Download Introduction to Stars: Their Properties

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http://stardate.org/radio/program/delta-lyrae
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Learning goals:
 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 arc second, parsec.
 Define brightness, apparent magnitude, absolute magnitude.
Describe the methods used to determine the temperature,
luminosity, and radius of a star.
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Questions:
Which stars are the brightest?
Which stars are putting out the most
watts? (luminosity = energy per
second)
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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You already know about the parallax effect:
Demonstrating parallax
Parallax of Stars
•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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Define arc second
How many degrees in a circle?
How many arc minutes in a degree?
How many arc seconds in an arc minute?
How many arc seconds in a degree?
How many arc seconds in a circle?
__?__ radians = 360 degrees
1 radian = 57.3 degrees
How many arc seconds in 1 radian?
360, 60, 60, 3600;
1,296,000; 2 pi; 206,265 arc sec/rad
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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:
• Define arc second, parsec
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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
parallax  0.75 arcseconds
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distance =
 1.3 pc  4.3 ly
0.75
parallax  0.15 arcseconds
1
distance =
 __?__
6.7 pc  __?__
22 ly
0.15
parallax  0.0015 arcseconds
1
distance =
 __?__
667 pc  __?__
2170lyly
0.0015
•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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•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
41 Cygni data (partial)
QuickTime™ and a
decompressor
are needed to see this picture.
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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Inverse square law for light
p. 494
QuickTime™ and a
decompressor
are needed to see this picture.
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How the star looks to US HERE ON EARTH.
L
apparent brightness =
4 D2
1000 times farther away

100 Watt
1000 Watt
Qui ckTime™ and a
decompressor
are needed to see thi s pi cture.

1 Watts
10 times farther away

Qui ckTime™ and a
decompressor
are needed to see thi s pi cture.
Qui ckTime™ and a
decompressor
are needed to see thi s pi cture.
Qui ckTime™ and a
decompressor
are needed to see thi s pi cture.
2 x farther away, 1/4 as bright
3 x farther away, 1/9 as bright
• Define brightness, apparent magnitude, absolute magnitude
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 Every 5 magnitudes
difference means 100 x
difference in brightness
 One magnitude difference
QuickTime™ and a
decompressor
are needed to see this picture.
is 2.512 times in brightness.
(2.5125 = 100)
• Define brightness, apparent magnitude, absolute magnitude
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When you see only “magnitude,” that means APPARENT magnitude.
1. The magnitude (m) of star A is 1, the magnitude (m) of star B is
6. How many times brighter is A than B?
a) 5
b) 10
c) 100
d) 1000
2. m of star C is 12, m of star D is 2: How many times brighter is
star D than star C? (Or, equally stated, how many times dimmer
is star C than star D?)
a) 10
b) 24
c) 100
d) 10,000
3. The Sun is the brightest star in the sky, with an apparent
magnitude of about -26.5 Sirius is next in line, with an apparent
magnitude of -1.5; how many times brighter is the Sun than
Sirius?
a) 25
b) 28
c) 100,000
d) 10,000,000,000
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Using SIMBAD to find the apparent magnitudes of the stars
of Exercise 2
41 Cygni data (partial)
QuickTime™ and a
decompressor
are needed to see this picture.
V = apparent magnitude through “visual” filter
Think of it as mv .
UV
QuickTime™ and a
decompressor
are needed to see this picture.
IR
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Absolute magnitude is the apparent magnitude a star would have
if its distance = 10 parsecs.
m  M  5log10 (d pc )  5
M  m  5log10 (d pc )  5
Relates luminosities by “placing” stars on common scale.
Smaller the absolute magnitude number, the more luminous the
star.
41 Cygni
dpc = 236 parsecs
mv = 4.016
 M v  mv  5log 10 (d pc )  5
M v  4.016  5log 10 (236)  5
M v  4.016  5(2.37)  5  2.8
What does the answer tell you?

• Define brightness, apparent magnitude, absolute magnitude
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Define brightness, apparent and absolute magnitude
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Supergiant
Bright-Giant
Giant
Sub-Giant
Main Sequence Star (dwarf)
I
II
III
IV
V
We estimate the luminosity of
a star by measuring how
broad the absorption lines are
in its spectrum.
At a given temperature, the
less luminous stars have
atoms colliding a lot more
than in the giant stars.
• Describe the methods used to determine temperature, luminosity, radius
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Luminosity
High
Low
High
Temperature
Low19
Using SIMBAD to find the parallaxes of the stars of Exercise 2
41 Cygni data (partial)
QuickTime™ and a
decompressor
are needed to see this picture.
F5 Iab
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The H-R
Diagram
L  4 R
2
 T
4
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Relationship between absolute magnitude and luminosity
- bring in the Sun!
Lstar



M Sun  M star  2.5log 10
LSun 

M Sun  M star
Lstar




log
10
2.5
LSun 

M Sun M star 
10
M Sun M star 
10
2.5
2.5
 10
L

log10  star L 

Sun
Lstar

LSun
M Sun M star 
Lstar
2.5
 10
LSun
4.74 (2.8)
Lstar
2.5
 10
 1070
LSun
Lstar 1070LSun
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Depends on
•Size (radius, R)
•Temperature
Luminosity
L  4 R
2
 T
4
L  4 R 2  T 4
2
4
Lstar  4 Rstar
 Tstar
2
LSun  4 RSun
 TSun4
Lstar 4 R

LSun 4 R
2
star
2
Sun
T
T
4
star
4
Sun

Rstar 2 Tstar 4
 
  
R
 Sun  TSun 
Lstar TSun 4 Rstar 2

   

L
T
R
 Sun  star   Sun 
Rstar  Lstar TSun 4 TSun 2 Lstar 

 
     

R
L
T
T
L
 Sun   Sun  star   star   Sun 
2
2
Rstar TSun  Lstar  5770  1070 
   
 

  
RSun Tstar  LSun  6440   1 
Rstar
 26 or Rstar  26RSun
RSun
• Describe the methods used to determine temperature, luminosity, radius
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The H-R
Diagram
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