Download Analyzing Starlight

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Analyzing Starlight
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Apparent brightness
2nd century BC  Hipparchus devised 6 categories of brightness.
In 1856 Pogson discovered that there is a 1:100 ratio in brightness
between magnitude 1 and 6  mathematical tools are possible.
m1-m2 = 2.5 log (I2/I1)
m1 and m2 are visual magnitudes, I1 and I2 are brightness.
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Example
Vega is 10 times brighter than a magnitude 1 star 
I2/I1 = 10.
m1 = 1
2.5 log (I2/I1) = 2.5 
1 - m2 = 2.5 
m2 = -1.5
Using the same calculations we can find that
Sun : -26.5
Full Moon : -12.5
Venus : -4.0
Mars : -2.0
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Inverse Square Law
Sun is very bright, because it is very near to us, but is the Sun really
a “bright” star.
The amount of light we receive from a star decreases with distance
from the star.
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Absolute Magnitude
If two pieces of information is known, we can find the absolute
magnitude, M, of a star:
1. Apparent magnitude, m
2. Distance from us.
Example:
Take the Sun, 1AU = 1 / 200,000 parsecs away from us.
At 10 parsecs the Sun will be (2,000,000)2 times less bright.
log(2,000,0002) = 31.5 magnitudes dimmer 
-26.5 (apparent) + 31.5 = 5 (absolute)
We define the absolute magnitude as the magnitude of a star as if
it were 10pc away from us.
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Distance modulus
m –M : distance modulus
Example: We have a table in our hands with distance moduli and
we need to find the actual distances to the stars.
How do we proceed??
Distance modulus = 10 means 
10(10/2.5) = 10,000 times dimmer than the apparent magnitude 
(10,000) = 1002
(inverse square law) 
10 pc x 100  1000 pc away
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20 Brightest Stars
Common
Luminosity
Name
Sirius
Canopus
Alpha Centauri
Arcturus
Vega
Capella
Rigel
Procyon
Betelgeuse
Achernar
Beta Centauri
Altair
Aldeberan
Spica
Antares
Pollux
Fomalhaut
Deneb
Beta Crucis
Regulus
Distance
Spectral
Proper Motion
R. A.
Declination
Solar Units LY
Type
arcsec / year
hours min
deg min
40
1500
2
100
50
200
80,000
9
100,000
500
9300
10
200
6000
10,000
60
50
80,000
10,000
150
A1V
F01
G2V
K2III
A0V
G5III
B8Ia
F5IV-V
M2Iab
B3V
B1III
A7IV-V
K5III
B1V
M1Ib
K0III
A3V
A2Ia
B0.5IV
B7V
06 45.1
06 24.0
14 39.6
14 15.7
18 36.9
05 16.7
05 12.1
07 39.3
05 55.2
01 37.7
14 03.8
19 50.8
04 35.9
13 25.2
16 29.4
07 45.3
22 57.6
20 41.4
12 47.7
10 08.3
-16 43
-52 42
-60 50
+19 11
+38 47
+46 00
-08 12
+05 13
+07 24
-57 14
-60 22
+08 52
+16 31
-11 10
-26 26
+28 02
-29 37
+45 17
-59 41
+11 58
9
98
4
36
26
46
815
11
500
65
300
17
20
260
390
39
23
1400
490
85
1.33
0.02
3.68
2.28
0.34
0.44
0
1.25
0.03
0.1
0.04
0.66
0.2
0.05
0.03
0.62
0.37
0
0.05
0.25
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Color and Temperature
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Wien’s Law
Wien’s Law:   1/T 
The higher the temperature 
The lower is the wavelengths 
The “bluer” the star.
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Temperature Dependence
Question: Where does the
temperature dependence of
the spectra come from?
Answer: Stars are made up of
different elements at
different temperatures and
each element will have a
different strength of
absorption spectrum.
Take hydrogen; at high
temperatures H is ionized,
hence no H-lines in the
absorption spectrum. At low
T, H is not excited enough
because there are not enough
collisions.
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Color Index
To categorize the stars
correctly, we pass the light
through filters. B is a blue
filter, V is a visible filter.
Hot stars have a
negative B-V color index.
Colder stars have a
positive B-V color index.
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Spectral Types
We now know that we can find the temperature of a star from its color.
To categorize the “main sequence” stars we have divided the colors into
seven spectral classes:
Color
Class
solar masses
solar diameters Temperature
---------------------------------------------------------------------------------bluest
O
20 – 100
12 - 25
40,000
bluish
B
4 - 12
4 - 12
18,000
blue-white
A
1.5 - 4
1.5 - 4
10,000
white
F
1.05 - 1.5
1.1 - 1.5
7,000
yellow-white
G
0.8 - 1.05
0.85 - 1.1
5,500
orange
K
0.5 - 0.8
0.6 - 0.85
4,000
red
M
0.08 - 0.5
0.1 - 0.6
3,000
Also each spectral class is divided into 10: Sun  G2
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What do we learn?
Temperature and Pressure: ionization of different atoms to different
levels.
Chemical Composition: Presence and strength of absorption lines of
various elements in comparison with the properties of the same elements
under laboratory conditions gives us the composition of elements of a
star.
Radial velocity: We can measure a star’s radial velocity by the shift of
the absorption lines using Doppler shift.
Rotation speed: Broadens the absorption lines, the broader the lines, the
higher the rotation speed.
Magnetic field: With strong magnetic fields, the spectral lines are split
into two or more components.