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Spring
2011
Name: ____________________________________
Richland College Phys 1412
H
–
R
D
iagram Lab
Part I: Introduction &
B
ackground
A
round 1911 to 1913, a Dutch astronomer named Ejnar Hertzsprung and an American astronomer Henry Norris Russell created a diagram of stars plotted using only their luminosity and their spectral types. A star’s spectral type is determined by the absorption lines found in its spectrum. Hertzsprung and Russell noticed that the spectra were related to the stars’ color and temperature. Their diagram, named the Hertzsprung-Russell, or H-R, diagram in their honor, has been like a Rosetta Stone to stellar astronomy.
Table 1
Spectral Type
Color of Star
Temperature (
K
)
O
Blue
>2
5
,000
Bluish-
White
11,000 – 25,000
7,500 – 11,000
F
Yellow
to White
6,000 – 7,500
G
5,000 – 6,000
Orange
3,500 – 5000
M
Red
<3,500
The spectral types are subdivided into
10
subgroups which are labeled 0 through 9. Stars are further grouped by their luminosity, which is denoted by a Roman numeral.
|
Luminosity Classes |
|
|
Ia |
bright supergiant |
|
Ib |
supergiant |
|
II |
bright giants |
|
III |
giants |
|
IV |
subgiants |
|
V |
main sequence |
|
VI |
subdwarf |
|
VII |
white dwarf |
The original H-R diagram plotted the star’s luminosity versus its spectral type. It only included stars within 100 pc of the
Sun
as that was the limit for determining distances using the helio-centric parallax method, the only known method at the time.
Since then, the H-R diagram has come to represent more than just the luminosity of a star versus its spectral type as it can be used to glean more information than just that. For one, luminosity and absolute magnitude are related. It is easy to see where different groups of stars, like main sequence, red giants, et cetera, are grouped on the diagram. Temperature and thus color information can also be found, as well as radius size. We can determine the mass of main sequence stars by using the diagram. We can also determine the distance to stars by plotting them on the H-R diagram. Other characteristics, including stellar densities, spectral lines, stellar life times, stellar interiors, types of nuclear processes taking place within the star, and interior temperatures can also be discovered.
Part II: Procedure
Section 1: Luminosity
Review/Go over solar luminosity as it relates to absolute magnitude. (See textbook section 15.1 Properties of Stars and Mathematical Insight 15.3.) Remember that for every change of 5 magnitudes, the luminosity changes by 100. So a star with an absolute magnitude of 10 will be 100 times more luminous than a star with an absolute magnitude of 15. (For a review on logarithms, see page 4 of this lab packet.) Note: the following graphing instructions are specifically for Excel 2003®; other products/Excel versions may have different instructions.
Section 2: Plotting
Once complete, begin section 3 of this lab. Plot all the stars listed in “Table 1: Bright Stars” on page 4 and “Table 2: Nearby Stars” on page 5 in the back of this lab packet. DO NOT label the stars with their names.
Step 1: Copy – Paste special – Unicode text the information from the two tables of stars into a spreadsheet. Make sure you have only 5 columns: Star, M(V), Log (L/Lsun), Temp, and Type. (You will notice that the tables were doubled-up to save space such that there are 10 columns per page.)
Step 2: Convert the Spectral class types into numbers, such that O is 0, B is 1, A is 2, et cetera. Highlight the data in the column labeled “Type.” Go to the “Edit” menu and choose “Replace.” In the pop-up search window, type “O” in the “Replace” line and “0.” in the “Replace with” line. (Don’t forget the period after the number!) Click on “Replace all.” Do this for all spectral class letters. Remove any stars from the lists which have two decimals or include the letter D.
Step 3: Graphing. First, highlight the data in the “Type” column and the “log (L/Lsun)” column for “Table 1: Bright Stars”. Click on the chart wizard icon in the menu bar. Select XY scatter and click next. Click on the Series tab on the top of the next window. Name this series “Bright Stars.” Be sure the cells within the “Type” column are set as your X values, and cells within the “log (L/Lsun)” column are set as your Y values.
Step 4: Now add a series. Name it “Nearby Stars” and again make sure the cells within the “Type” column for “Table 2: Nearby Stars” are set as your X values, and cells within the “log (L/Lsun)” column for “Table 2: Nearby Stars” are set as your Y values. (Define the x values by clicking on the little red, white and blue box. Now highlight the “Type” values only on the original sheet under the “Table 2: Nearby Stars” category. Define the y values by clicking on the little red, white and blue box. Now highlight the “log (L/Lsun)” values only on the original sheet under the “Table 2: Nearby Stars” category.) Click “Next.”
Step 5: Labeling. Click on the “Titles” tab on the next window. Give your chart the title “[your last name]’s H-R Diagram” Label the x values as “Spectral Type” and the y values as “log (L/Lsun).” In the Axes tab, both check boxes for Value (X) axis and Value (Y) axis should be checked. In the Gridlines tab, no check boxes should be checked. In the Legend tab, be sure the legend is shown. Choose where you would like it placed. In the Data Labels tab, but sure no check boxes are checked. Click Finished.
Step 6: Resize the graph such that it is more square-like and less rectangular-like. Extra credit: change the graph’s background color to approximately show the colors of the stars.
Step 7: Answer the questions at the end of the packet.
Section 3: Distance Calculations
Now you will use your H-R diagram to calculate the distance to some stars. Distance is calculated by using the distance modulus
(m
– M) and the distance formula,
ú
û
ù
ê
ë
é
+
=
5
5)
–
(m
10
D
where everything within the square brackets is the exponent of 10. Calculate the distance to each of the stars listed below in the chart. SHOW ALL MATH WORK FOR CREDIT.
Spectroscopic parallax distance determination
|
Star |
Apparent |
Spectral |
Absolute |
m – M |
Distance |
||||
|
Sirius |
-1.4 |
A1 |
|||||||
|
Spica |
1.0 |
B1 |
|||||||
|
Barnard’s Star |
9.5 |
M4 V |
|||||||
|
61 Cygni B |
5.2 |
K5 V |
|||||||
|
CN Leo (Wolf 359) |
1 3.5 |
M6 V |
|||||||
|
Tau Ceti |
3.5 |
G8 |
Type answers into the table above. Go to 2 decimal places. Show work for Sirius “below.”
Work space
Logarithm Review
Note:
In order to find L/LSun from the lists, you need to know about logarithms. Here is a quick reminder:
log(L/LSun)=x
means that
L/LSun=10x
Let’s use a real number to work this out. Suppose that x=2, so that
log(L/LSun)=2
Then
L/LSun=102
and therefore
L/LSun=100
So the star is 100 times as luminous as the Sun.
Table 1: Bright Stars
|
M(V) |
log(L/Lsun) |
Temp |
Type |
||||||||||||||||||
| Sun |
4.8 |
0.00 |
5840 |
G2 |
Sirius A |
1.4 |
1.34 |
9620 |
|||||||||||||
|
Canopus |
-3.1 |
3.15 |
7400 |
F0 |
Arcturus |
– 0.4 |
2.04 |
4590 |
K2 |
||||||||||||
|
Alpha |
4.3 |
0.18 |
Vega |
0.5 |
1.72 |
9900 |
A0 |
||||||||||||||
|
Capella |
– 0.6 |
2.15 |
5150 |
Rigel |
-7.2 |
4.76 |
12140 |
B8 |
|||||||||||||
|
Procyon A |
2.6 |
0.88 |
6580 |
F5 |
Betelgeuse |
– 5.7 |
4.16 |
3200 |
M2 |
||||||||||||
|
Achemar |
-2.4 |
2.84 |
20500 |
B3 |
Hadar |
-5.3 |
4.00 |
25500 |
|||||||||||||
|
Altair |
2.2 |
1.00 |
8060 |
A7 |
Aldebaran |
-0.8 |
2.20 |
4130 |
K5 | ||||||||||||
|
Spica |
-3.4 |
3.24 |
Antares |
-5.2 |
3.96 |
3340 |
M1 |
||||||||||||||
|
Fomalhaut |
2.0 |
1.11 |
9060 |
A3 |
Pollux |
1.0 |
1.52 |
4900 |
K0 |
||||||||||||
|
Deneb |
9340 |
A2 |
Beta Crucis |
-4.7 |
3.76 |
28000 |
B0 |
||||||||||||||
|
Regulus |
13260 |
B7 |
Acrux |
-4.0 |
3.48 |
||||||||||||||||
|
Adhara |
23000 |
B2 |
Shaula |
||||||||||||||||||
|
Bellatrix |
-4.3 |
3.60 |
Castor |
1.2 |
1.42 |
||||||||||||||||
|
Gacrux |
-0.5 |
2.10 |
3750 |
M3 |
Beta Centauri |
-5.1 |
3.94 |
||||||||||||||
|
Alpha Centauri B |
5.8 |
-0.42 |
4730 |
K1 |
Al Na’ir |
-1.1 |
2.34 |
15550 |
B5 |
||||||||||||
|
Miaplacidus |
2.14 |
9300 |
Elnath |
-1.6 |
2.54 |
12400 |
|||||||||||||||
|
Alnilam |
-6.2 |
4.38 |
26950 |
Mirfak |
-4.6 |
3.74 |
7700 |
||||||||||||||
|
Alnitak |
-5.9 |
4.26 |
33600 |
O9 |
Dubhe |
0.2 |
1.82 |
||||||||||||||
|
Alioth |
0.4 |
1.74 |
Peacock |
-2.3 |
2.82 |
||||||||||||||||
|
Kaus Australis |
-0.3 |
2.02 |
11000 |
B9 |
Theta Scorpii |
-5.6 |
4.14 |
||||||||||||||
|
Atria |
-0.1 |
1.94 |
Alkaid |
-1.7 |
2.58 |
||||||||||||||||
|
Alpha Crucis B |
-3.3 |
3.22 |
Avior |
-2.1 |
2.74 |
||||||||||||||||
|
Delta Canis Majoris |
-8.0 |
5.10 |
6100 |
F8 |
Alhena |
0.0 |
1.90 |
||||||||||||||
|
Menkalinan |
0.6 |
1.66 |
Polaris |
||||||||||||||||||
|
Mirzam |
-4.8 |
3.82 |
Delta Vulpeculae |
Table 2: Nearby Stars
|
*Proxima |
15.5 |
-4.29 |
2670 |
M5 .5 |
|||||||||||||||||||||
|
*Alpha |
*Alpha |
||||||||||||||||||||||||
|
Barnard’s Star |
13.2 |
-3.39 |
2800 |
M4 |
Wolf 359 (CN Leo) |
16.7 |
-4.76 |
M6 | |||||||||||||||||
|
HD 93735 |
10.5 |
-2.30 |
*L726-8 ( A) |
-4.28 |
|||||||||||||||||||||
|
*UV Ceti (B) |
1 6.0 |
-4.48 |
*Sirius A |
||||||||||||||||||||||
|
*Sirius B |
11.2 |
-2.58 |
14800 |
DA |
Ross 154 |
13.1 |
-3.36 |
||||||||||||||||||
|
Ross 248 |
14.8 |
-4.01 |
M5 |
Epsilon Eridani |
6.1 |
-0.56 |
|||||||||||||||||||
|
Ross 128 |
13.5 |
-3.49 |
L 789-6 |
14.5 |
-3.90 |
||||||||||||||||||||
|
*GX Andromedae |
10.4 |
-2.26 |
*GQ Andromedae |
13.4 |
-3.45 |
||||||||||||||||||||
|
Epsilon Indi |
7.0 |
-0.90 |
K3 |
*61 Cygni A |
7.6 |
-1.12 |
|||||||||||||||||||
|
*61 Cygni B |
8.4 |
-1.45 |
3870 |
*Struve 2398 A |
-2.56 |
3070 |
|||||||||||||||||||
|
*Struve 2398 B |
11.9 |
-2.88 |
2940 |
Tau Ceti |
5.7 |
-0.39 |
|||||||||||||||||||
|
*Procyon A |
6600 |
*Procyon B |
13.0 |
-3.30 |
9700 |
DF |
|||||||||||||||||||
|
Lacaille 9352 |
9.6 |
-1.93 |
G51-I5 |
17.0 |
-4.91 |
2500 |
M7 |
||||||||||||||||||
|
YZ Ceti |
14.1 |
-3.75 |
BD +051668 |
||||||||||||||||||||||
|
Lacaille 8760 |
8.7 |
-1.60 |
K5.5 |
Kapteyn’s Star |
10.9 |
-2.45 |
3480 |
M0 |
|||||||||||||||||
|
*Kruger 60 A |
-2.85 |
M3.5 |
*Kruger 60 B |
13.3 |
-3.42 |
||||||||||||||||||||
|
BD -124523 |
12.1 |
-2.93 |
Ross 614 A |
-3.35 |
|||||||||||||||||||||
|
Wolf 424 A |
15.0 |
-4.09 |
van Maanen’s Star |
14.2 |
-3.78 |
13000 |
DB |
||||||||||||||||||
|
TZ Arietis |
14.0 |
-3.70 |
HD 225213 |
10.3 |
-2.23 |
M1.5 |
|||||||||||||||||||
|
AD Leonis |
11.0 |
-2.50 |
|||||||||||||||||||||||
|
*40 Eridani A |
6.0 |
-0.50 |
*40 Eridani B |
11.1 |
-2.54 |
10000 |
|||||||||||||||||||
|
*40 Eridani C |
12.8 |
-3.20 |
*70 Ophiuchi A |
-0.40 |
4950 |
||||||||||||||||||||
|
*70 Ophiuchi B |
7.5 |
EV Lacertae |
11.7 |
-2.78 |
Questions
1. How many distinct groupings of plots (“dots”) do you see on your H-R Diagram?
[Type answer here]
2. Using the Stefan-Boltzmann relationship, (L ( R2 T4), determine the relative sizes of the groups you identified.
(a) Which group must contain larger stars? Explain your reasoning for this conclusion.
[Type answer here]
(b) Which group must contain smaller stars? Explain your reasoning for this conclusion.
[Type answer here]
3. On your H-R Diagram, find the Main Sequence. Can you find which dot represents the Sun?
(Highlight one): YES NO
4. If you answered “YES,” how did you determine which dot represents the Sun? If you answered “NO,” why could you not determine which dot represents the Sun?
[Type answer here]
5. What is the relationship between temperature and color?
[Type answer here]
6. What is the relationship between temperature and absolute brightness?
[Type answer here]
7. How can we tell red giant stars are very large in diameter by looking at their location on the H-R Diagram?
[Type answer here]
Page 7 of 7
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