Galactic Structure from 21-cm Radiation
Student Manual
PHYS 133 Laboratory Exercise Spring 2005
Adapted from:
Manual of Astronomy
R. W. Shaw and S. L. Boothroyd
Wm. C. Brown Company Publishers, 1967
Thomas Madura
Department of Physics and Astronomy
University of Delaware
Newark, DE 19716
Goals
To understand how the study of 21-cm radiation from neutral hydrogen enables astronomers to determine the structure of our galaxy, the Milky Way. To understand the basic structure of the Milky Way, as well as some of its properties.
Equipment
Plain paper, compass, computer, and pencil.
Background
The techniques of radio astronomy have contributed extensively to our knowledge of celestial objects. In certain instances though, the advances have been rather significant. Two such important discoveries are the prediction of 21-cm line radiation and its use in determining the structure of our own Milky Way galaxy.
The discovery of the 21-cm line can be credited to the Dutch astronomer Jan Oort (1900-1992) and his student, H.C. Van de Hulst. Oort learned of recent discoveries in radio astronomy and realized that a radio spectral line would be an important tool for discovering the structure of our galaxy. Oort had spent many years studying the rotation and structure of the galaxy using optical means, but he was frustrated by the extensive clouds of dust lying in the galactic plane, which block visible light. One can see only a few thousand light years towards the galactic center because the light of distant stars is absorbed. However, radio waves will penetrate the dust and show us the galactic center and indeed the opposite side of the galaxy. The importance of a spectral line is that the frequency of the line will be shifted by the Doppler Effect, which means that the velocity of the gas can be measured. One can then study the differential rotation of the galaxy and estimate distances to gas clouds, and thus map the distribution of matter in the galaxy.
Oort assigned his student, H.C. Van de Hulst, the job of figuring out what radio spectral lines might exist and what their frequencies would be. Since hydrogen is the most abundant element in the universe, he started his studies with hydrogen. He found that a "hyperfine" transition in the ground state of neutral hydrogen would produce radiation in the radio range, at a frequency of 1420 MHz, or about 21-cm wavelength. In the ground state of hydrogen, the electron can have its magnetic moment either parallel to that of the proton, or anti-parallel. The parallel state has a little more energy, so a transition to the anti-parallel state results in emission of 21-cm radiation. Van de Hulst's prediction was published in Dutch in Ned.Tijd.Natuurkunde, vol.11, p210, 1945. An English translation is published in "Classics in Radio Astronomy", by W.Sullivan, Reidel 1982.
Radio telescopes on Earth can be used to detect this 21-cm line radiation. During observations, the receiver of the radio telescope is tuned to receive the 21-cm radiation and then varied to receive slightly higher or lower wavelengths. If there is a relative motion of the observer and radiating hydrogen cloud, the received radiation will be displaced in wavelength according to the Doppler Effect. The measured radial velocities and intensities of the radiation allow one to distinguish radiation between sources at different distances along the line of sight. Radio astronomy observatories at Leyden, the Netherlands, and at Sydney, Australia, were especially active in the study of galactic structure. Work at Leyden covers mostly the northern portion of the Milky Way and that at Sydney the southern portion. We will use some of their early data in this lab.
Procedure
The data in Table I gives the distances in kiloparsecs at the specified galactic longitude at which hydrogen clouds of significant magnitude have been detected. We will let the zero of the scale be the zero of galactic longitude, and the center of the chart the position of the sun.
Provided on your computer you will find an Excel spreadsheet that contains data from Table I below. You will notice that the Sydney data has already been entered for you, but that the Leyden data is missing. Your first task will be to enter the Leyden data from Table I into the Excel spreadsheet so that a plot of the distribution of neutral hydrogen in the Milky Way can be made. To do this, simply enter the appropriate KPS values for each of the galactic longitude values in the column marked “R” (Note that there are multiple KPS values for each galactic longitude value). The excel spreadsheet will automatically compute the X and Y values for you.
Once you have finished entering in all of the appropriate values, you will need to plot the data. To do this, first highlight the x and y columns associated with the Sydney data, and choose to plot them as an XY(scatter) plot. Now, do the same for the Leyden data, but plot that data on the same plot as the Sydney data.
When the plot is complete, certain definite and continuous trends of points will be visible. This plot represents the spiral structure of our galaxy as determined by hydrogen radiation. When you are done, be sure to print your plot and turn it in. Also, be sure to answer the following questions.
Discussion and Observations
1. In the directions of galactic longitude 147.5° and 327.5° no data are available. Explain why these gaps exist.
2. Rotation is clockwise (longitudes around counterclockwise). Are the spiral arms trailing or leading? Is this situation typical of galaxies?
3. Keeping in mind the differences in techniques used in the analysis by the Leyden and Sydney observers, can we consider in the regions of data overlap that the results are confirmatory or contradictory with respect to general spiral structure?
4. Is the Milky Way galaxy a multi-arm or single-arm structure? Why?
For Questions Five and Six, Refer to the Appendix Located at the End of this Manual
5. What constellation do we see when we look toward the center of our galaxy? When we look in the opposite direction?
6. Toward what constellation does the sun appear to be moving because of rotation of the galaxy?
Table I: Positions of Hydrogen Clouds
Sydney Data / Leyden DataGalactic
Longitude / KPS / KPS / Galactic
Longitude
175° / 3.3 / 17, 16, 15, 12.9, 11, 9.4, 4.4, 1.9, 0.8 / 0°
190 / 4.2 / 17.4, 15, 12.5, 11, 9.7, 7.5, 6.6, 2.2, 0.8 / 5
200 / 4.6 / 16, 15, 14, 11.4, 10.5, 8.3, 2.6, 0.8 / 10
210 / 4.6 / 14, 10.3, 7.7, 6.6, 5.5, 3.9, 0.8 / 15
220 / 3.9, 6.8 / 13, 9.9, 1.1 / 20
225 / 4.8, 7 / 12.8, 9.2, 7.2, 1.1 / 25
230 / 5.9, 8.8 / 12, 8.6, 6.1, 2.2, 1.1 / 30
235 / 5.7, 11 / 11.4, 7.4, 5.5, 1.1, / 35
240 / 5.3, 7.5, 12.1 / 10.5, 7, 4.4 / 40
245 / 8.3, 12.9, 1.9-3.5 / 9.9, 6.6, 3.3 / 45
250 / 6.6, 10.1, 14.3, 2.6-4.8 / 9.4, 8.4, 6.1, 3.3, 2.2, 1.1 / 50
255 / 8.3, 11.2, 3.9-6.4 / 9, 8.3, 5.5, 2.2, 1.1 / 55
260 / 11.6, 2.4, 8.8 / 9.2, 7.7, 4.4, 2.2, 1.1 / 60
265 / 4.8, 9, 13.8 / 6.1, 3.9, 1.1 / 65
270 / 10.8, 14.5, 5.3-7.5 / 8, 5.2, 4.8, 0.6 / 70
275 / 13.2, 15.8, 3.7-8.3 / 7.8, 4.8, 3.5, 2.6, 0.6 / 75
280 / 13.6, 17.8, 8.6-11 / 7.6, 4.6, 3.3, 0.6 / 80
285 / 3.1, 11, 14.5, 20.2 / 7, 3.9, 2.8, 0.8 / 85
287 / 3.1, 12.5, 14.7 / 6.4, 3.9, 2.6, 0.6 / 90
290 / 3.1, 12.7, 14.9, 18.9 / 7, 3.9, 2.6, 0.6 / 95
295 / 2.6, 13.8, 16.3, 19.6, 7-11 / 6, 3.4, 2.6, 0.6 / 100
298 / 2.8, 13.8, 17.1, 21.8, 6.6-10.5 / 2.6, 0.6 / 105
300 / 2.8, 6.1, 11, 14.7, 17.6, 22.6 / 2.6, 0.6 / 110
303 / 2.2, 5.7, 19.1, 23.5 / 5.4, 3, 2.4, 0.6 / 115
305 / 2.2, 5.7, 11.6, 15.8, 25.9 / 5.4, 3, 2.2, 0.6 / 120
308 / 2.4, 5.5, 12.3, 20.9, 27.5 / 3.6, 2.2, 0.6 / 125
310 / 2.4, 5.5, 12.9, 17.1, 28.1 / 5, 3.4, 2, 0.6 / 130
315 / 18 / 1.7 / 335
320 / 19.1 / 17.6, 16.2, 1.7 / 340
335 / 18 / 19, 18, 17, 16, 13.2,11.8,2.2, 0.8 / 345
340 / 2.4, 18.9 / 18.8, 16, 15.2,13.6,11.6,2.4,0.8 / 350
345 / 2.6, 18.7 / 17.4, 15.6, 13.2, 9.9, 9, 6.6, 2.8, 0.8 / 355
350 / 18.2, 3.3-5.5
353 / 17.1, 2.8-7.7
355 / 17.1
0 / 3.4, 7, 15.8
3 / 3.5, 15.6
5 / 15.4
Distance to the Galactic Center
Another one of the great advances in astronomy in the first quarter of the twentieth century was the formulation, based on globular clusters, of the general shape of the Milky Way and the determination of the position and distance of the sun from its center. The steps used were the result of a brilliant analysis in 1918 by Shapley, Bailey, Leavitt, Hertzsprung, and others of the distribution of globular clusters and the application of the period-luminosity relation of RR Lyrae stars to determine distance. The result of their work was the emergence of the rough outline of the Milky Way as a disk of stars surrounded by a halo of clusters with the sun about 10 kiloparsecs or 32,000 light years from the center.
In this exercise, we will assume that the direction to the galactic center is given accurately by radio astronomy. It is then possible to express the positions of clusters for which distances are known in terms of X, Y, and Z coordinates derived from the usual galactic coordinates. X is the direction to the galactic center from the sun, Y is the coordinate in the galactic plane at right angles to X, and Z is the coordinate perpendicular to the galactic plane. Quantitatively we have:
X = D * cos(Gal. Lat.) * cos(Gal. Long.)
Y = D * cos(Gal. Lat.) * sin(Gal. Long.)
Z = D * sin(Gal. Lat.)
Where D is the distance determined by RR Lyrae stars.
Table II provides a selection of globular clusters for which fairly accurate distances are known, together with the corresponding X, Y, and Z coordinates already computed. If selection effects are ignored, it is possible to find the coordinates of the galactic center by the Shapley method, where,
X> = the average of all X values; <Y> = the average of all Y values;
Z> = the average of all Z values
Note that care must be taken to use the correct signs when computing these averages.
Table II: Globular Clusters
104 / + 3.79 / - 5.22 / -6.44 / 6284 / + 19.68 / - 0.54 / + 3.48
288 / - 0.01 / + 0.01 / -14.04 / 6293 / + 10.78 / - 0.44 / + 1.51
362 / + 5.21 / - 8.47 / - 10.39 / 6304 / + 9.05 / - 0.67 / + 0.86
1851 / - 6.13 / - 12.85 / - 9.99 / 6316 / + 13.71 / - 0.68 / + 1.39
1904 / - 9.81 / - 9.64 / - 7.41 / 6333 / + 8.91 / + 0.86 / + 1.69
2808 / + 2.28 / - 10.53 / - 2.16 / 6341 / + 3.17 / + 8.00 / + 6.01
3201 / + 0.97 / - 7.79 / + 1.20 / 6352 / + 6.80 / - 2.31 / - 0.90
4372 / + 4.54 / - 7.71 / - 1.57 / 6356 / + 16.20 / + 1.91 / + 2.94
4590 / + 4.79 / - 8.44 / + 7.06 / 6362 / + 7.86 / - 5.39 / - 3.02
4833 / + 4.77 / - 7.19 / - 1.21 / 6388 / + 13.86 / - 3.56 / - 1.68
5139 / + 5.07 / - 6.24 / + 2.15 / 6402 / + 7.85 / + 3.06 / + 2.22
5272 / + 2.00 / + 1.82 / + 13.54 / 6440 / + 7.52 / + 1.02 / + 0.50
5286 / + 9.00 / - 10.15 / + 2.54 / 6441 / + 10.39 / - 1.30 / - 1.00
5466 / + 3.16 / + 2.85 / + 14.48 / 6522 / + 15.08 / + 0.26 / -1.03
5694 / + 20.99 / - 11.33 / + 13.70 / 6541 / + 7.31 / - 1.38 / - 1.46
5824 / + 26.00 / - 13.45 / + 11.89 / 6624 / + 14.23 / + 0.69 / - 1.97
5897 / + 11.39 / - 3.48 / + 6.97 / 6626 / + 7.15 / + 0.98 / - 0.71
5904 / + 6.53 / + 0.45 / + 6.96 / 6637 / + 10.31 / + 0.30 / - 1.88
5927 / + 5.24 / - 3.46 / + 0.54 / 6638 / + 18.64 / + 2.58 / - 2.38
5986 / + 13.50 / - 5.74 / + 3.47 / 6652 / + 16.28 / + 0.43 / - 3.28
6093 / + 11.79 / - 1.51 / + 4.21 / 6656 / + 3.23 / + 0.56 / - 0.44
6101 / + 7.48 / - 6.78 / - 2.86 / 6681 / + 18.52 / + 0.93 / - 4.11
6121 / + 3.29 / - 0.52 / + 0.96 / 6712 / + 9.91 / + 4.68 / - 0.82
6139 / + 13.60 / - 4.32 / + 1.76 / 6715 / + 21. 15 / + 2.04 / - 5.26
6171 / + 9.64 / + 0.58 / + 4.11 / 6723 / + 12.02 / + 0.03 / - 3.74
6205 / + 3.48 / + 5.92 / + 5.96 / 6752 / + 7.89 / - 3.44 / - 4.13
6218 / + 6.55 / + 1.84 / + 3.36 / 6779 / + 5.45 / + 10.55 / + 1.73
6254 / + 7.06 / + 1.91 / + 3.11 / 6809 / + 6.27 / + 0.98 / - 2.74
6266 / + 10.35 / - 1.16 / + 1.33 / 6838 / + 3.62 / + 5.50 / - 0.53
6273 / + 7.49 / - 0.38 / + 1.24 / 6934 / +13.92 / + 17.91 / -7.78
1. Using the values in Table II, record here the values obtained for the averages of X, Y, and Z. Should the value of <X> be regarded as a maximum or a minimum value for the distance to the galactic center?
2. What is the physical significance of the small values of <Y> and <Z>?
Distribution in the X, Y Plane
On the same Excel spreadsheet as earlier, you will find data entered for all of the globular clusters found in Table II. Using Excel, plot the positions of the clusters using the given X, Y coordinates. Make sure that under Chart Options, Major Gridlines for both X and Y are turned on. Each large block on your graph then represents about 4 kps. Next, print your plot, and draw on the plot a circle with its center on the X-axis, such that the circle passes through the Sun (which is located at the origin) and such that it has a radius where all but a few outlying clusters are encompassed by the circle.
3. Record here the diameter of the circle and the distance of the center of the circle from the sun in kiloparsecs. Compare this value to the value of <X> from earlier.
4. Discuss the shape of the galaxy defined by globular clusters based on (a) the considerations of X, (b) the circle drawn in question 3 above, and (c) positive and negative Z coordinates.