The Size & Shape of the Galaxy

Transcription

1 name The Size & Shape of the Galaxy The whole lab consists of plotting two graphs. What s the catch? Aha visualizing and understanding what you have plotted of course! Form the Earth Science Picture of the day at The above picture is a schematic diagram of our current understanding of the shape and the size of the Milky Way. But if you look up at the night sky, the Milky Way looks very different, because we view it from inside itself. So determining the shape and size of our own Galaxy is quite a challenge. In this lab, you will analyze some of the original data of Shapley and Curtis. Both of them came up with some right and some wrong conclusions about the size and shape of our galaxy, the Milky Way. Their results led to new philosophical interpretations about our location, role and importance in the universe. Both of them used scientific methodology to prove their points. Your (final) task in this lab is to analyze their methods and to conclude for yourselves whether or not you can believe their interpretations. The Size & Shape of the Galaxy Lab 11 1

2 Part I The Milky Way according to Shapley The appropriate location of the center of the Milky Way was discovered by Harlow Shapley seventy years ago. Today, we have now located the center more precisely by observing at infrared and radio wavelengths (these can penetrate dust, thus eliminating the problem of extinction). Shapley s method is interesting nonetheless, and it is an example of how some thought and educated guessing can lead to a correct result. Shapley used globular clusters to define the skeleton of the Milky Way. Globular clusters are compact groups of stars, which are roughly spherical in shape. A globular cluster may contain a million stars and is therefore much brighter than a single star. Thus they can be spotted at large distances. Shapley reasoned that since globular clusters can be identified at great distances, he might be able to determine the edge and the center of our Galaxy. In this exercise you will repeat Shapley s study using the data on globular clusters given in Table 1. Your task is to make two plots, one of RA versus Dec, and another one with x versus z. However the real part of this exercise is visualizing and understanding what you have plotted, and drawing conclusions from those plots. Table 1 Globular Cluster Positions NAME RA DEC x (kpc) z (kpc) 1 NGC h 10.1m -64 o NGC h 07.6m +18 o NGC h 10.5m +18 o NGC h 23.7m -47 o M 5 15h 16.0m +02 o M 80 16h 14.1m -22 o M 13 16h 39.9m +36 o M 19 16h 59.5m -26 o NGC h 07.1m -26 o M 9 17h 16.2m -18 o NGC h 25.1m -05 o M 14 17h 35.0m -03 o NGC h 36.8m -63 o NGC h 46.8m -37 o NGC h 00.4m -30 o NGC h 04.4m -43 o M 28 18h 21.5m -24 o M 22 18h 33.3m -23 o NGC h 56.2m -36 o NGC h 06.4m -60 o M 56 19h 14.6m +30 o M 75 20h 03.2m -22 o Lab 11 The Size & Shape of the Galaxy

3 A Understanding and Visualizing the RA/Dec Plot 1) Write down the definitions of RA and dec and compare them to latitude and longitude. Base your answer on what you see in Figure 2. 2) Using the data in Table 1, make a plot of right ascension versus declination. (Plot your data into Figure 3. As in Figure 8, RA is along the x-axis and goes from 0 to 24 hours, Dec is on the y-axis and goes from +90 to 0 to 90 degrees.) 3) Visualize what you have drawn. Consult the Sky-Lab, the TOOLKIT and the plot below. You may want to orient the RA/dec plot in a similar fashion as the Figure below. Align the dec-axis in direction of the arrow pointing towards the North Celestial Sphere, and the RA-axis along the Celestial Equator. Declination Right Ascension Fig 2 The Size & Shape of the Galaxy Lab 11 3

4 4) Would you describe the distribution of clusters on the plot as random, or is there a pattern? 5) Now look at your plot and point in the direction in which you see most of the globular clusters. This is the general direction of the Galactic Center. Estimate the center of the distribution of the globular clusters. Also estimate (no calculation required just an educated estimate) the accuracy of determining this center. You have now determined the rough center of our Galaxy! RA = ± Dec = ± 6) Grab a Celestial Sphere from the shelf, and locate the position of the Galactic Center on the Celestial Sphere, i.e., locate the coordinates of RA and dec of the Galactic Center on the Celestial Sphere. In which constellation is the Galactic Center? The Galactic Center is in the constellation Most Celestial Spheres in the classroom have a drawing of the location of the Milky Way. Observe the Milky Way and convince yourself that your nominal position of the Galactic Center corresponds to the Center of the Milky Way on the Celestial Globe. 7) Orientate yourself. First answer the questions below, then show this to the instructor. a) In the classroom, locate the direction of North (e.g., Manhattan is northeast of Staten Island), then, using your fist, determine the position of Polaris (the altitude is 40 o ). Show your instructor the rough location of Polaris in the classroom. b) Also, show the location of the Celestial Equator in the classroom. c) Take the celestial sphere and orient it like you did in Sky-Lab-#1. [Position the Celestial Sphere so that the Zenith of a miniature person standing on the Globe in New York (see below) point to the same Zenith as you standing in the classroom (turn the Celestial Sphere until New York is at the top and pointing to the ceiling).] d) Locate the Galactic Center on the celestial sphere and point out where the Galactic Center would be projected onto the classroom wall. e) Does this location change throughout the day? f) If your answer is yes show your instructor how the Galactic Center appears to move the classroom. 4 Lab 11 The Size & Shape of the Galaxy

5 R.A. R.A. Dec Plot Dec = 90 o Dec Dec Dec Dec Dec =-90 o RA R.A.

6 8) Assuming you are in New York, make a drawing (label the Horizon, Celestial Equator and Polaris) for the moment of transit of the Galactic Center (i.e., turn the celestial sphere so that the Galactic Center reaches its highest possible altitude; the GC should then be on the Meridian). Now stand back and observe the shape of the rest of the Milky Way on the Celestial Sphere. Then draw in the disk of the Milky Way into the diagram below. Also draw the backside of the celestial sphere. Zenith NCP Fig 4 9) Now imagine that you slice this sphere open at RA=0 and you obtain plot 3. Compare this imaginary plot with plot 3. Observe the location of the entire disk of the Milky Way on the Celestial Sphere, and draw this disk into the RA/Dec Plot. How do the two plots compare? 10) Rotate the celestial sphere around its N-S axis and watch the path of the Galactic Center. Complete the diagram below (label the Zenith, Horizon, Celestial Equator and Polaris), showing this path throughout the night. Zenith NCP Fig 5

7 B Visualizing the x/z Plot Shapely was correct in thinking that the distribution of globular clusters could reveal something about the Galaxy as a whole. He went one step further. He used the locations of the globular clusters to determine the distance to the Galactic Center. His result was surprisingly accurate and differed from the modern value by less than 10%. So, let s follow in his footsteps. The next step is to determine the distance to the clusters. Shapely did this by using RR Lyrae stars. These are variable stars, which have a relatively narrow range of luminosities. From the difference between the apparent magnitudes (measured from his photographic plates) and the absolute magnitudes (calculated from the luminosities), he calculated the distances (via: m - M = 5logd - 5). You have done this in the Photometry and the Spectroscopy Labs! So now we have the distances and the directions of the globular clusters and we can determine the 3- dimentional distributions of the globular clusters relative to us. However, we will use a different coordinate system that is based on galactic latitude and longitude rather than RA and Dec. The plane of the Galaxy is designated as 0 latitude. Why would we want to do this? RA and Dec is a messy coordinate system that depends on our orientation in space and the earth s rotation around its axis. The system based on galactic latitude and longitude is therefore simpler. However, it means that we have to transform the measured RA and DEC positions of the globular clusters and galactic latitude and longitude. To simplify things even further, let s express the galactic latitude and longitude in terms of x, y, and z coordinates. The advantage of this is that x, y, and z have units of parsecs (rather than angles which is the case with galactic latitude and longitude). So now the z-coordinate tells us how far above or below the galactic plane we are, and the x-coordinate tells us how far away from the origin (in this case from the Galactic Center) we are! This is illustrated below. The y-coordinate tells us where in the x-y plane (in the Galactic Disk) we would be found (actually, where along the gray circle we would be). But since we assume that the disk is a round circle (i.e., it is symmetric), we only need to worry about the distance from the center in the disk. Basically, we are only concerned about two quantities: x and z, i.e., how far above and below the Galactic Disk the globular clusters can be found, and far away from the Galactic Center they are. z-axis z is distance above or below the x-y plane y-axis x-axis x-y plane corresponds to disk of galaxy The Size & Shape of the Galaxy Lab 11 7

8 Maybe all this coordinate system stuff may sound confusing, but all you need to know is that they basically express the same thing locations in space. However we can nevertheless try to visualize how these different coordinate systems describe the locations of objects in space. The diagram below shows this. You can see the Galactic Disk (the x-y plane) and the Galactic Center. Imagine that there is also another coordinate: everything that is located either above or below this disk (the z-axis). You can also see the location of our Earth: it is in the Galactic Disk but some distance away from the Galactic Center. However when on Earth we describe what we see in the sky relative to the North Pole and the Equator. (The direction of the North Pole from the Earth is shown in red. Perpendicular to that is the Celestial Equator.) And looking up the sky we see the Milky Way (like below) in the plane of the Galaxy. z NCP x Galactic Plane Earth Fig 6 This figure is taken from Chaisson and McMIllian s book Astronomy Today The mathematical transformation from RA and Dec to galactic longitude and latitude and then to x and z is a little messy, so this step has been done for you. Table 1 lists the final values of x and z. Your next task is to make this plot, and determine our location (the Sun s location!) in the Galaxy, the distance to the Galactic Center, and the size and shape of our Galaxy. After you have plotted the globular clusters, you ll see why we bothered transforming between all these coordinate systems. 8 Lab 11 The Size & Shape of the Galaxy

9 Understanding the x/z Plot 1) Plot x against z. 2) In Plot 2, the x-axis points towards the Galactic Center (same arrow as in Figure 6); the z-axis is perpendicular to that, with positive numbers pointing up, and negative numbers pointing down. Visualize what you have plotted. Understand which additional information you obtain from this plot. Plot 1 only tells you about the directions in which you see the globular clusters (the globular clusters are draw onto the celestial sphere and you have no idea about their distances). Plot 2 tells you about real distances (in kilo-parsecs) of globular clusters; i.e., how far above and below the galactic plane they are located, and how far away they are from us. (Note that the third dimension, the y-axis, is collapsed into the plane of the disk of the galaxy we only know how far away from the galactic center the globular clusters are found, we do not know where in the disk they are. However this is not important right now when trying to visualize this plot.) 3) Label the x and z-axis in Figure 6. Compare Plot 2 to Figure 6. Position yourself into the origin of Plot 2 (i.e., at x=0, z=0) and point the x-axis towards the Galactic Center of Figure 6. The x-axis then shows you HOW FAR away each globular cluster is from you in the direction of the Galactic center. The z-axis tells you how far above or below the galactic plane that globular cluster is located. 4) Sketch the Galaxy. Identify the disk, the bulge, and the halo of the Galaxy. Clearly label each component. [Remember that this is a two-dimensional drawing: the y-axis is collapsed into the plane of the Galaxy (i.e., the y-axis has been eliminated); you are only looking at the x-z plane]. 5) Assume that the center of the Galaxy is in the center of the distribution of the globular clusters. Figure out where you could draw a line parallel to the z-axis (the vertical axis) such that equal numbers of clusters fall on each side of the line. So then, the z-coordinate of the center should be set to 0. Using a pen of a different color mark the new scale in your plot. 6) Most globular clusters are located in a narrow range above and below the galactic plane. Roughly how may kiloparsecs above and below the galactic place are those globular clusters (i.e., how thick is the disk of the Galaxy in kilo-parsecs)? Estimate the uncertainty in that number. Thickness of Galactic Disk = ± kpc 7) Measure the distance in kilo-parsecs from you to the central point in the distribution of the globular clusters. How many kilo-parsecs away is the center? Estimate the uncertainty in that number. Distance to Galactic Center = ± kpc 8) How far above or below the Disk of The Galaxy would you place our Solar System? Distance to Disk of the Galaxy = ± kpc The Size & Shape of the Galaxy Lab 11 9

10 9) From that plot, what diameter would you infer for the disk of the Galaxy? Diameter of Disk of Galaxy = ± kpc 10) What diameter would you infer for the halo of the Galaxy? Diameter of Halo of Galaxy = ± kpc 11) We now know that the interstellar dust obscures much of the Galaxy from our view. The true center of the Galaxy suffers from a level of extinction that makes it appear 30 magnitudes fainter in visible light than it would appear without any presence of dust (this is when infrared or radio observations come in handy). What about the globular clusters in (a) the Galactic Center, (b) in the Disk away from the Galactic Center, and (c) in the Halo? Do you think dust could distort those quantities equally? Give a sentence or two of justification for each of your answers. 12) Look at your answers in parts 6, 7, 8, and 9. Which of those quantities have the largest uncertainty, which ones the least? Explain. 13) You have just plotted some of Shapley s original data. Now think about the conclusions he came up with! He figured out the location of the Galactic Center, he figured out the distance to the Galactic center, and he also concluded that there is a Halo of globular clusters surrounding the disk of the Galaxy. Would you have trusted the conclusions he came up with??? 10 Lab 11 The Size & Shape of the Galaxy

11 "x-z" Plot 25 Distance in kpc of our Plane relative to Disk of Galaxy Earth Distance in kpc from us in Disk of Galaxy Mark and label the x and z-axis Label the Galactic Center The Size & Shape of the Galaxy Lab 11 11

12 Part II Distribution of Novae Let s compare the data on globular clusters to data on novae. The work has been done for you and the distribution of the novae have been plotted. Your task is to understand and interpret this plot. 1) Compare Figures 3 and 8 the distribution of globular clusters to the distribution of novae. a) Sketch the Milky Way onto Figure 8, the plot of the novae. b) Determine the position of the Galactic Center from Figure 8. Estimate the uncertainties. RA = ± Dec = ± c) Figure 8 seems to have an additional arc of points for right ascensions ranging from 0 to 12 hours. What is this? Is this some type of illusion, or was that omitted in Figure 3? Explain. d) Compare the distributions of globular clusters and novae. Is the bulge equally big? Comment. e) Is the disk equally thick? Comment. f) Mark the globular clusters and nova in the halo of Figures 3 AND 8. g) Are there equally many halo objects? Comment. 12 Lab 11 The Size & Shape of the Galaxy

13 2) Would you expect to derive the same overall shape of the Galaxy from both data? Explain 3) In the Pre-Lab you read about the Curtis-Shapley debate. Based on what you have plotted decide on who of the two is more right about the shape of the Galaxy. Explain your reasoning. 4) Good News There is no separate Lab Report! The Size & Shape of the Galaxy Lab 11 13

14 14 Lab 11 The Size & Shape of the Galaxy