# H-R Diagram Lab - Astronomy

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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/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

 Star M(V) log(L/Lsun) Temp Type Star M(V) log(L/Lsun) 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/Lsun) Temp Type Star M(V) log(L/Lsun) 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?

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.

(b) Which group must contain smaller stars? Explain your reasoning for this conclusion.

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?

Question 5: What is the relationship between temperature and color?

Question 6: What is the relationship between temperature and absolute brightness?

Question 7: How can we tell red giant stars are very large in diameter by looking at their location on the H-R Diagram?

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 10x.)

In traditional format, is would look like this:

Sirus:

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