Expansion of the Universe-1

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Expansion of the Universe These lab activities have evolved over years of use in Clemson University’s Department of Physics and Astronomy general astronomy laboratory. Contributors include Tom Collins, Mark Leising, Neil Miller, Peter Milne, Grant Williams, Donna Mullenax, Jessica Crist, Keith Davis, Amber Porter, Lea Marcotulli, and David Connick. Please direct all questions, complaints, and corrections to David Connick (dconnic@clemson.edu) who is responsible for all errors and omissions. I. Introduction Astronomers have observed nebulae, fuzzy patches of light in the heavens, since the late 1700's, but it was not until the first decades of the 20th century that their importance to our understanding of the universe became clear. At Lowell Observatory in Arizona, Vesto Slipher studied the spectra of spiral shaped nebulae seen scattered around the sky. By examining their spectra, he was able to measure their velocity using the Doppler shift. Most of the spiral nebulae, he found, had Doppler shifts to longer wavelengths (red shifted), as if all of the nebulae were moving away from us. You might expect that if they were just moving around at random, as many would be coming toward us as are going away from us, but that was not the case. The work of Edwin Hubble, following on that of Slipher, produced an even more remarkable result. Hubble measured the distances to the spiral nebulae, showing that they were in fact distant galaxies like our own Milky Way (at distances of typically tens of millions of light years!). Then he went on to show that their radial velocities (their velocities of recession along the line of sight) were proportional to their distance from the Milky Way. The more distant the galaxy, the faster it seemed to be receding from us. Hubble's result can be displayed as a graph, as in the figure below. The Hubble "redshift-distance" relation can be expressed as V = HD, where H, called the "Hubble Parameter", is the slope of the line on the graph. What could account for Hubble's remarkable finding? Was there something that caused most galaxies to recede from our Milky Way? If that were so, what was special about the Milky Way? Rejecting the idea that we sit in a special place in the entire Universe, Hubble concluded that the universe was expanding in all directions. Galaxies generally appeared to be moving further away from all other ones in much the same way as do raisins embedded in rising bread dough. Once we accept this model for the expansion, the redshift-distance relationship is a natural result. Moreover, we can take the known expansion velocities of galaxies and their known

distances and run the clock backward, calculating how long it took them to separate as far as they have. At some time in the very distant past, the galaxies were touching, and just by dividing distance by velocity we can calculate what that time was. Today we identify this event as the Big Bang--the origin of the universe and the beginning of time. This lab will allow you to calculate how long ago the Big Bang (or really the time when all these galaxies were together) occurred. II. Working with the Data To measure the expansion and age of the Universe, we will need measurements of both the distances to, and the recession speeds of, a sample of galaxies. From the total apparent brightness of the galaxy, assuming we know its intrinsic brightness, you can determine its distance. From a spectrum of its light you can determine how much its spectral lines are shifted from their laboratory values, and therefore how fast it appears to be moving away from us. First you will analyze the spectrum of the NGC 1357 galaxy by looking for the signature dips in the absorption spectrum due to calcium. The H and K lines of calcium will be redshifted to longer wavelengths depending on how fast the galaxy is receding. The laboratory rest frame wavelengths of the H and K calcium lines are 396.847 and 393.367 nm, respectively. The doppler shift of the lines will cause them to appear at higher wavelengths but not change the ratio of the H and K lines. You can use this to your advantage to check you have selected the correct feature by referencing this ratio. Open the spectrum at this link https://depts.washington.edu/astroed/HubbleLaw/ngc1357_main.html The plot we are interested in is on the left side of the screen. This is an absorption spectrum so you will be looking for dips in the spectrum. You can click on the graph to have it display the wavelength precisely below the graph. Notice that the units for wavelength on this graph are angstroms, to convert angstroms to nanometers simply divide by 10. Use the graph and the information above to measure and record the wavelengths of the H and K lines in the first row of the data table. Make sure you record the wavelengths in nanometer units. Now that the spectral data table is complete you need to calculate the velocity of each galaxy using the doppler shift. You can now use either one of the two Ca lines (but the same one for all galaxies) for the velocity calculation, since you know the redshift is the same for both. Use your measured wavelengths and the rest frame wavelengths given above to calculate the redshift for each galaxy. After recording the redshift in your table use the Doppler shift formula:

where c is the speed of light, to calculate the velocity of each galaxy and record the velocity in the table. Use the speed of light given in the data table and check your units match what is requested for the table. We must also calculate the distance to each galaxy. The absolute magnitude, M, for all galaxies in this experiment can be assumed to be -22.0. Use the measured magnitudes provided and the assumed absolute magnitudes for each galaxy and derive the distances to each galaxy using the equation: where M is the absolute magnitude, m is the apparent magnitude and D is the distance in parsecs. Hint: First solve this equation for log D in terms of m and M. To find the distance, you must take the antilog, that is When you first solve the equation your distance will be in parsecs. Convert your result to megaparsecs and record both values in the data table in the appropriate columns. Copy your data table into your worksheet in the designated area. Now that you have completed all the calculations and the data table is complete you will plot your own Hubble Diagram. To do this you should create a scatter plot of the velocity (y axis) in km/s vs the distance(x axis) in megaparsecs. If you need a refresher on how to plot data in google docs refer to previous labs or ask your TA for assistance. Once you have formatted your plot appropriately, it may be wise to have your TA check it, add it to your worksheet in the designated area. You will now determine the approximate line of best fit for your data. Add a trendline to your plot in the google sheet and visually verify the trendline passes through the heart of your data. Look at the furthest right spot on your plot that your line passes through and record the approximate coordinates of that point on the worksheet for question 1. Verify the Hubble Parameter displayed by the trendline using the equation. Record the Hubble Parameter on the worksheet for question 2.

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III. Age of the Universe The equation above, known as the Hubble Law, can be used to determine the age of the universe. Using your value of H, calculate the recessional velocity of a galaxy that is 800 Mpc away. Here is the equation solved for velocity. Verify your velocity by looking it up on your Hubble diagram and record it on your worksheet for question 3. You now have two important pieces of information: how far away the galaxy is, and how fast it's moving away from the Milky Way. 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 at 60 miles per hour, your friend would know that you had been traveling two hours. Your trip started two hours ago. You know this because distance = rate times time: d v = t And so for your car trip Now determine when the universe "started its trip." The distance is 800 Mpc, but first convert Mpc into km because the velocity of the galaxy is in km/sec. For the conversion use: Record the distance in km on your worksheet for question 4. Use the equation above to determine how many seconds ago the universe started and record the number on your worksheet for question 5. Knowing there are about 3.15 x 10 7 seconds in one year, convert your answer into years and record the number of years on your worksheet for question 6. It was originally believed that the rate of expansion was much larger in the past and had since been slowed down by gravity acting on the mass of the universe. Recently it has been seen that the rate of expansion of the universe is currently increasing. With this knowledge in mind answer the final questions of the worksheet.

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