Download The Family of Stars

The Family of Stars
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The Family of Stars
We already know how to determine a star’s
• 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.
Distances of Stars
d in parsec (pc)
p in arc seconds
1
d = __
p
Trigonometric Parallax:
Star appears slightly shifted from different
positions of the Earth on its orbit
The further away the star is (larger d),
the smaller the parallax angle p.
1 pc = 3.26 LY
The Trigonometric Parallax
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
=> d ≤ 50 pc
This method does not work for stars
further away than 50 pc.
Sirius, the brightest star in the sky, has a
trigonometric parallax of p = 0.385 arc
seconds. What is its distance from Earth?
1.
2.
3.
4.
5.
0.385 pc
0.80 light years
1.255 pc
2.60 light years
8.47 light years
The method of trigonometric parallaxes
(from ground based telescopes) allows us to
measure distances …
1.
2.
3.
4.
5.
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.
Intrinsic Brightness /
Absolute Magnitude
The further away a light is,
the fainter it appears.
Intrinsic Brightness /
Absolute Magnitude (II)
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
__
F~ 2
d
The stars A and B have the same
intrinsic luminosity, but A is 5 times
further away from Earth than B. Then:
Star A
1.
2.
3.
4.
5.
Star B
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.
Earth
Distance and
Intrinsic Brightness
Example:
Magn. Diff.
Intensity Ratio
1
2.512
2
2.512*2.512 = (2.512)2
= 6.31
…
…
5
(2.512)5 = 100
For a magnitude difference of 0.41 –
0.14 = 0.27, we found: Rigel appears
1.28 times brighter than Betelgeuze
But Rigel and Betelgeuze may be at
quite different distances from us!
Betelgeuze
App. Magn. mV = 0.41
Rigel
App. Magn. mV = 0.14
Absolute Magnitude
To characterize a star’s 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 star’s absolute magnitude,
we can infer its distance by comparing
absolute and apparent magnitudes.
Absolute Magnitude (II)
Betelgeuze Rigel
mV
0.41
0.14
MV
-5.5
-6.8
d
152 pc
244 pc
Betelgeuze
Difference in absolute magnitudes:
6.8 – 5.5 = 1.3
=> Luminosity ratio = (2.512)1.3 = 3.3
Rigel is actually 3.3 times
brighter than Betelgeuze!
Rigel
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
B
Star B will be brighter than star A.
Specifically: Absolute brightness is
proportional to radius (R) squared, L ~ R2.
Example:
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.
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 sun’s radius.
1.
2.
3.
4.
5.
the same as
100 times larger than
100 times smaller than
10,000 times larger than
10,000 times smaller than
Organizing the Family of Stars:
The Hertzsprung-Russell Diagram
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
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 (II)
Same
temperature,
but much
brighter than
MS stars
→ Must be
much larger
→ Giant
Stars
Radii of Stars in the
Hertzsprung-Russell Diagram
Rigel
Betelgeuze
Polaris
Sun
100 times smaller than the sun
Ia Bright Supergiants
Ia
Luminosity
Classes
Ib
Ib Supergiants
II
II Bright Giants
III Giants
III
IV
IV Subgiants
V
V Main-Sequence
Stars
Examples:
• Our Sun: G2 star on the Main Sequence:
G2V
• Polaris: G2 star with Supergiant luminosity:
G2Ib