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1
Note that the following lectures include
animations and PowerPoint effects such as fly ins
and transitions that require you to be in
PowerPoint's Slide Show mode (presentation mode).
2
The Family of Stars

• Chapter 9

3
Guidepost
Science is based on measurement, but measurement
in astronomy is very difficult. Even with the
powerful modern telescopes described in Chapter
6, it is impossible to measure directly simple
parameters such as the diameter of a star. This
chapter shows how we can use the simple
observations that are possible, combined with the
basic laws of physics, to discover the properties
of stars. With this chapter, we leave our sun
behind and begin our study of the billions of
stars that dot the sky. In a sense, the star is
the basic building block of the universe. If we
hope to understand what the universe is, what our
sun is, what our Earth is, and what we are, we
must understand the stars. In this chapter we
will find out what stars are like. In the
chapters that follow, we will trace the life
stories of the stars from their births to their
deaths.
4
Outline
I. Measuring the Distances to Stars A. The
Surveyor's Method B. The Astronomer's Method C.
Proper Motion II. Intrinsic Brightness A.
Brightness and Distance B. Absolute Visual
Magnitude C. Calculating Absolute Visual
Magnitude D. Luminosity III. The Diameters of
Stars A. Luminosity, Radius, and Temperature B.
The H-R Diagram C. Giants, Supergiants, and
Dwarfs
5
Outline
D. Luminosity Classification E. Spectroscopic
Parallax IV. The Masses of Stars A. Binary
Stars in General B. Calculating the Masses of
Binary Stars C. Visual Binary Systems D.
Spectroscopic Binary Systems E. Eclipsing Binary
Systems V. A Survey of the Stars A. Mass,
Luminosity, and Density B. Surveying the Stars
6
Light as a Wave (1)
We already know how to determine a stars

• surface temperature

• chemical composition

• surface density

In this chapter, we will learn how we can
determine its

• distance

• luminosity

• radius

• mass

and how all the different types of stars make up
the big family of stars.
7
Distances to Stars
d in parsec (pc) p in arc seconds
__
1
d
p
Trigonometric Parallax
Star appears slightly shifted from different
positions of the Earth on its orbit
1 pc 3.26 LY
The farther away the star is (larger d), the
smaller the parallax angle p.
8
The Trigonometric Parallax
Example Nearest star, a Centauri, has a parallax
of p 0.76 arc seconds
d 1/p 1.3 pc 4.3 LY
With ground-based telescopes, we can measure
parallaxes p 0.02 arc sec gt d 50 pc
This method does not work for stars farther away
than 50 pc.
9
Proper Motion
In addition to the periodic back-and-forth motion
related to the trigonometric parallax, nearby
stars also show continuous motions across the sky.
These are related to the actual motion of the
stars throughout the Milky Way, and are called
proper motion.
10
Intrinsic Brightness/ Absolute Magnitude
The more distant a light source is, the fainter
it appears.
11
Brightness and Distance
(SLIDESHOW MODE ONLY)
12
Intrinsic Brightness / Absolute Magnitude (2)
More quantitatively The flux received from the
light is proportional to its intrinsic brightness
or luminosity (L) and inversely proportional to
the square of the distance (d)
L
__
F
d2
Star A
Star B
Earth
Both stars may appear equally bright, although
star A is intrinsically much brighter than star B.
13
Distance and Intrinsic Brightness
Example
Recall that
Betelgeuse
App. Magn. mV 0.41
Rigel
For a magnitude difference of 0.41 0.14 0.27,
we find an intensity ratio of (2.512)0.27 1.28
App. Magn. mV 0.14
14
Distance and Intrinsic Brightness (2)
Rigel is appears 1.28 times brighter than
Betelgeuse,
Betelgeuse
But Rigel is 1.6 times further away than
Betelgeuse
Thus, Rigel is actually (intrinsically)
1.28(1.6)2 3.3 times brighter than Betelgeuse.
Rigel
15
Absolute Magnitude
To characterize a stars intrinsic brightness,
define Absolute Magnitude (MV)
Absolute Magnitude Magnitude that a star would
have if it were at a distance of 10 pc.
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Absolute Magnitude (2)
Back to our example of Betelgeuse and Rigel
Betelgeuse
Rigel
Difference in absolute magnitudes 6.8 5.5
1.3 gt Luminosity ratio (2.512)1.3 3.3
17
The Distance Modulus
If we know a stars absolute magnitude, we can
infer its distance by comparing absolute and
apparent magnitudes
Distance Modulus mV MV -5 5 log10(d pc)
Distance in units of parsec
Equivalent d 10(mV MV 5)/5 pc
18
The Size (Radius) of a Star
We already know flux increases with surface
temperature ( T4) hotter stars are brighter.
But brightness also increases with size
Star B will be brighter than star A.
A
B
Absolute brightness is proportional to radius
squared, L R2.
Quantitatively L 4 p R2 s T4
Surface flux due to a blackbody spectrum
Surface area of the star
19
Example Star Radii
Polaris has just about the same spectral type
(and thus surface temperature) as our sun, but it
is 10,000 times brighter than our sun.
Thus, Polaris is 100 times larger than the sun.
This causes its luminosity to be 1002 10,000
times more than our suns.
20
Organizing the Family of Stars The
Hertzsprung-Russell Diagram
We know Stars have different temperatures,
different luminosities, and different sizes.
To bring some order into that zoo of different
types of stars organize them in a diagram of
Luminosity
Temperature (or spectral type)
versus
Absolute mag.
Hertzsprung-Russell Diagram
Luminosity
or
Temperature
Spectral type O B A F G K M
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The Hertzsprung-Russell Diagram
Most stars are found along the Main Sequence
22
The Hertzsprung-Russell Diagram (2)
Same temperature, but much brighter than MS stars
? Must be much larger
Stars spend most of their active life time on the
Main Sequence (MS).
? Giant Stars
Same temp., but fainter ? Dwarfs
23
The Radii of Stars in the Hertzsprung-Russell
Diagram
Rigel
Betelgeuse
10,000 times the suns radius
Polaris
100 times the suns radius
Sun
As large as the sun
100 times smaller than the sun
24
Luminosity Classes
Ia Bright Supergiants
Ia
Ib
Ib Supergiants
II
II Bright Giants
III
III Giants
IV Subgiants
IV
V
V Main-Sequence Stars
25
Example Luminosity Classes

• Our Sun G2 star on the Main Sequence G2V
• Polaris G2 star with Supergiant luminosity G2Ib

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Spectral Lines of Giants
Pressure and density in the atmospheres of giants
are lower than in main sequence stars.
gt Absorption lines in spectra of giants and
supergiants are narrower than in main sequence
stars
gt From the line widths, we can estimate the size
and luminosity of a star.
? Distance estimate (spectroscopic parallax)
27
Binary Stars
More than 50 of all stars in our Milky Way are
not single stars, but belong to binaries
Pairs or multiple systems of stars which orbit
their common center of mass.
If we can measure and understand their orbital
motion, we can estimate the stellar masses.
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The Center of Mass
center of mass balance point of the system.
Both masses equal gt center of mass is in the
middle, rA rB.
The more unequal the masses are, the more it
shifts toward the more massive star.
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Center of Mass
(SLIDESHOW MODE ONLY)
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Estimating Stellar Masses
Recall Keplers 3rd Law Py2 aAU3
Valid for the Solar system star with 1 solar
mass in the center.
We find almost the same law for binary stars with
masses MA and MB different from 1 solar mass
aAU3
____
MA MB
Py2
(MA and MB in units of solar masses)
31
Examples Estimating Mass
a) Binary system with period of P 32 years and
separation of a 16 AU
163
____
MA MB 4 solar masses.
322
b) Any binary system with a combination of period
P and separation a that obeys Keplers 3. Law
must have a total mass of 1 solar mass.
32
Visual Binaries
The ideal case
Both stars can be seen directly, and their
separation and relative motion can be followed
directly.
33
Spectroscopic Binaries
Usually, binary separation a can not be measured
directly because the stars are too close to each
other.
A limit on the separation and thus the masses can
be inferred in the most common case
Spectroscopic Binaries
34
Spectroscopic Binaries (2)
The approaching star produces blue shifted lines
the receding star produces red shifted lines in
the spectrum.
Doppler shift ? Measurement of radial velocities
? Estimate of separation a
? Estimate of masses
35
Spectroscopic Binaries (3)
Typical sequence of spectra from a spectroscopic
binary system
Time
36
Eclipsing Binaries
Usually, inclination angle of binary systems is
unknown ? uncertainty in mass estimates.
Special case Eclipsing Binaries
Here, we know that we are looking at the system
edge-on!
37
Eclipsing Binaries (2)
Peculiar double-dip light curve
Example VW Cephei
38
Eclipsing Binaries (3)
Example Algol in the constellation of Perseus
From the light curve of Algol, we can infer that
the system contains two stars of very different
surface temperature, orbiting in a slightly
inclined plane.
39
The Light Curve of Algol
40
Masses of Stars in the Hertzsprung-Russell Diagram
The higher a stars mass, the more luminous
(brighter) it is
Masses in units of solar masses
40
L M3.5
18
High-mass stars have much shorter lives than
low-mass stars
High masses
6
3
1.7
tlife M-2.5
1.0
Mass
0.8
0.5
Sun 10 billion yr.
Low masses
10 Msun 30 million yr.
0.1 Msun 3 trillion yr.
41
Maximum Masses of Main-Sequence Stars
Mmax 50 - 100 solar masses
a) More massive clouds fragment into smaller
pieces during star formation.
b) Very massive stars lose mass in strong stellar
winds
h Carinae
Example h Carinae Binary system of a 60 Msun
and 70 Msun star. Dramatic mass loss major
eruption in 1843 created double lobes.
42
Minimum Mass of Main-Sequence Stars
Mmin 0.08 Msun
At masses below 0.08 Msun, stellar progenitors do
not get hot enough to ignite thermonuclear fusion.
Gliese 229B
? Brown Dwarfs
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Surveys of Stars
Ideal situation
Determine properties of all stars within a
certain volume.
Problem
Fainter stars are hard to observe we might be
biased towards the more luminous stars.
44
A Census of the Stars
Faint, red dwarfs (low mass) are the most common
stars.
Bright, hot, blue main-sequence stars (high-mass)
are very rare
Giants and supergiants are extremely rare.
45
New Terms
stellar parallax (p) parsec (pc) proper
motion flux absolute visual magnitude
(Mv) magnitudedistance formula distance modulus
(mv Mv) luminosity (L) absolute bolometric
magnitude HR (HertzsprungRussell) diagram main
sequence giants supergiants
red dwarf white dwarf luminosity
class spectroscopic parallax binary stars visual
binary system spectroscopic binary
system eclipsing binary system light
curve massluminosity relation  
46
Discussion Questions
1. If someone asked you to compile a list of the
nearest stars to the sun based on your own
observations, what measurements would you make,
and how would you analyze them to detect nearby
stars? 2. The sun is sometimes described as an
average star. What is the average star really
like?
47
Quiz Questions
1. The parallax angle of a star and the two lines
of sight to the star from Earth form a long
skinny triangle with a short side of a. 1000
km. b. 1 Earth diameter. c. 1 AU. d. 2 AU. e. 40
AU.
48
Quiz Questions
2. What is the distance to a star that has a
parallax angle of 0.5 arc seconds? a. Half a
parsec. b. One parsec. c. Two parsecs. d. Five
parsecs. e. Ten parsecs.
49
Quiz Questions
3. Why can smaller parallax angles be measured by
telescopes in Earth orbit? a. Telescopes
orbiting Earth are closer to the stars. b.
Earth's atmosphere does not limit a telescope's
resolving power. c. Earth's atmosphere does not
limit a telescope's light gathering power. d.
Earth's atmosphere does not limit a telescope's
magnifying power. e. They can be connected to
Earth-based telescopes to do interferometry.
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Quiz Questions
4. At what distance must a star be to have its
apparent magnitude equal to its absolute
magnitude? a. One AU. b. Ten AU. c. One
parsec. d. Ten parsecs. e. One Megaparsec.
51
Quiz Questions
5. Which magnitude gives the most information
about the physical nature of a star? a. The
apparent visual magnitude. b. The apparent
bolometric magnitude. c. The absolute visual
magnitude. d. The absolute bolometric
magnitude. e. None of the above tells us anything
about the physical nature of a star.
52
Quiz Questions
6. For which stars does absolute visual magnitude
differ least from absolute bolometric
magnitude? a. Low surface temperature stars. b.
Medium surface temperature stars. c. High surface
temperature stars. d. Stars closer than 10
parsecs. e. Stars farther away than 10 parsecs.
53
Quiz Questions
7. The absolute magnitude of any star is equal to
its apparent magnitude at a distance of 10
parsecs. Use this definition, how light
intensity changes with distance, and how the
stellar magnitude system is set up to determine
the following. If a star's apparent visual
magnitude is less than its absolute visual
magnitude, which of the following is correct? a.
The distance to the star is less than 10 parsecs.
b. The distance to the star is 10 parsecs. c.
The distance to the star is greater than 10
parsecs. d. Its bolometric magnitude is greater
than its visual magnitude. e. Its bolometric
magnitude is less than its visual magnitude.
54
Quiz Questions
8. What is the distance to a star that has an
apparent visual magnitude of 3.5 and an absolute
visual magnitude of -1.5? a. 100 parsecs. b. 50
parsecs. c. 25 parsecs. d. 10 parsecs. e. 5
parsecs.
55
Quiz Questions
9. What is the luminosity of a star that has an
absolute bolometric magnitude that is 10
magnitudes brighter than the Sun (-5.3 for the
star and 4.7 for the Sun)? a. 1 solar
luminosity. b. 10 solar luminosities. c. 100
solar luminosities d. 1000 solar luminosities. e.
10000 solar luminosities.
56
Quiz Questions
10. How can a cool star be more luminous than a
hot star? a. It can be more luminous if it is
larger. b. It can be more luminous if it is more
dense. c. It can be more luminous if it is closer
to Earth. d. It can be more luminous if it is
farther from Earth. e. A cool star cannot be more
luminous than a hot star.
57
Quiz Questions
11. A star has one-half the surface temperature
of the Sun, and is four times larger than the Sun
in radius. What is the star's luminosity? a. 64
solar luminosities. b. 16 solar luminosities. c.
4 solar luminosities. d. 2 solar luminosities. e.
1 solar luminosity.
58
Quiz Questions
12. The Sun's spectral type is G2. What is the
Sun's luminosity class? a. Bright Supergiant
(Ia) b. Supergiant (Ib) c. Bright Giant (II) d.
Giant (III) e. Main Sequence (V)
59
Quiz Questions
13. A particular star with the same spectral type
as the Sun (G2) has a luminosity of 50 solar
luminosities. What does this tell you about the
star? a. It must be larger than the Sun. b. It
must be smaller than the Sun. c. It must be
within 1000 parsecs of the Sun. d. It must be
farther away than 1000 parsecs. e. Both a and b
above.
60
Quiz Questions
14. In addition to the H-R diagram, what other
information is needed to find the distance to a
star whose parallax angle is not measurable? a.
The star's spectral type. b. The star's
luminosity class. c. The star's surface
activity. d. Both a and b above. e. All of the
above.
61
Quiz Questions
15. What is the radius and luminosity of a star
that is classified as G2 III? a. About 0.1 solar
radii and 0.001 solar luminosities. b. About 1
solar radii and 1 solar luminosity. c. About 10
solar radii and 100 solar luminosity. d. About
100 solar radii and 10,000 solar luminosities. e.
About 1000 solar radii and 1,000,000 solar
luminosities.
62
Quiz Questions
16. For a particular binary star system star B is
observed to always be four times as far away from
the center of mass as star A. What does this
tell you about the masses of these two stars? a.
The total mass of these two stars is four solar
masses. b. The total mass of these two stars is
five solar masses. c. The ratio of star A's mass
to star B's mass is four to one. d. The ratio of
star B's mass to star A's mass is four to one. e.
Both b and c above.
63
Quiz Questions
17. For a particular binary star system the ratio
of the mass of star A to star B is 4 to 1. The
semimajor axis of the system is 10 AU and the
period of the orbits is 10 years. What are the
individual masses of star A and star B? a. Star
A is 1 solar mass and star B is 4 solar
masses. b. Star A is 4 solar masses and star B is
1 solar mass. c. Star A is 2 solar masses and
star B is 8 solar masses. d. Star A is 8 solar
masses and star B is 2 solar masses. e. None of
the above.
64
Quiz Questions
18. To which luminosity class does the
mass-luminosity relationship apply? a. The
Supergiants. b. The Giants. c. The Subgiants. d.
The Main Sequence. e. The mass-luminosity
relationship applies to all luminosity classes.
65
Quiz Questions
19. Which luminosity class has stars of the
lowest density, some even less dense than air at
sea level? a. The Supergiant. b. The Bright
Giant. c. The Giant. d. The Subgiant. e. The Main
Sequence.
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Quiz Questions
20. In a given volume of space the Red Dwarf (or
lower main sequence) stars are the most abundant,
however, on many H-R diagrams very few of these
stars are plotted. Why? a. Photographic film and
CCDs both have low sensitivity to low-energy red
photons. b. They are so very distant that
parallax angles cannot be measured, thus
distances and absolute magnitudes are difficult
to determine precisely. c. They have so many
molecular bands in their spectra that they are
often mistaken for higher temperature spectral
types. d. They have very low luminosity and are
difficult to detect, even when nearby. e. Most
of them have merged to form upper main sequence
stars.
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Answers
1. c 2. c 3. b 4. d 5. d 6. b 7. a 8. a 9. e 10. a
11. e 12. e 13. a 14. d 15. c 16. c 17. d 18. d 19
. a 20. d