ASTR 101
Name:
H-R Diagrams Lab, Part 1: Analyzing Star Populations on a Hertzprung-Russell
(H-R) Diagram
What are most stars like? Why are they like that? To take a first step toward finding
out, plot the nearby stars and the bright stars on the same H-R diagram.

Use a different symbol for each type of data; for instance, use dots for the nearby
stars and the + symbol for the bright stars. Or, if you have different colors to use,
you could use blue for the nearby and red for the bright.
Using the tables of nearby and bright stars, graph at least 25 of the nearby and 25 of the
bright stars on the HR diagram (attached). For a statistically better analysis, deeper
learning and a higher score, you should graph 30 or more of the nearby and 30 or more of
the bright stars.
Bright stars are the ones that appear bright in our night sky as we see them from Earth.
Nearby stars are the ones that are the shortest distance away.
Use a different symbol or different color for the nearby stars and the bright stars on your
graph. Be sure to include a legend showing which symbol (color) is which.
What gets plotted on a H-R diagram is spectral class (O1 through M9, which also
corresponds to higher-to-lower temperatures) vs. absolute magnitude (absolute visual
magnitude, MV).
Absolute visual magnitude relates to how bright the star really is, not just how
bright it appears to be as seen from Earth.
Remember that the SMALLER the MV number, the MORE LUMINOUS the star is, in
absolute terms. A star with MV = –5.0 is MUCH more luminous than an MV = 1.0 star.
To put it another way, a star with MV = –5.0 appears SPECTACULARLY more bright
– IF SEEN FROM THE SAME DISTANCE – than a star with MV = 1.0.
Five units of visual magnitude correspond to a hundred-fold difference in brightness.
For example, a star with MV = 1.0 is 100 times brighter than one with MV = 6.0, as seen
from the same distance.
When plotting stellar class, keep track of the 1-9 number. For instance, a
G0 star plots directly above the G mark on the horizontal axis of the graph,
but a G9 star plots above a point 9/10 of the way toward K along the
horizontal axis.
Also note that the spectral classes of stars correspond to a variation in temperature. O
stars have the hottest photosphere and atmosphere, and M stars the coldest. According to
the laws of physics for the behavior of blackbodies (Wien’s law and the StefanBoltzmann law), it is these temperatures that account for why O and B stars have a
bluish tint to their color and M stars have a reddish tint.
O stars, by the way, are rare. Few stars so massive form in the first place, and when they
do, they “live fast and die young,” having a very short stellar lifespan. Therefore, at a
given time in one sector of our galaxies spiral arms, you might find only a few O stars,
out of all the millions of stars.
When you are done plotting the nearby and bright stars on the H-R diagram, please
answer the following questions, USING COMPLETE SENTENCES:
1. What is meant by the “intrinsic brightness” of a star?
2. What are two different units that can be used to express the intrinsic brightness of
a star, and how is each of those units defined?
3. Why is it important to compare stars in terms of their intrinsic brightness?
4. Compared to the bright stars, do the nearby stars tend to plot toward one side of
the H-R diagram in terms of O through M? If so, which side?
5. Compared to the bright stars (bright as seen from Earth), do the nearby stars tend
to plot toward the top or bottom of the H-R diagram?
a. Are the nearby stars more luminous or less luminous than the bright stars, in
terms of their true, intrinsic luminosity?
6. Compared to the nearby stars, do the bright stars (bright as seen from Earth) tend
to plot toward one side of the H-R diagram in terms of O through M? If so, which
side? Or are the bright stars spread across the temperature spectrum from O/B to
M?
7. Are the nearby stars intrinsically bright or intrinsically dim, on average?
a. Why are the nearby stars that way?
(This may be the most important question in this part of the lab.)
8. Are the bright-looking stars intrinsically bright or intrinsically dim, on average?
a. Why do the bright-looking stars tend to be that way? Is it because of their
distance from Earth, or...what?
(This may be the second most important question in this part of the lab.
It’s not an easy answer to express clearly, but it can be done.)
Hertzprung-Russell Diagram
-10.0
( more
luminous )
-5.0
0.0
Mv
+5.0
+10.0
+15.0
( less
luminous )
+20.0
B
(  hotter )
A
F
G
Spectral Class
K
M
( colder  )
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
-3.3
B
3.22
20500 B3
Avior
-2.1
2.74
4900 K0
Delta Canis
Majoris
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
3.82
25500 B1
Delta
0.6
Vulpeculae
1.66
9900 A0
-8.0
-4.8
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
*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
9620 A1
*Sirius B
11.2 -2.58
1480
A2
0
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
Andromeda 10.4 -2.26
e
3340 M1
*GQ
Andromeda 13.4 -3.45
e
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
11.9 -2.88
2940 M4
Tau Ceti
5.7
-0.39
5150 G8
*Struve 2398 B
1.34
M5.
5
*Procyon A 2.6
0.88
6600 F5
*Procyon B 13.0 -3.30
9700 A4
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
3340 K5.5
Kapteyn's
Star
10.9 -2.45
3480 M0
-1.60
*Kruger 60
11.9 -2.85
A
2940
M3.
*Kruger 60 B 13.3 -3.42
5
2670 M5
BD -124523 12.1 -2.93
2940
M3.
Ross 614 A 13.1 -3.35
5
2800 M4
Wolf 424 A 15.0 -4.09
2670 M5
van Maanen's
Star
TZ Arietis
14.0 -3.70
2800 M4
HD 225213 10.3 -2.23
3200 M22
Altair
2.2
1.00
8060 A7
AD Leonis
11.0 -2.50
2940
-0.50
4900 K1
*40 Eridani B
11.1 -2.54
1000 A3
*40 Eridani A 6.0
14.2 -3.78
1300
A8
0
M3.
5
0
*40 Eridani C 12.8 -3.20
*70 Ophiuchi B
7.5
-1.12
2940
M3.
*70 Ophiuchi A 5.8
5
3870 K5
-0.40
4950 K0
EV Lacertae 11.7 -2.78
2800 M4
H-R Diagrams Lab, Part 2: Color-Magnitude Diagrams and Ages of Star Clusters
Summary
In this second part of the H-R Diagrams Lab, the problem is to find the ages of two
clusters by plotting stellar data on a color-magnitude diagram.
Background and Theory
Thus far in the course, if you have been paying attention, you have learned how to determine
many characteristics of the stars: distance, intrinsic luminosity, surface temperature,
composition, mass and radius.
In order to study the life cycle of stars, we would like to know the age of the stars we observe.
Stellar clusters give us an opportunity to determine the age of their member stars.
Normally, a Hertzsprung-Russell (H-R) diagram plots the spectral type of a star against the
star's intrinsic luminosity. As you have learned, a star's spectral type corresponds to the star's
color. We can measure a star's color by determining its brightness through two different filters;
say a blue filter and a yellow filter. We can therefore plot the color of a star against its
brightness (measured in magnitudes) as a way of building an H-R diagram without taking the
star's spectrum. This type of diagram is generally called a "color-magnitude" diagram," which
is really a type of H-R diagram. This method is particularly useful with star clusters where
taking the spectrum of thousands of closely spaced stars would be impossible.
Today we will be plotting actual data for two star clusters: an open cluster called M45 and a
globular cluster called 47 Tuc. Each cluster contains thousands of stars, but we will only plot
the data for a representative few, enough for statistical validity. The table below (next page)
provides the data.
B-V is a measure of the color of a star. (It is the difference between the star's brightness in a
blue filter and a yellow filter.) The important thing to know is that the higher numbers are
redder and the lower numbers are bluer, so just like the O-M spectral class sequence, it goes
from hotter stars to cooler stars.
Procedure
1. Plot the BV versus magnitude on a piece of graph paper or using a spreadsheet
program such as Microsoft Excel.
2. Draw a different chart (graph) for each cluster.
3. Your x-axis is the color (BV). Your divisions on the x-axis should be about 0.2.
4. The y-axis is the apparent magnitude, and is different in each chart (graph).
5. Do not forget that magnitudes are backwards, so that smaller numbers mean
brighter stars!!!!
You should put the y-axis values, the apparent magnitude numbers, IN REVERSE
ORDER on your graphs or Excel chart vertical axis scals.
Star Cluster 47 Tuc
Star
Number
10012
10170
10200
10206
10278
10335
10359
10489
10610
20028
20034
20049
20070
20104
20130
20185
20210
20239
20335
20364
30014
30103
40002
40022
40043
40130
40135
40144
40164
40351
40628
40821
41051
41107
41456
Star Cluster M45
Color (BV)
Magnitude
0.76
0.98
1.05
0.96
1.23
1.31
1.23
1.33
1.45
0.53
0.58
0.57
0.6
0.65
0.69
0.83
0.88
0.93
1.1
1.2
1.1
0.82
1.45
1.25
1.14
0.99
0.69
0.79
0.59
0.85
0.73
0.73
0.7
0.58
0.51
19.6
20.6
21
21
21.6
22
22.2
22.6
23
17.6
17.7
18
18.4
18.8
19.1
19.8
20.1
20.4
21.4
21.6
13.5
15.5
12
12.6
12.9
14
14
14
14
14.9
16.2
16.6
16.9
17
17.2
Star
Number
133
165
345
522
697
804
950
1040
1103
1234
1266
1305
1309
1355
1432
1454
1516
1766
1797
1924
2168
2181
2209
2406
2425
2588
2601
2655
2870
2881
Color (BV)
Magnitude
1.28
0.12
0.84
0.9
0.35
0.2
-0.1
1.44
1.47
0.02
0.36
1.18
0.47
1.23
-0.09
1.16
1.31
0.47
0.56
0.62
-0.08
-0.08
1.47
0.76
-0.05
1.22
1.55
1.36
1.07
0.86
14.4
7.6
11.6
11.9
8.6
7.9
4.2
15.8
14.8
6.8
8.3
13.5
9.5
14
2.9
12.8
14
9.1
10.1
10.3
3.6
5.1
14.4
11.1
6.2
13.1
15
15.5
12.5
11.8
Staple your two charts (graphs) to this page when finished. Answer the questions on the following
page.
1. We have always plotted absolute magnitude on the y-axis of an H-R diagram. Why can
we plot the apparent magnitude for cluster stars? (Hint: What is the point of using
absolute magnitude instead of apparent magnitude and how to stars in one cluster not
have this problem to overcome?)
2. On your plot for 47 Tuc, locate the red giant stars. Why are these stars so much brighter
than main sequence stars of the same color?
3. Which cluster is closer to the earth? (Hint: think about the method of spectroscopic
parallax.)
a. How can you tell it is closer?
4. Why don't we see O and B type stars on these diagrams (B-V color < -0.2)?
5. The lifetimes of different spectral types are given in Table 2 (below). Use these lifetimes
to estimate the age of 47 Tuc and M45. Explain your reasoning in each case!
Table 2: Main Sequence Lifetimes
Spectral Color Lifetime
Type B-V (years)
O
-0.4
< 106
B
-0.2
3 X 107
A
0.2
4 X 108
F
0.5
4 X 109
G
0.7 1 X 1010
K
1.0 6 X 1010
M
1.6
>1011