Spring 2001: Hubble Redshift-Distance Relation

Transcription

1 Cosmology is that branch of astronomy which deals with the structure and evolution of the Universe as a whole. It is a remarkable fact that a vital clue to the nature of the Universe is revealed by a very simple observation: the sky becomes dark after the Sun sets. In a stationary Universe of infinite extent and uniformly strewn with stars, our line of sight would always end at the surface of a star and the whole sky should therefore appear bright like the Sun. Why, then, is the sky dark at night? This contradiction is known as Olbers paradox. It is resolved nowadays as being due to the expansion of the Universe, distant sources receding from us at speeds so high that the intensity of light received from them is greatly reduced. Thus, from this simplest of astronomical observations can be deduced the expansion of the Universe, a phenomenon which manifests itself in the motion of galaxies away from the observer, no matter where in the Universe he is situated. Although this general recession of other galaxies had been known since about 1920 from the observations of Vesto M. Slipher and others, the discovery of the expansion of the Universe is invariably associated with the name of American astronomer Edwin Hubble. In the course of his investigation of the exterior galaxies, Hubble found that all of the galaxies outside of the local group were receding from the Milky Way at velocities that became larger with increasing distance. Astrophysicists readily interpreted Hubble s relation as evidence of a universal expansion. The distance between all galaxies in the Universe was getting bigger with time, like the distance between raisins in a rising loaf of bread, or ink marks on the surface of an inflating balloon. Any observer in any galaxy, not just our own, would see all the other galaxies traveling away, with the farthest galaxies traveling the fastest. This was a remarkable discovery. Today, the expansion is believed to be a result of a Big Bang which occurred between 10 and 20 billion years ago, a date which we can calculate by making measurements like those of Hubble. Hubble s relationship is a most important one to the astronomer not only because it provides a useful method of determining extragalactic distances, but also because its behavior at great distances from Earth theoretically can provide important clues concerning the overall properties of the visible Universe. In this exercise, you will derive the relationship for yourself and examine some of its properties. Objectives: Introduction to Cosmology Determine distances to astronomical objects given their absolute and apparent magnitudes Analyze and interpret spectral features from simulated data Use Doppler shifted spectral lines to calculate velocities of galaxies Determine the expansion rate of the Universe Calculate the age of the Universe Equipment: Calculator Lab notebook Set-Up: Skim through the exercise before you begin; get familiar with what you ll be doing so you have a better idea of how to arrange you notebook. Write up any preliminary information and Page 1 of 9

2 then begin. Make sure you clearly mark answers to questions along the way (don t make me search hard for them). Do not forget to credit any collaborators. I. REDSHIFT In 1929, Hubble found a correlation between the redshift or velocity of recession of galaxies and their distances, such that velocities are directly proportional to distances. His law can be expressed as follows: V = H D Equation 1 o where V is the velocity of recession, D is the distance in megaparsecs, and H o is the Hubble constant, which is usually expressed in units of km/s per Mpc (megaparsec); recall that 1 Mpc = 10 6 pc. Recall the Doppler formula vo λ λobserved λrest = = Equation 2 c λ λrest where we can see that positive velocities are redshifted, while negative velocities are blueshifted. Thus, given an object spectrum with identifiable features and a comparison spectrum whose features are at known wavelengths, we can calculate the redshift of the object. We will be observing two lines of singly ionized calcium (Ca II), the H and K lines, which are located in the near UV portion of the spectrum at and Ångstroms, respectively. First, you will measure the position of both Ca II lines in each of five galaxies. Then you will determine how far the galaxy is redshifted, calculate its recession velocities, and use these, in conjunction with the magnitudes of the galaxies, to derive the Hubble relation. ANSWER THE FOLLOWING QUESTIONS IN YOUR LAB NOTEBOOK. 1. Explain redshift and what it implies. 2. You should also note that the dimensions of H o can be expressed as s -1. Do the dimensional analysis to show how this is possible. (You will use this later to determine the age of the Universe.) II. THE DATA The data you will use in this exercise have been simulated using the Windows version of the CLEA exercise, The Hubble Redshift-Distance Relation. Five fields of view were selected for their magnitudes and populations of galaxies: (1) Coma Berenices, (2) Ursa Major I, (3) Ursa Major II, (4) Corona Borealis, and (5) Bootes. The telescope was pointed at each of the regions and one galaxy from each field of view was selected for spectrometer observations. The telescope was aligned so that the brightest part of the target galaxy fell across the slit of the spectrometer. Panel in each of Figures 1 through 5 shows the field of view of the finder scope with the telescope s field superimposed while panel in each figure shows the field of view of the telescope itself with the spectrograph slit superimposed. Here, you can tell the coordinates of the galaxy cluster (RA and DEC), the date and time of the observation, and telescope status. In the panels of Figures 1 through 5 we see the spectrum from the galaxy that is in the slit of the spectrometer. Our spectrometer works in the region from 3900 to 4900 Å, which is clearly the region we are interested in if we wish to observe the Ca II H and K features. The galaxies Page 2 of 9

3 Figure 1. Data from galaxy 1 in the Coma cluster. clearly show the characteristic H and K absorption features, but they are not in the right places. Normally, these lines would appear at wavelengths of and Å, respectively, if the galaxies were not in motion. However, the lines will be redshifted to longer wavelengths depending on how fast the galaxy is receding. Also in the panels, we find the object identifier, its apparent magnitude, photon count, integration time, and an estimate of the signal-to-noise (S/N) ratio. The S/N ratio is a measure of the quality of the data taken to distinguish it from the background noise level. In general, a spectrum must have a S/N of at least ten to be considered believable. On the x-axis of panel we have the wavelength in Ångstroms and on the y-axis, the relative intensity level. Page 3 of 9

4 Figure 2. Data from galaxy 2 in the Ursa Majoris I region. Go through each spectrum and measure the wavelength of each calcium line. You should be able to measure to the nearest Ångstrom. Record these values, along with the absolute and apparent magnitudes of each galaxy in a table similar to that in Table 1. Assume that the absolute magnitude of all these galaxies is 22 (this is not really correct, but it is close enough for our purposes here). Once you have this information, you can begin calculating redshifts and velocities via the methods in Section III. Page 4 of 9

5 Figure 3. Data from galaxy 1 in the Ursa Majoris II region. ANSWER THE FOLLOWING QUESTIONS IN YOUR LAB NOTEBOOK. 3. Why do the spectra have different S/N ratios? Hint: look at the ones with similar exposure times. 4. Why is the recession velocity of a galaxy always less than the speed of light? 5. What spectral lines are the measurements in this exercise based on? 6. Why are the spectral lines in different places in the spectra of the different galaxies? Page 5 of 9

6 Figure 4. Data from galaxy 1 in the Corona Borealis region. III. THE METHOD You should recall the distance modulus equation from your AST-301 course: M m = 5 5log D Equation 3 where M and m are the absolute and apparent magnitudes, respectively, and D is the distance to the object in parsecs. Solve this equation for D and calculate distance for each of the five galaxies. Enter this information in your table. Convert this to megaparsecs and include this in your table. Round off to one decimal place. Page 6 of 9

7 Figure 5. Data from galaxy 1 in the Bootes cluster. Calculate the change in wavelength of each of the calcium lines by finding the difference between the observed value and the rest wavelength. With this shift, you can calculate the velocity of recession of each galaxy from both of its lines, using the Doppler formula (Equation 2). Round the velocities to two decimal places. Find the average velocity of each galaxy using the information from its two spectral lines. Now make a Hubble plot by graphing the velocity of a galaxy in km/s vs. the distance to the galaxy in Mpc. Draw a best-fit straight line to the data; it should go through the origin. The slope of this line will be the value of the Hubble constant, H o. To calculate the slope of the line, pick Page 7 of 9

8 two points (not actual data points!) that lie exactly on the line and are easy to measure. Record the x,y coordinates of the two points and use Equation 4. y1 y2 slope = = H o Equation 4 x1 x2 Record your value for H o as the Average Value of H o and mark the points you used on your graph (mark them differently from your actual data points from the calcium lines). Make the graph as large as practical and do not forget to label it appropriately. [See the handouts on graphing techniques if you have questions.] Galaxy Field M (mag) m (mag) D (pc) D (Mpc) Coma 1 UMa 1-2 UMa 2-1 Boo 1 CrBor 1 λ observed K (A) λ observed H (A) λ K (A) λ H (A) v K (km/s) v H (km/s) v (km/s) average Table 1. Sample layout of data table. ANSWER THE FOLLOWING QUESTIONS IN YOUR LAB NOTEBOOK. 7. Why should you force your best-fit line through the origin and what does this mean? IV. THE AGE OF THE UNIVERSE The Hubble Law (Equation 1) can be used to determine the age of the Universe. Using your average value of H o, calculate the recessional velocity of a galaxy which is 800 Mpc away. Verify your answer by looking it up on your Hubble plot. You now have two important pieces of information: (1) how far away the galaxy is, and (2) how fast it is moving away from you. You can visualize the process if you 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 60 miles per hour, your friend would know you had been traveling for two hours. That is, your trip started two hours ago. You know this from the following relationship: Distance = Rate Time or Time = Distance Rate Thus, 2 hours = (120 miles) (60 miles/hour). Now let s determine when the Universe started its trip. The distance is 800 Mpc, but you must first convert it to km because the velocity is in km/s (1 pc = m). Calculate how many seconds ago the Universe started and convert this to years. Record these values in your notebook. This is your estimate of the age of the Universe! ANSWER THE FOLLOWING QUESTIONS IN YOUR LAB NOTEBOOK. 8. Based on what you know about the age of the Universe, does your age calculation seem reasonable? Why or why not? 9. From your results, at what distance does the velocity of recession equal the speed of light? What is the significance of this distance? Page 8 of 9

9 10. If the Hubble constant were found to be much smaller than your average value, how would this change the measured age of the Universe? Justify your answer. 11. Figure 6 is a spectrum of a galaxy at rest. Draw the spectrum if the galaxy were very nearby. Draw the spectrum if the galaxy were very distant. Relative Intensity Wavelength (Å) Figure 6. Artificial galaxy spectrum at rest. V. REFERENCES CLEA Project, The. Hubble Redshift-Distance Relation, Version 0.81, Department of Physics, Gettysburg College, Culver, R.B. An Introduction to Experimental Astronomy, W.H. Freeman and Company, Evans, A. Sky and Telescope, April 1978, pp Hackworth, M. PHYS 153 Lab Manual, Idaho State University, Hemenway, M.K. & Robbins, R.R. Modern Astronomy: An Activities Approach, Revised Edition, University of Texas Press, Hoff, D.B., Kelsey, L.J., & Neff, J.S. Activities in Astronomy, 3 rd Edition, Kendall/Hunt Publishing Company, Shaw, J.S., Dittman, M., & Magnani, L. Laboratory Textbook for Elementary Astronomy, 7 th Edition, Contemporary Publishing Company, Walker, C. Activities for Natural Sciences 102, University of Arizona, Page 9 of 9