Hr diagram lab – astronomy
HR Diagram Lab
Part I: Introduction & Background
Around 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 HertzsprungRussell, or HR, diagram in their honor, has been like a Rosetta Stone to stellar astronomy.
Table 1
Spectral Type 
Color of Star 
Temperature (K) 
O 
Blue 
>25,000 
B 
BluishWhite 
11,000 – 25,000 
A 
White 
7,500 – 11,000 
F 
Yellow to White 
6,000 – 7,500 
G 
Yellow 
5,000 – 6,000 
K 
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 HR 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 heliocentric parallax method, the only known method at the time.
Since then, the HR 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 HR 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 doubledup 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 popup 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 HR 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 squarelike and less rectangularlike. 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 HR diagram to calculate the distance to some stars. Distance is calculated by using the distance modulus (m – M) and the distance formula,
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. (20 pts)
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) 
13.5 
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/L_{Sun} from the lists, you need to know about logarithms. Here is a quick reminder:
log(L/L_{Sun})=x
means that
L/L_{Sun}=10^{x}
Let’s use a real number to work this out. Suppose that x=2, so that
log(L/L_{Sun})=2
Then
L/L_{Sun}=10^{2}
and therefore
L/L_{Sun}=100
So the star is 100 times as luminous as the Sun.
Star 
M(V) 
log(L/L_{sun}) 
Temp 
Type 
Star 
M(V) 
log(L/L_{sun}) 
Temp 
Type 
Sun 
4.8 
0.00 
5840 
G2 
Sirius A 
1.4 
1.34 
9620 
A1 
Canopus 
3.1 
3.15 
7400 
F0 
Arcturus 
0.4 
2.04 
4590 
K2 
Alpha 
4.3 
0.18 
5840 
G2 
Vega 
0.5 
1.72 
9900 
A0 
Capella 
0.6 
2.15 
5150 
G8 
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 
B1 
Altair 
2.2 
1.00 
8060 
A7 
Aldebaran 
0.8 
2.20 
4130 
K5 
Spica 
3.4 
3.24 
25500 
B1 
Antares 
5.2 
3.96 
3340 
M1 
Fomalhaut 
2.0 
1.11 
9060 
A3 
Pollux 
1.0 
1.52 
4900 
K0 
Deneb 
7.2 
4.76 
9340 
A2 
Beta Crucis 
4.7 
3.76 
28000 
B0 
Regulus 
0.8 
2.20 
13260 
B7 
Acrux 
4.0 
3.48 
28000 
B0 
Adhara 
5.2 
3.96 
23000 
B2 
Shaula 
3.4 
3.24 
25500 
B1 
Bellatrix 
4.3 
3.60 
23000 
B2 
Castor 
1.2 
1.42 
9620 
A1 
Gacrux 
0.5 
2.10 
3750 
M3 
Beta Centauri 
5.1 
3.94 
25500 
B1 
Alpha Centauri B 
5.8 
0.42 
4730 
K1 
Al Na’ir 
1.1 
2.34 
15550 
B5 
Miaplacidus 
0.6 
2.14 
9300 
A0 
Elnath 
1.6 
2.54 
12400 
B7 
Alnilam 
6.2 
4.38 
26950 
B0 
Mirfak 
4.6 
3.74 
7700 
F5 
Alnitak 
5.9 
4.26 
33600 
O9 
Dubhe 
0.2 
1.82 
4900 
K0 
Alioth 
0.4 
1.74 
9900 
A0 
Peacock 
2.3 
2.82 
20500 
B3 
Kaus Australis 
0.3 
2.02 
11000 
B9 
Theta Scorpii 
5.6 
4.14 
7400 
F0 
Atria 
0.1 
1.94 
4590 
K2 
Alkaid 
1.7 
2.58 
20500 
B3 
Alpha Crucis B 
3.3 
3.22 
20500 
B3 
Avior 
2.1 
2.74 
4900 
K0 
Delta Canis Majoris 
8.0 
5.10 
6100 
F8 
Alhena 
0.0 
1.90 
9900 
A0 
Menkalinan 
0.6 
1.66 
9340 
A2 
Polaris 
4.6 
3.74 
6100 
F8 
Mirzam 
4.8 
3.82 
25500 
B1 
Delta Vulpeculae 
0.6 
1.66 
9900 
A0 
Star 
M(V) 
log(L/L_{sun}) 
Temp 
Type 
Star 
M(V) 
log(L/L_{sun}) 
Temp 
Type 
Sun 
4.8 
0.00 
5840 
G2 
*Proxima 
15.5 
4.29 
2670 
M5.5 
*Alpha 
4.3 
0.18 
5840 
G2 
*Alpha 
5.8 
0.42 
4900 
K1 
Barnard’s Star 
13.2 
3.39 
2800 
M4 
Wolf 359 (CN Leo) 
16.7 
4.76 
2670 
M6 
HD 93735 
10.5 
2.30 
3200 
M2 
*L7268 ( A) 
15.5 
4.28 
2670 
M6 
*UV Ceti (B) 
16.0 
4.48 
2670 
M6 
*Sirius A 
1.4 
1.34 
9620 
A1 
*Sirius B 
11.2 
2.58 
14800 
DA 
Ross 154 
13.1 
3.36 
2800 
M4 
Ross 248 
14.8 
4.01 
2670 
M5 
Epsilon Eridani 
6.1 
0.56 
4590 
K2 
Ross 128 
13.5 
3.49 
2800 
M4 
L 7896 
14.5 
3.90 
2670 
M6 
*GX Andromedae 
10.4 
2.26 
3340 
M1 
*GQ Andromedae 
13.4 
3.45 
2670 
M4 
Epsilon Indi 
7.0 
0.90 
4130 
K3 
*61 Cygni A 
7.6 
1.12 
4130 
K3 
*61 Cygni B 
8.4 
1.45 
3870 
K5 
*Struve 2398 A 
11.2 
2.56 
3070 
M3 
*Struve 2398 B 
11.9 
2.88 
2940 
M4 
Tau Ceti 
5.7 
0.39 
5150 
G8 
*Procyon A 
2.6 
0.88 
6600 
F5 
*Procyon B 
13.0 
3.30 
9700 
DF 
Lacaille 9352 
9.6 
1.93 
3340 
M1 
G51I5 
17.0 
4.91 
2500 
M7 
YZ Ceti 
14.1 
3.75 
2670 
M5 
BD +051668 
11.9 
2.88 
2800 
M4 
Lacaille 8760 
8.7 
1.60 
3340 
K5.5 
Kapteyn’s Star 
10.9 
2.45 
3480 
M0 
*Kruger 60 A 
11.9 
2.85 
2940 
M3.5 
*Kruger 60 B 
13.3 
3.42 
2670 
M5 
BD 124523 
12.1 
2.93 
2940 
M3.5 
Ross 614 A 
13.1 
3.35 
2800 
M4 
Wolf 424 A 
15.0 
4.09 
2670 
M5 
van Maanen’s Star 
14.2 
3.78 
13000 
DB 
TZ Arietis 
14.0 
3.70 
2800 
M4 
HD 225213 
10.3 
2.23 
3200 
M1.5 
Altair 
2.2 
1.00 
8060 
A7 
AD Leonis 
11.0 
2.50 
2940 
M3.5 
*40 Eridani A 
6.0 
0.50 
4900 
K1 
*40 Eridani B 
11.1 
2.54 
10000 
DA 
*40 Eridani C 
12.8 
3.20 
2940 
M3.5 
*70 Ophiuchi A 
5.8 
0.40 
4950 
K0 
*70 Ophiuchi B 
7.5 
1.12 
3870 
K5 
EV Lacertae 
11.7 
2.78 
2800 
M4 
Questions
Question 1: How many distinct groupings of plots (“dots”) do you see on your HR Diagram?
[Type answer here]
Question 2: Using the StefanBoltzmann relationship, (L µ R^{2} T^{4}), 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]
Question 3: On your HR Diagram, find the Main Sequence. Can you find which dot represents the Sun?
(Highlight one): YES NO
Question 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]
Question 5: What is the relationship between temperature and color?
[Type answer here]
Question 6: What is the relationship between temperature and absolute brightness?
[Type answer here]
Question 7: How can we tell red giant stars are very large in diameter by looking at their location on the HR Diagram?
[Type answer here]
The equation is:
When we look at the star Sirius, we see we have the following values for the listed variables:
m = 1.4
M = 1.4
Plug those values in to the numerator of the fraction and we have:
(1.4) – 1.4 + 5
which equals 2.2
Next, divide that by the denominator, which is 5, to get: 2.2/5 = 0.44
This is the power (or exponent) of 10, giving us:
10^0.44 = 2.7542287033381664486312106594222, or 2.75 (taken to 2 decimal places). (To do this step on the calculator, look for the key that is labeled 10^{x}.)
In traditional format, is would look like this:
Sirus: