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Stellar Masses and Luminosity
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If we know the Spectral type of a star (i.e. its
luminosity), and its temp, then we can determine
its size from Stephan’s law:
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L = Area of Star x temp4 x constant
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This means that small hot stars can be MUCH
brighter than larger cooler stars.
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Since Temp is easily measured from the peak
wavelength of the spectrum, we can immediately
know the size of the star.
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For Example, Deneb has a luminosity of 170,000
times the luminosity of the sun. Its spectral type
is A2, which means its temp is about 10,000 Kelvin
(remember the sun;s temp is 5800 kelvin).
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This Makes the Area of Deneb about 40000 x the
area of the sun, so its radius and diameter are
about 200x the diameter of the sun.l
Don’t worry..you won’t have do this math..
. So, is there any way we can find the mass of a star
like Deneb?
Masses of Stars
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Mass is the single most important property of any star.
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at each stage of a star’s life, mass determines…
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The mass of a star can only be measured directly by …
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
what its luminosity will be
what its spectral type will be
observing the effect which gravity from another object has on
the star
This is most easily done for two stars which orbit one
another…a binary star!
Binary Stars
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(two stars which orbit one another)
Optical doubles
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two unrelated stars which are in the same area of
the sky
Visual binaries
• a binary which is spatially resolved, i.e. two
stars are seen (e.g. Sirius)
Binary Stars
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Spectroscopic binaries
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a binary which is spatially unresolved, i.e only one
star is seen; the existence of the second star is
inferred from the Doppler shift of lines.
Binary Stars
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Eclipsing binaries
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a binary whose orbital plane lies along our line of
sight, thus causing “dips” in the light curve.
Binary Stars
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The stars orbit each other via gravity.
So the laws of Kepler & Newton apply!
Remember Newton’s version of Kepler’s
Third Law:
2
2
3
P = 4 a / G (m1 + m2)
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If you can measure the orbital period of the
binary (P) and the distance between the stars
(a), then you can calculate the sum of the
masses of both stars (m1 + m2).
The Hertzsprung-Russell Diagram
• A very useful diagram for understanding stars
• We plot two major properties of stars:
• Temperature (x) vs. Luminosity (y)
• Spectral Type (x) vs. Absolute Magnitude (y)
• Stars tend to group into certain areas
bright
MV
faint
hot Spectral type
cool
Here are the Stars of Orion.
Betelguese: 1000
x the diameter of
the sun. Temp =
3000K (burr!)
The Orion
Nebula—a star
forming region!
Rigel: 70,000x Lsun
Temp = 10,000Kelvin.
Whis the most Luminious? The Largest? Which isn’t a star at
all?
BRIGHT
HOT
COOL
FAINT
The Main Sequence (MS)
90% of all stars
lie on the main
sequence!
Stellar Luminosity
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Review: The luminosity of a star depends on 2 things:
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surface temperature
surface area (radius)
4
L=T 4R
2
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The stars have different sizes!!

The largest stars are in the upper right corner of the HR Diagram.
Note that Absolute Magnitude is a measure of the
Luminosity of the Star
Apparent visual Magnitude is a measure of the
Apparent Brightness (or Intensity) of the starlight
reaching the observer.
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Regions of the H-R Diagram
Stellar Luminosity Classes
Stellar Masses on the H-R Diagram
We use binary stars to measure directly the masses
of stars of every type. This leads to the:
Mass-Luminosity Relation
3.5
L m
for main sequence stars only
• As one moves to the upper-left of the main sequence:
• stars become more massive
• stars become more luminous
• stars become fewer in number
Mass–Luminosity Relation
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All main sequence stars fuse H into He in their cores.
Luminosity depends directly on mass because:
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more mass means more weight from the star’s outer layers
nuclear fusion rates must be higher in order to maintain
gravitational equilibrium
Lifetime on the Main Sequence
How long will it be before MS stars run
out of fuel? i.e. Hydrogen?
How much fuel is there?
M
How fast is it consumed? L  M
How long before it is used up? Time =
Amount/(rate it is being used)
3.5
M/L = M/M
3.5
=M
-2.5
Lifetime on the Main Sequence
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O & B Dwarfs burn fuel like a Hummer!
M Dwarfs burn fuel like a compact Hybrid
(Prius!
Our Sun will last 1010 years on the Main
Sequence. Let
 = (Lifetime of Sun)/(Lifetime of Star)
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MS Lifetime  = 10 yrs / M2.5
10
Lifetime on the Main Sequence
So for example:
B2 dwarf (10 M) lasts
F0 dwarf (2 M) lasts
M0 dwarf (.5 M) lasts
3.2 x 107 yr
1.8 x 109 yr
5.6 x 1010 yr
But the Universe is 1.37 x 1010 yr old!
Every M dwarf that was ever created is still
on the main sequence!!
Another Rung on the distance ladder:
Cepheid Variables
She studied the
light curves of
variable stars in
the Magellenic
clouds.
Assumption: all stars
are at the
Same distance
Henrietta Leavitt
(1868-1921)
Cepheid Variables
The brightness of the stars varied
in a regular pattern.
Cepheid Variables
prototype:  Cephei
F - G Bright Giants (II) whose
pulsation periods (1-100 days) get
longer with brightness (MV = -2 to -6)
Distance Indicator!!
Cepheid Variables
The Instability Strip
There appears to be an
almost vertical region on
the H-R Diagram where
all stars within it (except
on the Main Sequence)
are variable.
They pulsate due to partial ionization!