H-r diagram lab – astronomy

H-R 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 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	>25,000
B	Bluish-White	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 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,

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 Magnitude (m)	Spectral Class	Absolute Magnitude (M)	*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=10²

and therefore

L/L_Sun=100

So the star is 100 times as luminous as the Sun.

Table 1: Bright Stars

*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 Centauri A	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

Table 2: Nearby Stars

*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 Centauri	15.5	-4.29	2670	M5.5
*Alpha Centauri A	4.3	0.18	5840	G2	*Alpha Centauri B	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	*L726-8 ( 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 789-6	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	G51-I5	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 H-R Diagram?

[Type answer here]

Question 2: Using the Stefan-Boltzmann relationship, (L µ 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]

Question 3: On your H-R 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 H-R 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:

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H-r diagram lab – astronomy

Spectroscopic parallax distance determination

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