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Lecture 16 Review
Spectra
An early scheme to class stars was by strength of the hydrogen absorption lines,
thus, A,B,C,... → weaker lines.
A later scheme, called the B-V Index, classed stars according to a logarithmic ratio
of the peak amount of radiation in the blue and violet colors.
The current scheme is to class stars according to color in a way which is more or
less logarithmically proportional to temperature. In this scheme stars are
labeled from M (red, cool stars), K, G, F, A, B, O(blue, hot stars) with
subclasses running from 1 to 10. In this scheme the Sun is a G2 type yellow
star. The mnemonic for this sequence is Oh Be A Fine Girl, Kiss Me.
Principle Spectral Classes of Stars
Type
Spectral
Class
Temperature (K)
Source of Prominent
Spectral Lines
Representative Stars
Bluest-hot
O
40,000
Singly Ionized Helium atoms 24.6 eV
Blue
B
18,000
Neutral Helium atoms
Blue-white
A
10,000
Neutral Hydrogen atoms
White
F
7,000
Neutral Hydrogen atoms
Yellow-white
G
5,500
Neutral Hydrogen, ionized Calcium 6.1
eV
Sun
Orange
K
4,000
Neutral metal atoms
Arcturus (
Coolest-red
M
3,000
Molecules and neutral metals
ζ Orionis)
Spica ( α Virginis)
Sirius ( α Canis Majoris)
Procyon ( α Canis Minoris)
Alnitak (
α Bootes)
Antares ( α Scorpii)
Note: This scale is not linear in temperature. It is close to logarithmic.
The following spectra illustrate the visible spectra for O, B, A, F, G, K, and M
stars. The broad white band in each spectrum reflects blackbody radiation
characteristic of each class of star. Tracking upward the blackbody radiation is
peaking at shorter wavelengths, thus, according to Wien’s Law, higher
temperatures.
Stefan-Boltzmann Law
L is the bolometric luminosity. Given the surface area of a star is A = 4BR2, then
L = 4BFR T in Watts or L - R T
2
4
2
4
R
L  Tsun 
⇒
=


R sun
Lsun  T 
2
This equation shows the radius, luminosity, and temperature of a star in
comparison to the Sun.
Example: What is the radius of Sirius, where the temperature, T = 10,000 K, and
luminosity, L = 23 Lsun, are determined from spectrum of Sirius.
From the above equation
⇒ R sirius = R sun
2
23  5700 

 = 1.56 R sun
1  10 ,000 
Doppler Shift
We have discussed Doppler Shift before. Spectra are wavelength shifted
according to whether a star is approaching or receding from the Earth.
∆λ
v
=−
λ
c
From an absorption spectra one can learn about proper motion with respect to the
Earth and infer various things about stellar atmospheres.
Mass
Most stars form in combinations, many of them are binary systems in which
two stars rotate about each other. If one can measure the distance D between the
stars, their distances from the center of rotational mass r1 and r2, and the period of
rotation T, one can write two equations:
center of mass:
m1 r1 = m2 r2
4π 2
Kepler’s 3 Law:
T =
D3
G( m1 + m2 )
These are two equations in two unknowns from which
the individual masses can be determined.
rd
2
Important Observation: Stars with identical spectra usually have the same mass.
Zeeman Effect
Magnetic fields can split a spectroscopic transition line into two lines. The
width of the separation is a measure of the magnetic fields in the stellar atmosphere
where the transitions occur.
12 Basic Properties of Stars and How They are Measured
Property
Method of Measurement
Distance
Luminosity
Temperature
Diameter
Mass
Composition
Magnetic field
Rotation
Atmospheric motions
Atmospheric structure
Circumstellar material
Motion
Trigonometric parallax - 1000 to 2000 nearest stars
Distance combined with apparent brightness
Color or spectra
Luminosity and temperature - Stefan-Boltzmann Law
Measures of binary stars and use of Kepler’s Laws
Spectra - absorption lines, widths, strengths
Spectra, using Zeeman effect
Spectra, using Doppler effect
Spectra, using Doppler effect
Spectra, using opacity effects, limb darkening
Spectra, using absorption lines and Doppler effect
Astrometry or spectra, using Doppler effect
Systematics
How do we find relationships between the stars? First, from the stars near enough
to determine we obtain distance and relative luminosity. Then, using the
procedures outlined above we determine absolute luminosity and radius . From
Doppler shift data on double star systems we can determine masses. Finally, from
spectra we can determine spectral composition. From this information on a subset
of the nearest stars for which these data can be obtained you recognize two
important facts:
1)
Stars have different masses ⇒ different sizes ⇒ different temperatures
⇒ different evolutions ⇒ different evolutionary rates ⇒ different endings
2)
Stars don’t all form at the same time ⇒ we see new and old stars. The Sun is
about 4.6 billion years old, but the Big Bang happened 15 billion years ago.
Stars Within 4 Parsecs
Distance
(pc)
Name
Part
Apparent
Magnitude
Absolute
Magnitude
Spectral
Type
Mass (MSun)
Radius (RSun)
0.0
Sun
Jupiter
A
B
-27
5
G2
1.0
0.001
1.0
0.1
1.3
Alpha Centauri
A
B
C
0
1
11
4
6
15
G2
K0
M5
1.1
0.9
0.1
1.2
0.9
?
1.8
Bernard’s Star
10
13
M5
?
?
2.3
Wolf 359
14
17
M8
?
?
2.5
BD +36o2147
8
10
M2
0.35
?
2.7
L726-8
A
B
12
13
15
16
M6
M6
0.11
0.11
?
?
2.9
Sirius
A
B
-2
8
1
11
A1
A5 Wh Df
2.3
1.0
1.8
0.02
2.9
Ross 154
11
13
M5
?
?
3.1
Ross 248
12
15
M6
?
?
3.2
L789-6
12
15
M6
?
?
3.3
ε Eridani
4
6
K2
0.9
?
3.3
Ross 128
11
14
M5
?
?
3.3
61 Cygni
5
6
8
8
K5
K7
0.63
0.6
?
?
3.4
ε Indi
5
7
K5
?
?
3.5
Procyon
A
B
0
11
3
13
F5
Wh Dwarf
1.8
0.6
1.7
0.01
3.5
Σ
2398
A
B
9
10
11
12
M4
M5
0.4
0.4
?
?
3.5
BD +43o44
A
B
C
8
11
?
10
13
?
M1
M6
K?
?
?
?
?
?
?
3.6
τ Ceti
4
6
G8
?
1.0
3.6
CD -36o15693
7
10
M2
?
?
3.7
o
BD +5 1668
10
?
12
?
M4
?
?
?
?
?
3.7
G51-15
15
17
?
?
?
3.8
L725-32
12
14
M5
?
?
3.8
CD -39o14192
7
9
M0
?
?
3.9
Kapteyn’s Star
9
11
M0
?
?
4.0
Kruger 60
A
B
C
10
11
?
12
13
?
M4
M6
?
0.27
0.16
0.01
0.51
?
?
4.0
Ross 614
A
B
11
15
13
17
M5
?
0.14
0.08
?
?
4.0
BD -12o4523
10
12
M5
?
?
A
B
A
B
Variations Observed
mass
luminosity
surface temperature
radius
0.1 to 60 Solar masses
10-6 to 106 Solar luminosities
a to 10 Solar temperatures
.01 to 100 Solar radii
In Our Neighborhood
1) Most stars are like our sun, a yellowish white G2 star.
2) Most have similar masses.
Hertzsprung and Russell published luminosity versus spectral class information in
1914. They plotted log(luminosity) versus color index, where color index is
roughly proportional to log(temperature). With the exception of a few white
dwarfs, they found that the nearby stars were positioned around a single line called
the main sequence. Roughly 93% of known stars fall on this same line.
What does this say? It says that differences in stellar spectra arise from a single
condition in the stars. This condition is mass. The initial mass of a star says
everything about the life of a star.
Hydrogen burning is the most efficient, lowest temperature energy producer.
Radiation pressure from the thermonuclear fusion of hydrogen atoms prevents the
star from collapsing. Hydrostatic equilibrium occurs when Helmholtz gravitational
contraction equals the outward radiation pressure.
Example: Consider a star with greater mass than the sun
more mass ⇒ more gravitational pressure ⇒ more energetic collisions
⇒ more nuclear interactions ⇒ more radiation to prevent collapse
⇒ higher temperatures ⇒ hotter surface ⇒ faster rate of burning
⇒ shorter lifetime
At the same time
more mass ⇒ higher density ⇒ larger radius ⇒ greater luminosity
What we see in the sky, for the most part, is not the main sequence stars, but the
brightest stars. These stars have evolved from the main sequence. These stars may
be much further away than nearby, more prevalent, main sequence stars, but their
intrinsic luminosity is so great that they are visible over great distances.
17 Brightest Stars in the Sky
Star Name
Apparent
Magnitude
Bolometric
Luminosity (LSun)
Star Type
Radius
(RSun)
Distance
(pc)
Sun
-26.7
1.0
Main sequence
1.0
0.0
Sirius
-1.4
23
Main sequence
1.8
2.7
Canopus
-0.7
1400?
Super giant
30
34
Arcturus
-0.1
115
Red giant
25?
11
Rigel Kent
0.0
1.5
Main sequence
1.1
1.33
Vega
0.0
58?
Main sequence
3?
8.3
Capella
0.1
90?
Red giant
13
14
Rigel
0.1
60,000?
Supergiant
40?
280?
Procyon
0.4
6
Main sequence
2.2
3.5
Achernar
0.5
650?
Main sequence
7?
37
Hadar
0.7
10,000?
Giant
10?
150
Betelgeuse
0.7
10,000
Super Giant
800
160
Altair
0.8
9?
Main sequence
1.5
5
Aldebaran
-.9
125
Red giant
40?
21
Acrux
0.9
2500?
Main sequence
3?
110?
Antares
0.9
9000?
Supergiant
600?
160?
Spica
1.0
2300?
Main sequence
8
84