Astronomy 100 Name(s): Exercise 8: Galaxies and the Hubble Law The large-scale structure of the universe is governed by gravity. The Sun orbits the center of our galaxy, the Milky Way. The Milky Way, in turn, orbits the center of the Local Group, a cluster of galaxies. The Local Group orbits the center of the Virgo Supercluster, a cluster of clusters of galaxies. Classifying galaxies The Hubble Deep Field project, taken by the Hubble Wide Field Planetary Camera 2, took images of galaxies even more distant than our supercluster. Each of the three laminated photos (A, B and C) has about 3000 objects in it; the estimate for the number of galaxies in the universe is between 50 and 100 billion. Obtain one of the laminated sheets, and classify the numbered objects by color (hopefully obvious) and by shape: stars have spikes due to light scattering in the telescope spiral galaxies which have arms when viewed from above or look like a fried egg from the side elliptical galaxies which have a smooth, featureless appearance, either round or oval irregular galaxies which do not have a uniform or regular appearance 1. Fill in the table below with the number of the object in the appropriate cell. Color Star Elliptical galaxy (E0 to E7) Spiral galaxy (S and SB) Irregular galaxy Blue White Yellow Red
Pool your data with the class; all of the numbers from 1 to 45 should show up in your table. 2. Are there any empty cells? Yes. Identify what color and type of objects are missing from these images. 3. Suggest a reason for the empty cells. In other words, what about those objects makes them rare and/or nonexistent? 4. Suggest a reason for the large number of blue, irregular galaxies. Hint: consider current theories of irregular galaxy formation. 5. Do spiral galaxies tend to be a particular color or colors? Suggest a reason for this trend. Distances to galaxies Galaxies are a bit more difficult to determine the distance away that stars. A quick illustration: Depending on the Hubble Deep Field image you have in front of you, find the following objects (you only have to do one set): Camera A: 3, 4, 7, 13, 14 Camera B: 19, 21, 22, 27, 29 Camera C: 33, 36, 41, 42, 44
6. Order one of the sets of objects from nearest to furthest (identify by number). 7. What criterion or criteria did you use to order the objects? 8. The actual order from nearest to furthest are: Camera A: 4, 14, 13, 7, 3 Camera B: 29, 21, 19, 27, 22 Camera C: 36, 33, 41, 44, 42 How accurate were you? Is the criterion or criteria you used a good way to find galaxy distances? In fact, galaxies can be analyzed spectroscopically, so that they can grouped in such a way that the apparent size of a galaxy is related to its distance from Earth. This is method similar to the main-sequence fitting we did in an earlier exercise for star clusters. Figure 8.1 shows the images and visible spectra of five elliptical galaxies. The spectrum of each galaxy is shown to the right of the image of the galaxy (the dark line spectrum sandwiched between emission spectra); all of the galaxy sizes are on the same scale. 9. Measure the apparent diameter of each galaxy in millimeters, and enter that information into the appropriate column in the table. If the galaxy is not round, use an average between the long and short axes of the galaxy. 10. Convert the diameter to the distance the galaxy is away from us by using the formula, and entering the result in the appropriate column in the table: dis tance = 1000 diameter where the diameter is in units of millimeters and the resulting distance is in units of megaparsecs (Mpc).
Now, turn your attention to the spectra next to each galaxy shown in figure 8.1. The spectra show well-defined (laboratory) emission lines above and below the nearly continuous emission spectrum of the galaxy. The arrows a through f represent strong helium emission lines. 10. Which direction is towards the red end of the spectrum? On each galaxy s continuous spectrum, note there are two relatively strong absorption (dark) lines (there s a small horizontal white arrow that points between the lines) which represent the H (the right one) and K (the left one) absorption lines of calcium, which normally exist at 396.8 nm and 393.3 nm. 11. What happens to the position of the calcium absorption lines as you go down the rows of spectra for each galaxy? (Don t worry about intensity that has to do with object luminosity). What is this phenomenon called? 12. Measure the distance d between the K line of calcium of each galaxy (the right dark line of the pair on the continuous spectrum) and the 388.8 nm helium emission line (the left arrow) millimeters is a good unit to use. A simple way to measure this is simply to measure the length of the horizontal white arrow. Enter this information in the table on the next page. 13. Measure the distance D in millimeters between arrow d (which marks the helium emission line at 588 nm) and arrow f (which marks the helium emission line at 707 nm). 14. Use the following formula to calculate the observed wavelength λobs of the calcium K absorption line, and enter the result in the appropriate table column: λ obs = 707 588 ( ) d D + 397 15. Now calculate the velocity v that the galaxy is receding from us by using the Doppler shift formula, and enter the velocity (in km/s) in the appropriate column of the table: v = c λ obs 397 397 c is the speed of light and is equal to 300,000 km/s.
The factor in the parenthesis in the equation above is called the redshift of the galaxy, and is value is represented by the letter z. 16. What happens to the value of z and the speed of the galaxy away from us increases? Table for results of analyzing figure 8.1 Cluster d (mm) λobs (nm) v (km/s) Diameter (mm) Distance (Mpc) Virgo Ursa Major Corona Borealis Bootes Hydra 17. Plot distance to the galaxy (in Mpc on the x-axis) versus its recessional velocity (in km/s on the y-axis) on a piece of graph paper. Make sure to include units on the axes. Where should the Milky Way be plotted? 18. Describe the mathematical relationship between the distance to a galaxy and its recessional distance. Congratulations! You ve discovered the Hubble Law. 19. Since 1 Mpc = 1,000,000 pc, and 1 pc = 3.26 ly, how old (in years) is the light from the oldest object on your plot?
Figure 8.1 Visible wavelength images of galaxies (left, note that the smaller galaxies are indicated by an arrow) and their spectra (right, note the galaxy s dark line spectrum is flanked above and below by the emission line spectra of various gases measured in the laboratory). The arrow in the dark line spectrum shows how far the calcium H and K lines have been shifted from the laboratory values for these absorptions.