Stars
All Chapter 9
“The stars are distant and
unobtrusive, but bright and
enduring as our fairest and most
memorable experiences.”
Henry David Thoreau (1849)
Are Stars similar to our Sun?
How far away are they?
Where did they come from?
What do they do?
Do they live forever?
Panorama view of the sky
The Four Basic Parameters of Stars
Luminosity
Size
Mass
Surface
Temperature
To understand the physics of stars, we need to
measures these four parameters and compare
them with the predictions of the theory
However…
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To measure Luminosity I need DISTANCE
All I can really measure is FLUX
FLUX is the amount of energy that hits my
detector. It is not the amount of energy that is
emitted by the source.
Luckily:
 Flux = L / 4pD2
Questions to be addressed
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How may a star’s luminosity be inferred?
How may a star’s Temperature be inferred?
How may a star’s distance be inferred
Parallax as a measure of distance: how does
the parallax of a star depend on its distance?
How may a star’s radius be inferred?
Luminosity
Luminosity is the total amount of power given
off by a star.
-Since it’s a power, Luminosity is measured in Watts
Lsun=3.0x1026 Watt
-For convenience, we often refer to the luminosity of
a star in terms of the luminosity of the Sun.
-Eg,
-“That star has a luminosity of 22LSun”
-“That galaxy has a luminosity of 2x1014LSun ”
Brightness, Distance, and
Luminosity
L=4pD2 B
luminosity
distance
B=L/(4p D2 )
apparent brightness
or flux
Magnitudes and Distance Modulus
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Apparent magnitude:
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Absolute magnitude: M
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m = -2.5 x Log(B) + const
the magnitude you would observe, were the source placed at
10 pc
m – M = -5 + 5 x Log (d)
d = 10(m-M+5)/5
Bolometric magnitude:
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From the flux that includes all wavelengths (not only those in
a given band)
There is a Big Range of Stellar
Luminosities Out there!
Star
Sun
Proxima Centauri
Rigel (Orion)
Deneb (Cygnus)
Luminosity (in units
of solar Luminosity)
1
0.0006
70,000
170,000
Back to the distance: how do we measure it?
Parallax (a.k.a. triangulation)
For getting distances
Using triangulation; requires
1. A baseline (distance over
which observer moves).
2. Measurement of angles to
the object from each end
of the baseline.
3. Mathematical
relationships between
angles and lengths of
sides of triangle. This is
called trigonometry.
Stellar Parallax:
Takes advantage of the fact that Earth orbits the Sun
The measurements are taken six months apart.
The baseline is the diameter of the Earth’s orbit.
What is seen
What is seen
The ½ of the angle between the current location and the
6-month location is called the stellar parallax = P.
Parallax Distance
1 (AU)
D (in Parsecs) =
P (in arcseconds)
P, the parallax angle, is measured in arcseconds
60 arcseconds = 1 arcminute
60 arcminutes = 1 degree
There are 3600 arcseconds in a degree
The larger P, the smaller D
The smaller P, the larger D
1 parsec = 3.26 light years
= 3.086x1016 meter
Parallax would be easier to measure if
1) the stars were further away.
2) Earth's orbit were larger.
3) Earth moved backwards along its orbit.
4) none of these.
Star A has a parallax angle that is twice that
of Star B. What is the relationship between
their distances?
Star A is closer than Star B
 Star B is closer than Star A
 The stars are at the same distance
 Not enough information is given
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How to measure the surface
temperature of a star?
1.
2.
Overall spectral shape (the peak of the
blackbody continuous spectrum)
More accurately, spectroscopically
Spectral Types
For historical reasons,
astronomers classify the
temperatures of stars on a
scale defined by spectral
types, called O B A F G
K M, ranging from the
hottest (type O) to the
coolest (type M) stars.
The sun has a spectral type: G2
Stellar Size
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Stars are very spherical so we characterize a
star’s size by its radius.
R
Stellar Radii vary in size
from ~1500xRSun for a
large Red Giant to
0.008xRSun for a White
Dwarf.
How do we measure the radius of
a star? Except for the Sun, we
don’t! We infer it!
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:
A
Star B will be
brighter than
star A.
B
Absolute brightness is proportional to radius squared, L ~ R2
Quantitatively:
L = 4 p R2 s T4
Surface area of the star
Surface flux due to a
blackbody spectrum
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 sun’s.
Temperature, Luminosity, and Size –
pulling them all together
A star’s luminosity, surface temperature, and size
are all related by the Stefan-Boltzmann Law:
Stefan-Boltzmann Law
L=4πR2 σT4
Luminosity
Stellar
radius
Surface
temperature
In terms of Solar quantities:
L/LSun = (R/RSun)2 x (T/TSun)4
L=4πR2 σT4
Two stars have the same surface temperature, but
the radius of one is 10 times the radius of the other.
The larger star is
1) 10 times more luminous
2) 100 times more luminous
3) 1000 times more luminous
4) 1/10th as luminous
5) 1/100th as luminous
L=4πR2 σT4
L=4πD2 B
Suppose two stars are at equal distance and have the same
radius, but one has a temperature that is twice as great as the
other. The apparent brightness of the hotter star is ____ as
the other.
1) 1/2 as great
2) 1/4 as great
3) the same
4) 4 times
5) 16 times as great
In Review
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There are four principal characteristics of a
star:
Luminosity
 Surface Temperature
 Size
 Mass
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How can we put all this together so that we can classify
stars and understand how they evolve?
We can take a census of stars and see what is out there.
Measurements of Star Properties
Apparent brightness Direct measurent
Parallax
Distance
Distance + apparent brightness
Luminosity
( L=4pD2 B)
Spectral type (or color)
Temperature
Luminosity + temperature
Radius
(L=4pR2 sT4)
Luminosity and temperature are the two
independent intrinsic parameters of stars.
Classificagtion of Stars:
The H-R diagram
“The stars are distant and
unobtrusive, but bright and
enduring as our fairest and most
memorable experiences.”
Henry David Thoreau (1849)
Are Stars similar to our Sun?
How far away are they?
Where did they come from?
What do they do?
Do they live forever?
How can we study the evolution of
stars, their phases of life?
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One approach is to collect a large number of stars (statistical
approach).
The idea is that a large sample of stars will contain examples
of all life stages (newborn, adult, moribund) and of all types
of stars.
The hope is that by looking at some carefully selected
observable properties of the stars, we will see trends that are
the telltale of stellar evolution
A large sample is also expected to contain all the star types
that exist, except, maybe, the most rare ones
But which observables to look at? And how?
Discussion Question
How can I understand the performance of CARS
P = P(Weight; Power; Overall Built)
Make a plot that shows the general relationship
between Weight and Horsepower of cars.
-now add to your plot sports cars…
-… racing cars…
-… and economy models
This kind of plots summarizes in a powerful way
general features of most cars
Classification of Stars:
Statistical Study
1) Collect information on
a large sample of stars:
surveys of stars.
2) Measure their
luminosities
(need the distance!)
3) Measure their surface
temperatures
(need their spectra or at
least their color)
Organizing the Family of Stars:
The Hertzsprung-Russell Diagram
We know:
Stars have different temperatures,
different luminosities, and different sizes.
Absolute mag.
or
Luminosity
To bring some order into that zoo of different
types of stars: organize them in a diagram of
Luminosity
versus
Temperature (or spectral type)
Hertzsprung-Russell Diagram
Spectral type: O
Temperature
B
A
F
G
K
M
The Hertzsprung-Russell Diagram
The Hertzsprung-Russell Diagram
Same
temperature,
but much
brighter than
Main
Sequence
stars
The Hertzsprung-Russell Diagram
Mass of
Star
Size of Star
The Radii of Stars in the
Hertzsprung-Russell Diagram
Betelgeuse
Rigel
Polaris
Sun
The Relative Sizes of Stars
in the HR Diagram
The Hertzsprung-Russell Diagram
The Hertzsprung-Russell Diagram
The Hertzsprung-Russell Diagram
The Main Sequence
- all main sequence
stars have
nuclear fusion of
H into He
in their cores
- this is the defining
characteristic of a
main sequence star.
The Hertzsprung-Russell Diagram
Red Giants
- Red Giant stars
are very large, cool
and quite bright.
Ex. Betelgeuse is
100,000 times more
luminous than the Sun
but is only 3,500K on
the surface. It’s radius
is 1,000 times that of the
Sun.
The Hertzsprung-Russell Diagram
The Hertzsprung-Russell Diagram
White Dwarfs
- White Dwarfs
are hot but since
they are so small,
they are not very
luminous.
The Hertzsprung-Russell Diagram
More mass,
more fuel,
very fast burning.
Shorter
Lifetime
of Star
Less mass,
less fuel,
slow, steady burning.
Think
SUV vs a Honda Civic
Longer
How do we know the age of a star?
The H-R diagram
O
What is the order of stellar evolution of
a star like the Sun?
Which is the faintest? the
sun, an O star, a white dwarf,
or a red giant?
Which of these star is the
hottest?
What are Sun-like stars (0.4
Msun < M < 8 Msun) in
common?
What about red dwarfs (0.08
Msun < M < 0.4 Msun) ?
Where do stars spend most
of their time?
Mass-Luminosity relation
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Most stars appear on the Main Sequence, where stars
appear to obey a Mass-Luminosity relation:
L  M3.5
For example, if the mass of a star is doubled, its
luminosity increases by a factor 23.5 ~ 11.
Thus, stars like Sirius that are about twice as massive as
the Sun are about 11 times as luminous.
The more massive a Main Sequence star is, the hotter
(bluer), and more luminous.
The Main Sequence is a mass sequence!
L=4πR2 σT4
To calculate a star's radius, you must
know its
1) temperature and luminosity.
2) chemical composition and temperature.
3) color and chemical composition.
4) luminosity and surface gravity.
L=4πR2 σT4
If a star is half as hot as our Sun, but has
the same luminosity, how large is its radius
compared to the Sun?
1) ½ times as large
2) ¼ times as large
3) 4 times larger
4) the same
What is burning in stars?
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Gasoline
Nuclear fission
Nuclear fusion
Natural gas
Review Questions
1.
2.
3.
What is the Hertzsprung-Russell Diagram?
Why are most stars seen along the so-called
main sequence?
What makes more massive stars hotter and
brighter?