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 <

 

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 <