ASTRONOMY 130
THE SUN
PURPOSE: To determine the temperature, luminosity, radiation flow, and some properties of the sunspot cycle.
PROCEDURE: Use observational data to calculate the temperature and luminosity of the sun. By graphical methods, determine the period of the sunspot cycle.
CONTINUOUS SPECTRUM
The distribution of the solar energy by wavelength constitutes what is referred to by astronomers as the continuous spectrum or continuum. You will analyze the solar continuum by assuming that the sun radiates like a black body.
Using the data from Table 1, plot the flux, fl , versus its corresponding wavelength on a sheet of graph paper and sketch a curve through all of the points. This work should be carefully done, since it is the basis for the first part of the exercise.
As accurately as possible, determine from your plot the wavelength at which fl takes on its greatest value. Record this on the upper right part of the graph paper. This wavelength of maximum light, lmax , can be related to the Kelvin temperature of the sun by Wein’s Law.
T = 2.89 x 107 / lmax
where lmax is in Angstroms and T is in degrees Kelvin. Record the temperature of the sun on the graph paper, below the value of lmax .
Next, find the total area (A) under the curve. This is accomplished by counting the number of squares. Once you have determined the area, convert the result into ergs/cm2/sec by multiplying the number of squares by the conversion factor. This will give you the area under the curve which is known as the solar constant and is the total energy (ET) at all wavelengths striking one square centimeter of the top of the atmosphere in one second. Record the number of squares counted and the conversion factor on your graph paper.
It is now necessary to calculate the total energy per unit area at the surface of the sun, E¤. This is given by:
E¤ = ET (a2 / r2)
where a is the earth-sun distance in centimeters and r is the solar radius in centimeters. Once E¤ is known, then the luminosity of the sun in ergs/sec should be determined by:
L¤ = 4pr2E¤ = 2.8 x 1027 x ET
RADIATION FLOW
The radiation flow out of the sun is not smooth and uniform because each photon of radiation can interact with the atoms it encounters and its path can be affected in a random manner. The photon’s path becomes a very crooked line as the radiation is repeatedly absorbed, re-radiated, and scattered on its way from the center to the surface where it escapes into space.
The diagram on Table 2 is a two-dimensional representation of a star, where each dot represents an atom or electron. When a photon encounters a particle, its path may be changed in some random direction. You will use this diagram to move photons from the center to the surface. Each time your photon reaches a particle, roll a die to select randomly the direction of re-radiation. Mark the path of your photon in pencil and count the number of interactions (rolls) required to get your photon to the surface. Repeat the process at least twice so an average number of interactions can be obtained.
Mathematicians can show that the average for many such photons should be close to N2, where N is the number of layers in the diagram. How does the theoretical value compare with the number of rolls it took your photon to get to the surface?
If this was applied to the sun, being three-dimensional, it would take a photon nearly 1,000,000 years to reach the surface, even though it would be traveling at the speed of light.
SUNSPOT CYCLE:
The law of variation of the number of spots on the solar disk is of prime importance in solar physics and in relations between solar and terrestrial phenomena. It was suspected at a very early date that the variations were periodic with time, though it was only after the work of Schwabe in 1843 that the period of maximum sunspot frequency was shown to be approximately 11 years. The degree of spottedness of the solar disk is commonly expressed by a system of relative numbers, which are known as sunspot numbers. On Table 3, the sunspot numbers from 1900 to the present are given. Construct a graph of these values for the years 1900 to the present. The sunspot number is to be plotted on the vertical axis and time on the horizontal axis.
From a study of the graph and the earlier part of the table, determine the years of sunspot maximum and minimum and record the data in table form. Find the mean interval between successive minima and repeat for successive maxima.
One of the most striking features of sunspot activity is the variation in latitude with time of the general area of spot activity. This variation was studied by Sporer and others. The law of spot variation consists of two main propositions:
(a) the mean latitude of sunspots diminishes gradually to about ± 5O at the end of the cycle.
(b) before a sunspot cycle is completed, a second cycle begins abruptly by the appearance of sunspots at high latitude.
Values of mean heliographic latitudes of spot activity for both northern and southern hemisphere of the sun are given in Table 4. Plot this data on a sheet of graph paper with latitude vertical and time horizontal. Arrange the graph so that zero latitude runs through the center. Plots for both hemispheres may be made on the same sheet. Draw smooth curves through the points plotted.
Questions:
1. What is a “black body”?
2. What was your value for the solar constant? How does is compare to the listed value of
(1.4 x 106 ergs/cm2/sec)? Determine the percentage error.
3. What was your value for the luminosity of the sun? How does it compare to the listed value of (3.89 x 1033 ergs/sec)? Determine the percentage error.
4. How many interactions did it take to get your photon from the center to the edge of the star? How did it compare to the predicted value?
5. What is the period of the sunspot cycle?
6. How does the rise to a maximum compare to the rate of decline to a minimum?
7. Where are we in the sunspot cycle today? When is the next maximum?
8. What was the “Maunder Minimum”?
9. Are the two main propositions of Sporer’s Law verified by the observations from 1913-1936?
10. In general, do the areas of spot activity move toward the equator at the same rate? Explain.
Table 1
THE CONTINUOUS SPECTRUM OF THE SUN
l fl l fl
(Å) (ergs/cm2/ Å /sec) (Å) (ergs/cm2/ Å /sec)
2000 1.2 5500 198
2200 4.5 6000 187
2400 6.4 6500 167
2600 13 7000 149
2800 25 7500 129
3000 59 8000 114
3200 85 9000 90
3400 114 10000 74
3600 115 11000 61
3700 127 12000 50
3800 121 14000 33
3900 115 16000 22
4000 160 18000 15
4100 187 20000 10
4200 189 25000 5.0
4300 183 30000 2.6
4400 201 40000 0.93
4500 213 50000 0.41
4600 215 60000 0.21
4800 213 80000 0.06
5000 204 100000 0.02
Table 2
RADIATION FLOW
Table 3
SUNSPOT NUMBERS
SUNSPOT SUNSPOT SUNSPOT
YEAR NUMBER YEAR NUMBER YEAR NUMBER
1900 15.7 1951 98.3 2002 163.6
01 4.6 52 45.0 03 99.3
02 8.5 53 20.1 04 65.3
03 40.8 54 6.6 05 45.8
04 70.1 55 54.2 06 24.7
05 105.5 56 200.7 07 12.6
06 90.1 57 269.3 08 4.2
07 102.8 58 261.7 09 4.8
08 80.9 59 225.1 2010 24.9
09 73.2 1960 159.0 11 80.8
1910 30.9 61 76.4 12 84.5
11 9.5 62 53.4 13 94.0
12 6.0 63 39.9 14 113.3
13 2.4 64 15.0 15 69.8
14 16.1 65 22.0 16 39.9
15 79.0 66 66.8
16 95.0 67 132.9
17 173.6 68 150.0
18 134.6 69 149.4
19 105.7 1970 148.0
1920 62.7 71 94.4
21 43.5 72 97.6
22 23.7 73 54.1
23 9.7 74 49.2
24 27.9 75 22.5
25 74.0 76 18.4
26 106.5 77 39.3
27 114.7 78 131.0
28 129.7 79 220.1
29 108.2 1980 218.9
1930 59.4 81 198.9
31 35.1 82 162.4
32 18.6 83 91.0
33 9.2 84 60.5
34 14.6 85 20.6
35 60.2 86 14.8
36 132.8 87 33.9
37 190.6 88 123.0
38 182.6 89 211.1
39 148.0 1990 191.8
1940 113.0 91 203.3
41 79.2 92 133.0
42 50.8 93 76.1
43 27.1 94 44.9
44 16.1 95 25.1
45 55.3 96 11.6
46 154.3 97 28.9
47 214.7 98 88.3
48 193.0 99 136.3
49 190.7 2000 173.9
1950 118.9 01 170.4
Table 4
MEAN HELIOGRAPHIC LATITUDES
NORTHERN HEMISPHERE SOUTHERN HEMISPHERE
YEAR MEAN LATITUDE YEAR MEAN LATITUDE
1913 24.6 1913 20.1
1914 21.1 1914 23.1
1915 17.9 1915 19.7
1916 13.1 1916 17.1
1917 13.8 1917 15.5
1918 11.9 1918 13.7
1919 9.8 1919 11.6
1920 11.3 1920 10.0
1921 7.5 1921 8.9
1922 8.8 1922 6.6
1923 5.5 1923 5.0
24.5 27.5
1924 22.2 1924 25.5
1925 20.7 1925 19.4
1926 19.3 1926 18.0
1927 17.7 1927 18.5
1928 11.9 1928 15.2
1929 10.7 1929 10.3
1930 10.6 1930 8.9
1931 7.9 1931 9.4
1932 8.2 1932 8.6
1933 6.2 1933 6.5
26.3 31.8
1934 4.1 1934 4.4
25.4 29.5
1935 22.4 1935 25.7
1936 19.4 1936 21.0