78ASTRONOMY 113LaboratoryThe Expansion of the Universe(Hubble Expansion)Introduction and GoalsVirtually all the galaxies in the Universe (with the exception of a few nearby ones) are moving awayfrom our galaxy, the Milky Way. This curious fact was first discovered in the early 20th century byastronomer Vesto Slipher, who noted that absorption lines in the spectra of most spiral galaxies hadlonger wavelengths than those observed from stationary objects. Assuming that these "redshifts" werecaused by the Doppler shift, Slipher concluded that the redshifted galaxies were all moving away fromus.In the 1920's Edwin Hubble measured the distances to a sample of galaxies. When he plotted thesedistances against the velocities of the galaxies he found a remarkable trend: the further a galaxy wasfrom the Milky Way, the faster it was moving away. Hubble's plot is shown in Figure 1.Was there something special about our place in the universe that made us a center of cosmic repulsion?No. Astrophysicists readily interpreted Hubble's relation as evidence of a universal expansion. Thedistances between all galaxies in the Universe were getting larger with time, like the distances betweenraisins in a rising loaf of bread. An observer on any galaxy, not just our own, would see all the othergalaxies traveling away, with the furthest galaxies traveling the fastest.Thus the entire Universe is expanding, one of the truly remarkable discoveries in intellectual history. Toappreciate its significance, one must recognize that if we measure the rate of the expansion we can “turntime around” and determine when the expansion began. This moment - associated with the concept ofthe Big Bang - marks the beginning of the present day Universe. And thus Hubble's discovery of thecorrelation between velocity and distance ultimately provides the answer to one of the most fundamentalof all questions, when was the Universe formed.As you might expect, determining precisely the rate of expansion and thus the age of the Universe is oneof the primary endeavors of observational cosmologists today. It also is the aim of this lab. Usingmodern instrumentation you will repeat Hubble's observations and come to understand both how theexpansion of the Universe is observed and measured, and what are the uncertainties in measuring its age.79Figure 1: Graph of Hubble's GalaxiesThe goal of this lab is to introduce you to the relationship between the redshifts of distant galaxies andthe rate of expansion of the universe. You will be introduced to:• Using a spectrograph to obtain spectra of galaxies.• The concept of signal, noise, and signal-to-noise ratio in data.• Measuring Doppler shifted spectral lines to determine velocities.• Determining distances using the brightnesses of galaxies.Once you have applied these techniques to a sample of galaxies, you will be able to:• Calculate the Hubble Constant Ho, a measure of the rate of expansion of the Universe.• Calculate the expansion age of the Universe.Before You Come to Class...Read the lab completely. Your time in the lab is best used observing the "sky", not reading this manual.Bring to class this lab manual, your lab book, a pencil or erasable pen, a straight edge, and a scientificcalculator.80Section 1 - Instrumentation and StrategyYou have been allocated observing time on a large optical telescope equipped with both a televisioncamera and a spectrograph. Using this equipment, you will determine the distances and velocities ofgalaxies located in selected clusters of galaxies around the sky.How does the equipment work? The TV camera acts in place of an eyepiece, allowing you to see thegalaxies. Observing with the TV camera you can center a galaxy of interest in the field of view. Oncecentered, you direct the light of the galaxy to the spectrograph. (The selection of TV or spectrograph isdone with a small flat mirror.) The entrance to the spectrograph is a small slit which allows only thelight of the galaxy into the spectrograph. Once you have carefully centered the galaxy on the slit, youinstruct the spectrograph to begin counting the photons from the galaxy. As it is doing so the counts aredisplayed on a computer screen as a spectrum - a plot of the number of photons collected versuswavelength. When a sufficient number of photons are collected, you will be able to see the spectrallines of the galaxy.Your spectrograph is set up to observe the blue end of the visible spectrum. Figure 3 shows the spectrumof a typical galaxy in this wavelength region. The two deep lines are a pair of absorption lines ofCalcium3 called the H and K lines for historical reasons. In the laboratory, i.e. at rest, the wavelengthsof the two lines are approximately 3969 Å and 3934 Å, respectively. Since galaxies are in motion, thelines will be found at different wavelengths in your observed spectra. Fortunately, the H and K lines ofCalcium are easy to recognize. They are about the same strength and they are always 35 Å apart, sinceboth are Doppler shifted by the same amount in any one spectrum.You will measure the wavelengths of the H and K lines in each galaxy spectrum. The spectrograph alsodetermines the brightness of each galaxy based on how many photons it counts per second. Thecomputer determines this number automatically and gives it to you as the "apparent magnitude" of thegalaxy. (Here "apparent" simply means "as seen from Earth".) So for each galaxy you will record thewavelengths of the Calcium H and K lines and the apparent magnitude. You can calculate how fast thegalaxy is moving away from us - known as the recession velocity - with the Doppler formula. You cancalculate the distance of the galaxy from its brightness - here we will make the simple assumption thatall galaxies in the Universe have the same luminosity. Thus you will have a velocity (in km/sec) and adistance (in units of millions of parsecs or megaparsecs, abbreviated as Mpc) for each galaxy.Most galaxies are found in clusters. You will observe a few galaxies in each of five clusters. Eachcluster is at a different distance from the Milky Way. Thus you will be able to explore the change inrecession velocity with distance. From your data you will derive Ho, the Hubble Constant, which is ameasure of the rate of expansion of the Universe. Once you have Ho, you can take its reciprocal to findthe expansion age of the Universe. 3 Why do we see Calcium absorption lines when we observe galaxies? When