resources you used for this experiment.