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Stars
up to Chapter 9.3, page 194
“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
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 stsar’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:

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
Stellar Parallax
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 determine the
radius of a star?
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?
We can take a census of stars and see what’s
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 T4)
Luminosity and temperature are the two
independent intrinsic parameters of stars.