Post on 22-Dec-2015
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Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star.
Define brightness (see text), apparent magnitude, absolute magnitude.
Describe the methods used to determine the temperature, luminosity, and radius of a star.
Learning goals:Learning goals:
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Questions:Questions:
Which stars are the brightest?
Which stars are putting out the most watts? (luminosity = energy per second)
NEED TO KNOW:NEED TO KNOW:
Distances
The most fundamental and accurate (within a certain range) means of finding distances is measuring the parallaxes of stars.
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PARSEC: Parallax ARc SECond
A star having a parallax of 1 arc second is 1 parsec away
1 parsec (pc) = 3.26 light years
1 kiloparsec (1 kpc) = 1000 pc; 1 megaparsec (1 Mpc) = 1,000,000 pc
Baseline is 1 Astronomical Unit
Small angle formula for distance in AU’s:
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Works accurately for stars within about 200 pc (Hipparchos satellite)
Biggest problem: measuring the miniscule shift of a star against more distant stars
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parallax = 0.75 arcseconds
distance = 1
0.75=1.3 pc = 4.3 ly
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parallax = 0.15 arcseconds
distance = 1
0.15= __?__ pc = __?__ ly
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parallax = 0.0015 arcseconds
distance = 1
0.0015= __?__ pc = __?__ ly
6.7 22
667 2170 ly
•Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star.
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Using SIMBAD to find the parallaxes of the stars of Exercise 2
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41 Cygni data (partial)
Parallax = 4.24 ± 0.16 mas or 0.00424 ± 0.00016 arc seconds
Distance = 1/parallax = 1/0.00424 = 236 pc or ~770 ly
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Every 5 magnitudes difference means 100 x difference in brightness
One magnitude difference is 2.512 times in brightness.
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• Define brightness, apparent magnitude, absolute magnitude
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Using SIMBAD to find necessary measured (observed) quantities
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41 Cygni data (partial)
V = apparent magnitude through “visual” filterThink of it as mv .
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Work on star table -- Work on star table -- SIMBAD SearchSIMBAD Search
Star ID Spectral
Type Surface
Temp. (K) App. Mag
Parallax (mas)
Dist. (pc)
Abs. Mag Lstar/Lsun Rstar/Rsun
41 Cygni
52 Cygni
69 Cygni
xi Cygni
F5 Iab 4.02 4.246,900
G9.5 III 4.23 16.224,800
B0 Ib 5.94 0.3626,000
K4.5 Ib-II 3.72 3.873,900
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Solar dataSolar data
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Absolute magnitude is the apparent magnitude a star would have if its distance = 10 parsecs.
Relates luminosities by “placing” stars on common scale.Smaller the absolute magnitude number, the more luminous the star.
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m − M = 5log10(dpc ) − 5
M = m − 5log10(dpc ) + 5
• Define apparent magnitude, absolute magnitude
41 Cygni dpc = 236 parsecs
mv = 4.016
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Mv = mv − 5log10(dpc ) + 5
Mv = 4.016 − 5log10(236) + 5
Mv = 4.016 − 5(2.37) + 5 = −2.8
What does the answer tell you?
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€
m − M = 5log10(dpc ) − 5
M = m − 5log10(dpc ) + 5
52 Cygni52 Cygni
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parallax = _____ arcseconds
distance = 1
parallax= ______
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Relationship between absolute magnitude and luminosity Relationship between absolute magnitude and luminosity - bring in the Sun! 41 Cygni’s calculations- bring in the Sun! 41 Cygni’s calculations
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MSun − Mstar = 2.5log10Lstar
LSun
⎛ ⎝ ⎜ ⎞
⎠ ⎟
MSun − Mstar( )2.5 = log10
LstarLSun
⎛ ⎝ ⎜ ⎞
⎠ ⎟
10M Sun −M star( )
2.5 =10log10
LstarLSun
⎛ ⎝ ⎜ ⎞
⎠ ⎟
10M Sun −M star( )
2.5 =Lstar
LSun
Lstar
LSun
=10M Sun −M star( )
2.5
Lstar
LSun
=104.74 −(−2.8)( )
2.5 =1070
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Lstar =1070LSun
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52 Cygni52 Cygni
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Lstar
LSun
=10M Sun −M star( )
2.5 = ________
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Depends on•Size (radius, R)•Temperature
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L = 4πR2( ) σT 4
• Describe the methods used to determine temperature, luminosity, radius€
L = 4πR2( ) σT 4
Lstar = 4πRstar2
( ) σTstar4
LSun = 4πRSun2
( ) σTSun4
Lstar
LSun
=4πRstar
2
4πRSun2
σTstar4
σTSun4 =
Rstar
RSun
⎛
⎝ ⎜
⎞
⎠ ⎟
2Tstar
TSun
⎛
⎝ ⎜
⎞
⎠ ⎟
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Lstar
LSun
⎛
⎝ ⎜
⎞
⎠ ⎟TSun
Tstar
⎛
⎝ ⎜
⎞
⎠ ⎟
4
=Rstar
RSun
⎛
⎝ ⎜
⎞
⎠ ⎟
2
Rstar
RSun
⎛
⎝ ⎜
⎞
⎠ ⎟=
Lstar
LSun
⎛
⎝ ⎜
⎞
⎠ ⎟TSun
Tstar
⎛
⎝ ⎜
⎞
⎠ ⎟
4
=TSun
Tstar
⎛
⎝ ⎜
⎞
⎠ ⎟
2Lstar
LSun
⎛
⎝ ⎜
⎞
⎠ ⎟
LuminosityLuminosity
€
Rstar
RSun
=TSun
Tstar
⎛
⎝ ⎜
⎞
⎠ ⎟
2Lstar
LSun
⎛
⎝ ⎜
⎞
⎠ ⎟ =
5770
6440
⎛
⎝ ⎜
⎞
⎠ ⎟2
1070
1
⎛
⎝ ⎜
⎞
⎠ ⎟
Rstar
RSun
= 26 or Rstar = 26RSun
41 Cygni
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52 Cygni52 Cygni
€
Rstar
RSun
=TSun
Tstar
⎛
⎝ ⎜
⎞
⎠ ⎟
2Lstar
LSun
⎛
⎝ ⎜
⎞
⎠ ⎟ =
Rstar
RSun
= _______
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Work on star table -- Work on star table -- SIMBAD SearchSIMBAD Search
Star ID Spectral
Type Surface
Temp. (K) App. Mag
Parallax (mas)
Dist. (pc)
Abs. Mag Lstar/Lsun Rstar/Rsun
41 Cygni
52 Cygni
69 Cygni
xi Cygni
F5 Iab 4.02 4.246,900
G9.5 III 4.23 16.224,800
B0 Ib 5.94 0.3626,000
K4.5 Ib-II 3.72 3.873,900