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Properties of Stars
Types of Stars and the HR diagram
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This section presents the results of using the tools described above. In order to get a better idea of what
stars are like, put them into groups of some sort. Then you can see how the other quantities differ among
the various groups. Astronomers group stars into general types based on their temperature. Temperature
is chosen because the color of a star depends on the temperature and color is a easily seen characteristic,
regardless of the distance.
However, using color as a temperature probe gives only a crude measurement of the star's temperature.
Astronomers use another method of determining the temperature more accurately. It uses the strength of
different absorption lines in a star's spectrum. Once astronomers developed this method, they began to
look for correlations of temperature with other quantities such as mass, size, and luminosity in the hope
that the underlying physical principles of stars could be understood. But are the stars you easily see from
Earth typical of other stars in other parts of the universe? You will see how that important question can
be answered.
Temperature Dependence of Absorption Lines
The strength and pattern of the absorption lines does vary among the stars. Some stars have strong (dark)
hydrogen lines, other stars have no hydrogen lines but strong calcium and sodium lines. Are their
abundances different? No. When scientists learned more about the physics of the atom, they discovered
that the temperature of the star's photosphere determines what pattern of lines you will see. Because of
this, you can determine the temperature of a star from what pattern of absorption lines you see and their
strength. As a way to check this, the spectra from all of the gas clouds from which stars form show
approximately the same abundances everywhere.
Measuring the strength of the hydrogen absorption lines is usually the first step for determining a star's
temperature. If the star is too hot or too cold, the hydrogen lines will be weak. To produce strong, dark
hydrogen lines, the star's temperature must be within a certain range. To produce a hydrogen absorption
line in the visible (optical) band of the electromagnetic spectrum, the atom's electron must be in the
second energy level when it absorbs a photon.
If the hydrogen atoms are heated to high temperatures, the atomic collisions can ionize the hydrogen
atoms. If there are no electrons bound to the nuclei, there are no hydrogen absorption lines. If the star's
temperature is too low, then there are few electrons in the second energy level. Most of the electrons are
in the ground state because there are not that many atomic collisions.
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Properties of Stars
Hydrogen lines will be strong for temperatures = 4,000 to 12,000 K. Helium atoms hang onto their
electrons more strongly and, therefore, require higher temperatures of 15,000 to 30,000 K to produce
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Properties of Stars
absorption lines in the visible band. Calcium atoms have a looser hold on their electrons so calcium lines
are strong for cooler temperatures of 3000 to 6000 K. The strengths of each element's absorption lines are
sensitive to temperature. Cross-referencing each elements' line strengths gives an accurate temperature
with an uncertainty of only 20 to 50 K. This technique is the most accurate way to measure the
temperature of a star.
A star's temperature found from the continuous spectrum is not as accurate. One reason for this is that
some stars have the peaks of their continuous spectrum outside of the visible band so you cannot use
Wien's law (see the Wien's Law section) to determine the temperature. Also, stars are not perfect thermal
radiators, so the continuum spectrum (Wien's law) gives only a rough temperature (within a few hundred
Kelvin). The spectral lines seen for different types of stars are summarized in the Main Sequence Star
Properties table below.
Spectral Types
Stars are divided into groups called spectral types which are based on the strength of the hydrogen
absorption lines. The A-type stars have the strongest (darkest) hydrogen lines, B-type next strongest,
F-type next, etc. Originally there was the whole alphabet of types, based on hydrogen line strengths, but
then astronomers discovered that the line strengths depended on the temperature. Also, the figure above
shows that more than just the hydrogen lines must be used.
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After some rearranging and merging of some classes, the class sequence is now OBAFGKM when
ordered by temperature. The O-type stars are the hottest stars and the M-type stars are the coolest. Each
class is subdivided into 10 intervals, e.g., G2 or F5, with 0 hotter than 1, 1 hotter than 2, etc. About 90%
of the stars are called main sequence stars. The other 10% are either red giants, supergiants, white
dwarfs, proto-stars, neutron stars, or black holes. The characteristics of these types of stars will be
explored in the following chapters. The table below gives some basic characteristics of the different
spectral classes of main sequence stars. Notice the trends in the table: as the temperature of the main
sequence star increases, the mass and size increase. Also, because of the relation between luminosity and
the size and temperature of a star, hotter main sequence stars are more luminous than cooler main
sequence stars. However, there are limits to how hot a star will be, or how massive and large it can be.
Understanding why the constraints exist is the key to understanding how stars work.
Class M*/Msun
Color
bluest
bluish
blue-white
white
yellow-white
orange
red
O
B
A
F
G
K
M
20 - 100
4 - 20
2-4
1.05 - 2
0.8 - 1.05
0.5 - 0.8
0.08 - 0.5
Main Sequence Star Properties
M*/Msun Temperature
12 - 25
4 - 12
1.5 - 4
1.1 - 1.5
0.85 - 1.1
0.6 - 0.85
0.1 - 0.6
40,000
18,000
10,000
7,000
5,500
4,000
3,000
Prominent Lines
ionized helium
neutral helium, neutral hydrogen
neutral hydrogen
neutral hydrogen, ionized calcium
neutral hydrogen, strongest ionized calcium
neutral metals (calcium, iron), ionized calcium
molecules and neutral metals
Red giants can get up to about 50 times the size of the Sun. Supergiants are between 20 times the size of
the Sun for the BO supergiants and 1000 times the size of the Sun for the M0 supergiants. Despite the
tremendous size of some stars, even the largest supergiant is only 1/7000 light years across. Since stars
are several light years from each other, they do not collide with each other (even the fat ones!).
Vocabulary
main sequence
spectral type
Review Questions
1. What is the main reason why some stars have strong (dark) hydrogen lines and others have weak
(light) H lines?
2. Why do very hot stars have no hydrogen lines?
3. Why do very cool stars have no hydrogen lines?
4. What is the grouping of stars by spectral type based on?
5. A star of spectral type A has the strongest hydrogen lines. What is its temperature?
6. Two stars have equal strengths of their hydrogen lines. Star A has lines from helium present while
star B has lines of ionized calcium present. Which star is hotter? Explain your reasoning.
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7. What are two reasons why determining a star's temperature from Wien's law (see the
electromagnetic radiation chapter) is usually not as accurate as using the spectral lines?
8. What are the 7 basic spectral types in order of temperature (hottest to coldest)?
9. If our Sun has a surface temperature of 5840 K, how many times hotter than the Sun is the hottest
O-type star? How many times cooler than the Sun is the coolest M-type star?
10. What fraction of the stars are main sequence stars?
11. What is the range of temperatures found on the surface of main sequence stars?
12. What is the range of luminosities produced by main sequence stars? Compare them to the Sun
(Watts are ridiculously small energy units to use).
13. What is the range of diameters for main sequence stars? Compare them to the Sun (miles and
kilometers are ridiculously small length units to use). Red giants, supergiants, white dwarfs are not
main sequence stars.
14. What is the trend in the stellar diameters vs. temperature for main sequence stars? (As temperature
increases, the diameter _________.)
15. What is the trend in the stellar luminosities vs. temperature for main sequence stars? (As
temperature increases, the luminosity _________.)
16. What is the likelihood that even the largest supergiant stars will run into another star (of any size)?
17. What is the range of stellar masses for main sequence stars? Compare them to the Sun (pounds and
kilograms are ridiculously small mass units to use).
18. What is the trend in the stellar masses vs. temperature for main sequence stars? (As temperature
increases, the mass _________.)
19. What is the trend in the stellar masses vs. luminosity for main sequence stars? (As luminosity
increases, the mass _________.)
Hertzsprung-Russell Diagram
In order to better understand how stars are constructed, astronomers look for correlations between stellar
properties. The easiest way to do this is make a plot of one intrinsic property vs. another intrinsic
property. An intrinsic property is one that does not depend on the distance the star is from the Earth (e.g.,
temperature, mass, diameter, composition, and luminosity). By the beginning of the 20th century,
astronomers understood how to measure these intrinsic properties. In 1912, two astronomers,
Hertzsprung and Russell, independently found a surprising correlation between temperature (color) and
luminosity (absolute magnitude) for 90% of the stars. These stars lie along a narrow diagonal band in the
diagram called the main sequence. This plot of luminosity vs. temperature is called the
Hertzsprung-Russell diagram or just H-R diagram for short.
Before this discovery astronomers thought that it was just as easy for nature to make a hot dim star as a
hot luminous star or a cool luminous one or whatever other combination you want. But nature prefers to
make particular kinds of stars. Understanding why enables you to determine the rules nature follows. A
correlation between mass and luminosity is also seen for main sequence stars: Luminosity = Mass3.5 in
solar units. The hot, luminous O-type stars are more massive than the cool, dim M-type stars. The
mass-luminosity relationship tells about the structure of stars and how they produce their energy. This
will be explored further in the next chapter.
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The H-R diagram is also called a color-magnitude diagram because the absolute magnitude is usually
plotted vs. the color. The H-R diagram below is for all stars visible to the naked eye (down to apparent
magnitude = +5) plus all stars within 25 parsecs. Luminous stars are easier to observe because they can
be seen from great distances away but they are rarer in the galaxy. They tend to reside in the top half of
the H-R diagram. Faint stars are harder to see but are more common in the galaxy. They tend to reside in
the bottom half of the H-R diagram.
Spectroscopic Parallax
You can use the correlation between luminosity and temperature (spectral type) for main sequence stars
to get their distances. This method is called spectroscopic parallax because a distance is found from
knowledge of a star's spectral type. Distances for stars too far away to show a detectable trigonometric
parallax are found this way. Here are the steps you use to find a star's distance using the spectroscopic
parallax method:
1. Determine the star's spectral type from spectroscopy and measure the star's apparent brightness
(flux).
2. Use a calibrated main sequence to get the star's luminosity. The Hyades cluster in the Taurus
constellation is the standard calibrator.
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3. Use the Inverse Square Law for Brightness to get the distance: unknown distance = calibrator
distance × Sqrt[calibrator flux/unknown star's flux.]
How do you do that?
A G2 star appears 25 times dimmer than it would if it was at the standard distance of 10 parsecs used
for the absolute magnitude. The G2 star is at a distance of = 10 × Sqrt[1/(1/25)] = 10 × Sqrt[25/1] = 50
parsecs from us.
Distances to red giant and supergiant stars are found in a similar way but you need to investigate their
spectra more closely to see if they are the very large stars you think they are. Their position in the
calibrated H-R diagram is found and their apparent brightness gives you the distance. Also, this process
can be used to find the distance of an entire cluster. The entire color-magnitude diagram for the cluster is
compared with a calibration cluster's color-magnitude diagram. The calibration cluster is a known
distance away. Some adjustments for the cluster's age and composition differences between the stars in
the cluster and the calibration cluster must be made. Such fine-tuning adjustments are called
``main-sequence fitting''.
What is a ``Typical'' Star?
The Sun is often said to be an ``average'' or ``typical'' middle-aged star. What is ``average'' depends on
how you choose your sample!
1. Compared to the nearby stars, the Sun is luminous, hot, and big.
2. Compared to the apparently bright stars, the Sun is dim, cool, and small.
3. Compared to the stars in globular clusters, the Sun is very young.
4. Compared to the stars in open (galactic) clusters, the Sun is very old.
If you picked stars at random from our galaxy, what would they tend to look like? How the stars are
selected can give you very different answers of what a typical star is like. The figure below shows where
the 100 apparently brightest stars in our sky would be plotted and where the 100 nearest stars would be
plotted on the H-R diagram. Both data sets are from the recently released Hipparcos survey. The stars
that appear bright in our sky also are intrinsically luminous for the most part. They are the diamonds in
the diagram. The near stars are all within 7.63 parsecs of the Sun. They are plotted with the upside-down
triangles. A great majority of the near stars are cool and faint.
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Another way to compare them is to plot the proportions of the spectral types for each group. As shown in
the figure below, most of the apparently bright stars are the hot and luminous A and B-type stars. The
sample includes a few of the very hot O-type stars. All but one of the K-type stars in the bright star
sample are giants or supergiant stars. All of the M-type stars are giants or supergiants.
The graph for the near star sample looks very different: the majority of stars are the cool and faint K and
M-type stars. Only one star in the entire sample is a giant star. The rest are main sequence stars.
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Which of these samples is more representative of the entire population of stars in our galaxy? A
representative sample includes all parts of the population of the objects your are investigating in their
proper proportions. The relative proportion of common things will be greater than the relative
proportions of rare things. In fact, the uncommon things may not be found in a small representative
sample because they are so rare!
A poorly selected sample that is unrepresentative of the larger set can lead to biased results. Such biases
can be found in any sample of objects or people. Public officials and politicians who base their decisions
on what the polls say people believe or think about different issues, are usually working with biased
samples of opinions. The pollsters will interview between 1000 to 2000 people across the nation and
from that set, they get an idea of what the entire nation of several hundred million people believe. They
get accurate results only if they have a sample of people that properly represents the entire population. It
is extremely difficult (if not impossible) to get a representative sample for political polls. The situation
for astronomy is easier and standard statistical methods can be used to find a representative sample of
stars.
In our example of the types of stars, the bright star sample is very biased. The average distance between
each star in the bright star sample is about 20 times greater than the average distance between each star in
the near star sample. This gives us a rough idea of how spread out the luminous stars and faint stars---the
luminous stars are much more spread out than the cool faint stars. Therefore, in a given volume of space,
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there will be many more cool faint stars than luminous stars. The faint stars cannot be seen from the great
distances the luminous stars are seen, so a sample based on the apparent brightness biases against the
very numerous faint stars.
Vocabulary
color-magnitude diagram
spectroscopic parallax
Hertzsprung-Russell diagram
representative sample
Review Questions
1. How it is known that luminosity and temperature are correlated for about 90% of the stars?
2. Where are luminous and faint stars plotted in the H-R diagram (color-magnitude diagram)? Where
are cool and hot stars plotted?
3. Where are red giants, main sequence stars, and white dwarfs plotted in the H-R diagram?
4. Which main sequence stars are hotter and which are cooler? Which ones are more massive and
which ones are the lightweights?
5. Which main sequence stars are bigger in diameter than others? How can we tell that they are
bigger?
6. What is the relation between stellar luminosity and stellar mass?
7. Which spectral classes are more common than others? How do you know without having to survey
the entire galaxy?
8. Of the two ways of selecting stars, grouping by proximity or by apparent brightness, which gives
you a representative sample of stars? Why is the other way a biased way of selecting stars?
9. If you wanted to find an accurate proportion of the galaxies that are faint and the proportion of the
galaxies that are luminous, should you select all galaxies within a certain volume of space of all
galaxies above a certain apparent brightness? Explain why!
10. Which telescope should you use if you want to get a more accurate proportion of faint stars to
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luminous stars: a 15-centimeter objective telescope or 90-centimeter objective telescope? Explain
why!
Go to Stellar Composition section
Go to Astronomy Notes beginning
Go to Astronomy 1 homepage
last update: 03 March 1999
Nick Strobel -- Email: [email protected]
(661) 395-4526
Bakersfield College
Physical Science Dept.
1801 Panorama Drive
Bakersfield, CA 93305-1219
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