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 1100 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
• Apparent magnitude, m
• 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 Distance Spectral Proper
Motion R. A. Declination Name Solar
Units LY Type arcsec / year hours min deg min
Sirius 40 9 A1V 1.33 06 45.1 -16
43 Canopus 1500 98 F01 0.02 06 24.0 -52 42
Alpha Centauri 2 4 G2V 3.68 14 39.6 -60 50
Arcturus 100 36 K2III 2.28 14 15.7 19 11
Vega 50 26 A0V 0.34 18 36.9 38 47
Capella 200 46 G5III 0.44 05 16.7 46 00
Rigel 80,000 815 B8Ia 0 05 12.1 -08 12
Procyon 9 11 F5IV-V 1.25 07 39.3 05 13
Betelgeuse 100,000 500 M2Iab 0.03 05
55.2 07 24 Achernar 500 65 B3V 0.1 01
37.7 -57 14 Beta Centauri 9300 300 B1III
0.04 14 03.8 -60 22 Altair 10 17 A7IV-V
0.66 19 50.8 08 52 Aldeberan 200 20 K5III
0.2 04 35.9 16 31 Spica 6000 260 B1V
0.05 13 25.2 -11 10 Antares 10,000 390 M1Ib
0.03 16 29.4 -26 26 Pollux 60 39 K0III
0.62 07 45.3 28 02 Fomalhaut 50 23 A3V
0.37 22 57.6 -29 37 Deneb 80,000 1400 A2Ia
0 20 41.4 45 17 Beta Crucis 10,000 490 B0.5I
V 0.05 12 47.7 -59 41 Regulus 150 85 B7V
0.25 10 08.3 11 58
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Color and Temperature
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Wiens Law
Wiens 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
stars 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.