Download Introduction to Stars: Their Properties

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 brightness (see text), apparent magnitude, absolute
magnitude.
Describe the methods used to determine the temperature,
luminosity, and radius of a star.
1
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.
2
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:
3
 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
1
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.
4
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
5
 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
6
Using SIMBAD to find necessary measured (observed) quantities
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
7
Work on star table -- SIMBAD Search
Star ID
41 Cygni
Spectral
Type
F5 Iab
52 Cygni G9.5 III
69 Cygni
B0 Ib
xi Cygni K4.5 Ib-II
Surface
Temp. (K)
App .
Mag
Paralla x
(mas)
Dist.
(pc)
Abs . Mag
Lstar/Lsun
Rstar/Rsun
6,900 4.02
4.24
4,800 4.23 16.22
26,000 5.94
3,900 3.72
0.36
3.87
8
QuickTime™ and a
decompressor
are needed to see this picture.
9
Solar data
QuickTime™ and a
decompressor
are needed to see this picture.
10
Absolute magnitude is the apparent magnitude a star would have
m  M  5log10 (d pc )  5
if its distance = 10 parsecs.
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 apparent magnitude, absolute magnitude
11
52 Cygni
parallax  _____ arcseconds
distance =
1
 ______
parallax
m  M  5log10 (d pc )  5
M  m  5log10 (d pc )  5
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Relationship between absolute magnitude and luminosity
- bring in the Sun! 41 Cygni’s calculations
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
13
52 Cygni
M Sun M star 
Lstar
2.5
 10
 ________
LSun
14
Luminosity
Depends on
•Size (radius, R)
•Temperature
L  4 R
2
 T
4
L  4 R 2  T 4
2
4
Lstar  4 Rstar
 Tstar
2
LSun  4 RSun
 TSun4

2
4
Rstar 2 Tstar 4
Lstar 4 Rstar
Tstar

  
2
4  
LSun 4 RSun TSun RSun  TSun 
Lstar TSun 4 Rstar 2

   

LSun Tstar  RSun 
41 Cygni
2
2






1070 
R
T
L
5770
star
Sun
star
4
2
 

Rstar  Lstar TSun  TSun  Lstar  R  T  L   




6440
1

 
     
 Sun  star   Sun 
RSun  LSun Tstar  Tstar  LSun  Rstar
 26 or Rstar  26RSun
RSun
• Describe the methods used to determine temperature, luminosity, radius
15
52 Cygni
Rstar
RSun
TSun 2 Lstar 
   
 
Tstar  LSun 
Rstar
 _______
RSun
16
Work on star table -- SIMBAD Search
Star ID
41 Cygni
Spectral
Type
F5 Iab
52 Cygni G9.5 III
69 Cygni
B0 Ib
xi Cygni K4.5 Ib-II
Surface
Temp. (K)
App .
Mag
Paralla x
(mas)
Dist.
(pc)
Abs . Mag
Lstar/Lsun
Rstar/Rsun
6,900 4.02
4.24
4,800 4.23 16.22
26,000 5.94
3,900 3.72
0.36
3.87
17