The Family of Stars

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The Family of Stars
We already know how to determine a stars

• surface temperature

• chemical composition

Now, see how we can determine its

• distance

• luminosity

• radius

• mass

and how all the different types of stars make up
the big family of stars.
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Distances of Stars
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d in parsec (pc) p in arc seconds
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d
p
Trigonometric Parallax
Star appears slightly shifted from different
positions of the Earth on its orbit
1 pc 3.26 LY
The further away the star is (larger d), the
smaller the parallax angle p.
Animation
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The Trigonometric Parallax
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Example Nearest star, a Centauri, has a
parallax of p 0.76 arc seconds
d 1/p 1.3 pc 4.3 LY
With ground-based telescopes, we can measure
parallaxes p 0.02 arc sec gt d 50 pc
This method does not work for stars further away
than 50 pc.
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Sirius, the brightest star in the sky, has a
trigonometric parallax of p 0.385 arc seconds.
What is its distance from Earth?

• 0.385 pc
• 0.80 light years
• 1.255 pc
• 2.60 light years
• 8.47 light years

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The method of trigonometric parallaxes (from
ground based telescopes) allows us to measure
distances

• only to objects in our solar system.
• only to stars in our solar neighborhood within
  the Milky Way.
• to stars throughout the entire Milky Way.
• to stars and galaxies throughout the Local Group.
• even to other clusters of galaxies.

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Intrinsic Brightness / Absolute Magnitude
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The further away a light is, the fainter it
appears.
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Intrinsic Brightness / Absolute Magnitude (II)
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More quantitatively The flux received from the
light is proportional to its intrinsic brightness
or luminosity (L) and inversely proportional to
the square of the distance (d)
L
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F
d2
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The stars A and B have the same intrinsic
luminosity, but A is 5 times further away from
Earth than B. Then

• Both stars will appear equally bright.
• A will appear 5 times brighter than B.
• B will appear 5 times brighter than A.
• A will appear 25 times brighter than B.
• B will appear 25 times brighter than A.

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Star B
Star A
Earth
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Distance and Intrinsic Brightness
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Example
Betelgeuze
App. Magn. mV 0.41
Rigel
For a magnitude difference of 0.41 0.14 0.27,
we found Rigel appears 1.28 times brighter than
Betelgeuze
App. Magn. mV 0.14
But Rigel and Betelgeuze may be at quite
different distances from us!
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Absolute Magnitude
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• To characterize a stars intrinsic brightness,
  define Absolute Magnitude (MV)

Absolute Magnitude Magnitude that a star would
have if it were at a distance of 10 pc.
If we know a stars absolute magnitude, we can
infer its distance by comparing absolute and
apparent magnitudes.
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Absolute Magnitude (II)
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Betelgeuze
Difference in absolute magnitudes 6.8 5.5
1.3 gt Luminosity ratio (2.512)1.3 3.3
Rigel
Rigel is actually 3.3 times brighter than
Betelgeuze!
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The Size (Radius) of a Star
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We already know flux increases with surface
temperature ( T4) hotter stars are brighter.
But brightness also increases with size
A
B
Star B will be brighter than star A.
Specifically Absolute brightness is proportional
to radius (R) squared, L R2.
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Example
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Both Spica B and Sirius B are B-type stars, but
Sirius B is a white dwarf star, with a radius
560 times smaller than Spica B.
Thus, since L R2, Sirius B is
intrinsically 5602 320,000 times fainter than
Spica B.
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Polaris has just about the same spectral type
(and surface temperature) as our sun, but it is
10,000 times brighter. Thus, Polaris radius is
the suns radius.

• the same as
• 100 times larger than
• 100 times smaller than
• 10,000 times larger than
• 10,000 times smaller than

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Organizing the Family of Stars The
Hertzsprung-Russell Diagram
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We know Stars have different temperatures,
different luminosities, and different sizes.
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
Luminosity
Temperature
Spectral type O B A F G K M
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The Hertzsprung Russell Diagram
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Most stars are found along the Main Sequence
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The Hertzsprung-Russell Diagram (II)
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Same temperature, but much brighter than MS stars
? Must be much larger
Stars spend most of their active life time on the
Main Sequence (MS).
? Giant Stars
Same temp., but fainter ? Dwarfs
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Radii of Stars in the Hertzsprung-Russell Diagram
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Rigel
Betelgeuze
10,000 times the suns radius
Polaris
100 times the suns radius
Sun
As large as the sun
100 times smaller than the sun
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Luminosity Classes
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Ia Bright Supergiants
Ia
Ib
Ib Supergiants
II
II Bright Giants
III
III Giants
IV Subgiants
IV
V
V Main-Sequence Stars
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Examples
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• Our Sun G2 star on the Main Sequence G2V
• Polaris G2 star with Supergiant luminosity G2Ib