. Examine color-magnitude diagrams of clusters of stars.

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July 2010 Name: ________________________________

Lab Report for Lab #7: Reading the Stars

Description:

Stars come in many sizes and colors. It turns out that knowing a star’s color and size can tell you where it is in its evolutionary cycle. Stars evolve from protostars to stellar remnants on timescales of hundreds of millions to hundreds of billions of years. Astronomy has not been around that long – humans haven’t been around that long! How can astronomers know that stars change on those timescales?

The answer is that astronomers came up with a clever experiment to determine this information. This exercise presents students with the information necessary to deduce the basic outline of stellar evolution. Using astronomical data, students will analyze plots to determine which stages come first and how a star changes on the H-R Diagram throughout its existence.

Students will repeat a clever experiment. The purpose of repeating this experiment is many-fold. First, science requires that any theory be repeatable. That is, it must be that no matter who does the experiment, the same result occurs. Second, repeating this experiment will deepen a student’s understanding of the astronomy concepts and science processes involved in the experiment.

Introduction:

In order to piece together the story of stellar evolution, you have to have all the data. In this exercise, the focus is on analysis of data, so data will be presented to you and explained to you and you will have to analyze and interpret the data to draw conclusions about stellar evolution.

1. Examine color-magnitude diagrams of clusters of stars. Since a cluster of stars is a group of stars that were formed at the same time from the same cloud of gas and dust, we can learn a lot about the stars within that cluster. A color-magnitude diagram is a kind of H-R Diagram. The horizontal axis is for the color, which is correlated to temperature, as on the H-R Diagram. The vertical axis is for apparent magnitude, which is similar to absolute magnitude or luminosity, as on the H-R Diagram. Because all the stars in a cluster are at the same location in space, the apparent magnitude (how bright a star appears) can be treated as a kind of absolute magnitude (how bright a star would appear if it were at a standard distance from Earth). At the end of this exercise you will find modified color-magnitude diagrams (the vertical axis has been changed to absolute magnitude for comparison purposes) for several clusters of stars: h + ( Persei, the Pleiades, M11, the Hyades, Praesepe, and M67.

2. Identify trends you see in the color-magnitude diagrams. (a) Do you see any trends among these color-magnitude diagrams? (b) Can you determine the sequence from youngest to oldest? (c) What do you notice about the main sequence, red giants and white dwarfs on these diagrams? (d) Can you put them in some order that makes sense based on what you see? (e) Once you have put the diagrams together, compare your order to other small group members in your small group via your small group discussion board. If your order is different from that of another member, discuss to determine which way makes more sense. Try to come to consensus on an order and an explanation for your order. When you are confident that your ordering is complete, show your instructor.

[Type answers here]

3. (a) Based on the order you have derived, what can you say about what happens to a star during its existence? (b) Does a star begin as a white dwarf, main sequence or red giant star? (c) Following that stage, what does the star become? (d) Do all stars evolve the same way, at the same pace? (e) How can you tell which stage comes first? When you have arrived at a sequence of stages for stellar evolution, run this by your instructor.

[Type answers here]

4. Write up a summary of the sequence you have derived from the data. Include any other information you know about these various stages in stellar evolution: the type of nuclear fusion going on in the core (if at all), the size and temperature, relative to the previous stage.

[Type answer here]

OPTIONAL STEP 5: Create a story of the life cycle of a star based on your findings. Be as creative as you want. Feel free to take artistic license (by making the stars anthropomorphic, for example), but include actual accurate scientific information (like which stage comes first, relative temperatures and sizes, etc. Please limit your paper to 5 pages, single spaced.

CMDs:

Pleiades: http://personal.tcu.edu/~mfanelli/imastro/pleiades_cmd_webda.png

image1.jpg

M11: http://www.ucolick.org/~kirsten/COSMOS05/m11cmdiso.jpg

image2.jpg

Hyades: http://homepage.mac.com/andjames/Page030b.htm

image5.png

“Einstein survey of stars in the Hyades: Optical Properties and X-ray Luminosities.”, Micela, et.al. AJ., 325, 798 (1988)

M67: http://www.aanda.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/aa/full/2006/17/aa4291-05/aa4291-05.html

image3.png

h + ( Persei (or h + chi Persei):

image6.png http://iopscience.iop.org/1538-3881/122/1/248/201081.fg3.html

Praesepe:

image4.jpg

Zero Age Main Sequence (ZAMS) Color Magnitude Diagram (CMD):

http://www.eso.org/public/outreach/eduoff/cas/cas2002/cas-projects/germany_ngc1960_1/

image7.jpg

� EMBED MSPhotoEd.3 ���

 

 

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image8.png

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H-R Diagram Lab

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Spring 2011 Name: ____________________________________

Richland College Phys 1412

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,

 

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û

ù

ê

ë

é

+

=

5

5)

 

M

 

–

 

(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 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

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]

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MINI CASE: SCANDI HOME FURNISHINGS, INC.

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MINI CASE: SCANDI HOME FURNISHINGS, INC.

 

Kaj Rasmussen founded Scandi Home Furnishings as a corporation during mid-2002.  Sales during the first full year (2003) of operation reached $1.3 million.  Sales increased by 15 percent in 2004 and another 20 percent in 2005.  However, profits after increasing in 2004 over 2003 fell sharply in 2005 causing Kaj to wonder what was happening to his “pride and joy” business venture.  After all, Kaj has continued to work as close as possible to a 24/7 pace beginning with the startup of Scandi and through the first three full years of operation.

            Scandi Home Furnishings, located in eastern North Carolina, designs, manufactures, and sells to home furnishings retailers Scandinavian-designed furniture and accessories.  The modern Scandinavian design has a streamlined and uncluttered look.  While this furniture style is primarily associated with Denmark, both Norway and Sweden designers have contributed to the allure of Scandinavian home furnishings.  Some say that the inspiration for the Scandinavian design can be traced to the “elegant curves” of art nouveau from which designers were able to produce aesthetically pleasing, structurally strong modern furniture.  Danish, and the home furnishings produced by the other Scandinavian countries—Sweden, Norway, and Finland, are made using wood (primarily oak, maple, and ash), aluminum, steel, and high-grade plastics.

            Kaj grew up in Copenhagen, Denmark and received a college degree from a technical university in Sweden.  As is typically in Europe, Kaj began his business career as an apprentice at a major home furnishings manufacturer in Copenhagen.  After “learning the trade,” he quickly moved into a management position in the firm.   However, after a few years, Kaj realized that what he really wanted to do was to start and operate his own Scandinavian home furnishings business.  At the same time, after traveling throughout the world including the U.S., he was sure that he wanted to be an entrepreneur in the United States.  Thus, while it was hard to give up the Tivoli Gardens with its many entertainment and dining activities, as well as the other attractions in Copenhagen, Kaj moved to the U.S. in early 2002.  With $140,000 of his personal assets, and $210,000 from venture investors, he began operations in mid-2002.  Kaj, with a 40 percent ownership interest and industry-related management expertise, was allowed to operate the venture in a way that he thought was best for Scandi.  Four years later, Kaj is sure he did the right thing.

 

            Following are the three years of income statements and balance sheets for the Scandi Home Furnishings Corporation.  Kaj has felt that in order to maintain a competitive advantage that he would need to continue to expand sales.  After first concentrating on selling Scandinavian home furnishings in the northeast in 2003 and 2004, he decided to enter the west coast market.  An increase in expenses associated with identifying, contacting, and selling to home furnishings retailers in California, Oregon, and Washington.  Kaj Rasmussen was hoping that you could help him better understand what has been happening to Scandi Home Furnishings both from operating and financial standpoints.

Distributing Company Sells Small Appliances To Hardware Stores

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Comprehensive Problem | Bailey Distributing Company sells small appliances to hardware stores in the southern California area. Michael Bailey, the president of the company, is thinking about changing the credit policies offered by the firm to attract customers away from competitors. The current policy calls for a 1/10, net 30, and the new policy would call for a 3/10, net 50. Currently 40 percent of Bailey customers are taking the discount, and it is anticipated that this number would go up to 50 percent with the new discount policy. It is further anticipated that annual sales would increase from a level of $200,000 to $250,000 as a result of the change in the cash discount policy. The increased sales would also affect the inventory level. The average inventory carried by Bailey is based on a determination of an EOQ. Assume unit sales of small appliances will increase from 20,000 to 25,000 units. The ordering cost for each order is $100, and the carrying cost per unit is $1 (these values will not change with the discount). The average inventory is based on EOQ/2. Each unit in inventory has an average cost of $6.50. Cost of goods sold is equal to 65 percent of net sales; general and administrative expenses are 10 percent of net sales, and interest payments of 12 percent will be necessary only for the increase in the accounts receivable and inventory balances. Taxes will equal 25 percent of before-tax

Income

. a. Compute the accounts receivable balance before and after the change in the cash discount policy. Use the net sales (Total sales – Cash discounts) to determine the average daily sales and the accounts receivable balances.

b. Determine EOQ before and after the change in the cash discount policy. Translate this into average inventory (in units and dollars) before and after the change in the cash discount policy.

c. Complete the income statement. |

| | Before Policy Change | After Policy Change |

| Net sales (sales – cash discounts) | | |

| Cost of goods sold | | |

| Gross profit | | |

| General and administrative expense | | |

| Operating profit | | |

| Interest on increase in accounts receivable

and inventory (12%) | | |

| Income before taxes | | |

| Taxes | | |

| Income after taxes | | |

 

| d. Should the new cash discount policy be utilized? Briefly comment. |