Stars
The Pleiades Star Cluster
about 400 light years away
• Stars are very far away.
• The nearest star is over
270,000 AU away! (Pluto is 39
AU from the Sun)
• That is equal to 25 trillion
miles!
• At this distance it takes light
4.3 years to travel from this
star. In other words the star is
4.3 light years away.
• The space shuttle travels
17,500 miles/hour, at this
speed it would take over
160,000 years to get to the
nearest star!
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How Do We Know the Distance to the Stars?
Using the size of the shift due to
parallax and knowing the distance
from the Earth to the Sun we can
find the distance to nearby stars.
• The ancient Greeks
realized that if the Earth
moved we should see
shifts in the positions of
the stars over one year.
• We do see these shifts
in star positions but
they are very,very
small.
• This shift in an object’s
position due to the
motion of the observer
is called parallax.
• The farther an object
the smaller the shift and
the harder it is to find
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its distance.
How Do We Know Anything About Stars?
• Since stars are so far away they
almost always appear just as
points of light.
• But as we already know we can
learn a lot from light!
• Light can tell us about a star’s:
–
–
–
–
–
The Trapezium Star Cluster
in the Orion Nebula
about 1500 light years away
surface temperature
distance
motion
rotation
composition
• and if the star is part of binary
star system we can determine its
mass.
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Luminosity
• Luminosity is the amount of
energy a body radiates each
second.
• Stars appear brighter or dimmer to
us for two reasons:
– they are at various distances from us
and
– some stars are naturally more
luminous than other stars
Large stars have a higher
luminosity than small stars.
Hot stars have a higher
luminosity than cool stars.
• If we know a stars distance and we
measure its apparent brightness we
can determine its luminosity.
• A stars luminosity is related to both
its temperature and its radius.
• So if we also know a star’s
temperature we can determine its
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radius.
Luminosity
For stars with the same temperature,
larger stars are more luminous.
For stars with the same radius,
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hotter stars are more luminous.
The Inverse-Square Law
• The inverse-square law
(IS) is:
L
B
2
4 d
• B is the brightness at a
distance d from a source
of luminosity L
• This relationship is
called the inversesquare law because the
distance appears in the
denominator as a square
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Stellar Spectra
• The temperature of a star can
be determined two ways.
– from Wien’s law
– from the presence or absence of
certain spectral lines.
A) A spectrum from a star hotter than the
Sun with strong Hydrogen lines.
B) A spectrum from a star like our Sun.
C) A spectrum from a star cooler
than our Sun.
• Strong Hydrogen lines are
only seen in stars that have
surface temperatures between
8,000 and 15,000 Kelvin.
• The Sun does not show strong
Hydrogen lines even though it
is more than 70% Hydrogen!
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Spectral Classification
Annie Jump Cannon
1863 - 1941
• To understand the properties of stars
astronomers gathered hundreds of
thousands of stellar spectra.
• To understand the patterns they saw
they developed spectral classification
systems in order to help understand
the nature of stars.
• The first system was developed in
1866 by Pietro Angelo Secchi an
Italian priest and scientist. He
grouped stars by their color.
• The system used today was
developed by Annie Jump Cannon
who ordered stars by temperature.
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Spectral Classes
In order from hottest to coldest stars
the letter classification is
O, B, A, F, G, K, M
In this system our Sun is a G star.
• In 1901 Cannon
developed a system
where letters were
assigned to stars of
different temperature.
• In the 1920’s another
astronomer Cecilia
Payne explained why
spectral lines change
with temperature and
confirmed the system
that Cannon
developed.
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Measuring a Star’s Composition
• To find the quantity of a given atom in the star, we
use the darkness of the absorption line
• This technique of determining composition and
abundance can be tricky!
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Measuring a Star’s Composition
• Possible overlap of absorption lines from
several varieties of atoms being present
• Temperature can also affect how strong (dark)
an absorption line is
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Example: Measuring the Radius of Sirius
• Solving for a star’s radius can be simplified if
we apply L = 4R2sT4 to both the star and the
Sun, divide the two equations, and solve for
radius:
1
2
2
Rs  Ls   Ts 
   
R  L   T 
• Where s refers to the star and  refers to the
Sun
• Given for Sirius Ls = 25L, Ts = 10,000 K,
and for the Sun T= 6000 K, one finds Rs =
12
1.8R
Binary Stars
The two stars of a binary star
system orbit around their
common center of mass.
Using Newton’s modified form
of Kepler’s 3rd Law the mass
of the stars can be found.
• Most stars in the sky
actually exist as part of a
group of 2 or more stars.
• Two stars gravitationally
bound are called binary
stars.
• Binary stars provide a
means of determining the
masses of stars.
• Other properties can also
sometimes be determined
from binary stars.
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Types of Binary Stars
Example
of a visual
binary
Example of a spectroscopic binary
• If both stars in a
binary star system are
visible this is a visual
binary. The motion
of the two stars can be
observed directly.
• Sometimes only one
point of light is seen
but the spectra of this
star shows two sets of
lines. This is a
spectroscopic
binary. The motion
of the two stars can
found from the
Doppler shift of the
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lines.
Eclipsing Binaries
• When the orbit of a
binary is viewed
edge-on from Earth
the stars may
actually eclipse one
another. This is an
eclipsing binary.
• Eclipsing binaries
can give
information on the
radius, mass and
shape of the stars.
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Summary of Measurement Methods
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The Hertzprung-Russell Diagram
or The H-R Diagram
• The H-R diagram puts into
one figure many of the
properties of stars already
discussed.
• Where a star is located on
this diagram depends on
– its luminosity and
– its spectral class or
temperature
• Stars tend to show up in
distinct groups when
plotted in this way.
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Main Sequence, Giants and Dwarfs
• Nearly 90% of the stars lie
along a line on the H-R
diagram called the Main
Sequence.
• Those stars in the upper
right of the figure are very
luminous but also very
cool. Therefore they must
be very large. These are
the Red Giant stars.
• Those stars in the lower
left are very hot but have
low luminosity. They must
be very small. These are
Betelgeuse is almost as big as the orbit White Dwarf stars.
of Jupiter. Sirius B is as small as Earth.
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The Mass of Stars on the Main Sequence
• Where stars are located
along the Main Sequence
depends almost
exclusively on the star’s
mass.
• More massive stars are
more luminous, they
release energy at a higher
rate and are located
towards the upper left of
the Main Sequence. (They
also consume Hydrogen
much faster).
• Less massive stars are
located at the lower right.
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The Mass-Luminosity Relation
• Main-sequence stars obey
a mass-luminosity
relation, approximately
given by:
LM
3
• L and M are measured in
solar units
• Consequence: Stars at top
of main-sequence are
more massive than stars
lower down
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Luminosity Classes
• Another method was discovered to measure the
luminosity of a star (other than using a star’s
apparent magnitude and the inverse square law)
– It was noticed that some stars had very narrow
absorption lines compared to other stars of the
same temperature
– It was also noticed that luminous stars had
narrower lines than less luminous stars
• Width of absorption line depends on density:
wide for high density, narrow for low density
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Luminosity Classes
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Luminosity Classes
• Luminous stars (in upper right
of H-R diagram) tend to be less
dense, hence narrow absorption
lines
• H-R diagram broken into
luminosity classes: Ia (bright
supergiant), Ib (supergiants),
II (bright giants), III (giants),
IV (subgiants), V (main
sequence)
– Star classification example: The
Sun is G2V
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Luminosity Class as Distance
Estimator
• Measure spectral line widths to get
Luminosity Class  yields luminosity of
the star
• Use inverse-square rule to find distance to a
star from its luminosity and measured
brightness.
• Useful for stars that are beyond the reach of
the parallax method.
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Summary of the HR Diagram
• Most stars lie on the main
sequence
– Of these, the hottest stars
are blue and more
luminous, while the coolest
stars are red and dim
– Star’s position on sequence
determines its mass, being
more near the top of the
sequence
• Three classes of stars:
– Main-sequence
– Giants
– White dwarfs
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Summary
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