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Transcript
1
Lecture 26
The HertzsprungRussell Diagram
January 13b, 2014
2
Hertzsprung-Russell Diagram
• Hertzsprung and Russell found a correlation
between luminosity and spectral type
(temperature)
10000
Hot, bright stars
100
Luminosity
(Solar units)
Sun
1
Cool, dim stars
0.01
Main Sequence
0.0001
hot
O B A F G K M
cooler
3
4
• Most stars (~90%) are on the main sequence
– The greater the temperature, the more luminous
the star
– M type stars are the most common.
– O type stars are the least common.
5
Sizes of Stars
• Size of star is related to the temperature and
the luminosity by:
Luminosity  Temperature  Radius
4
L   T  4 R
4
2
2
– If you know the position on HR diagram you
know the size of the star.
6
A star is twice as luminous as the Sun and has
twice the surface temperature. What is its radius
relative to the Sun’s radius?
A.
B.
C.
D.
Rstar/RSun = 4.0
Rstar/RSun = 2.8
Rstar/RSun = 0.5
Rstar/RSun = 0.35
7
A star is twice as luminous as the Sun and has
twice the surface temperature. What is its radius
relative to the Sun’s radius?
L   T 4 R
4
Rstar

RSun
2
 R  L 4 T
Lstar 4 T
4
star
LSun 4 T
4
Sun
4

2 1

   0.35
12
4
Lstar  TSun 


LSun  Tstar 
4
8
100 R
10 R
Supergiants
10000
100 1 R

Luminosity
(Solar units)
Sun
1
0.01
Cool, dim stars
White
Dwarfs
0.0001
Giants
Main Sequence
0.1 R
0.01 R
hotter
O
B
A
F
G
Spectral Classification
K
M
cooler
9
• Supergiants -- cool, bright, red, large stars
• Giants -- cool, bright red, less large stars
• Main Sequence -- spans range from hot,
bright stars to cool, dim stars.
• White dwarfs -- hot, small, dim stars.
• These classifications will give clues to
stages in the evolution of stars.
10
Stars come in
many sizes!
11
Sizes of Objects in our Universe
Images from webisto.com/space
12
Sizes of Objects in our Universe
13
Sizes of Objects in our Universe
14
Sizes of Objects in our Universe
15
Sizes of Objects in our Universe
16
Masses of Stars
• We cannot directly measure the mass of an
isolated star.
• If something is orbiting the star, can use the
general form of Kepler’s Third Law
M 1  M 2 P
2
a
3
• Luckily, 2/3 of all stars are binary stars, two
stars that orbit one another
17
A binary star system consists of one star that is twice as
massive as the other. They are 2.0 AU apart and have an
orbit period of 0.50 y. What is the mass of the smaller
star in terms of solar masses?
A. 11 MSun
B. 4 MSun
C. 0.50 MSun
D. 0.125 MSun
18
A binary star system consists of one star that is twice as
massive as the other. They are 2.0 AU apart and have an
orbit period of 0.50 y. What is the mass of the smaller
star in terms of solar masses?
A. 11 MSun  m  2m  P 2  a 3
3
B. 4 MSun
3
2.0 AU 

a
 11 M
C. 0.50 MSun m  3P 2 
2
3  0.50 y 
D. 0.125 MSun
19
Mass-Luminosity Relation
• True ONLY for
Main Sequence stars
• As the mass
increases, the
luminosity increases
rapidly
Luminosity  Mass3
20
HR Diagram:
Main sequence
stars labeled by
mass in units of
solar masses.
21
Question
How do the following properties differ with respect to the Sun for
the listed main sequence types? What properties would not change
for non-main sequence stars?
O
Temperature
Mass
Size
Color
Luminosity
G
M
22
Question
How do the following properties differ with respect to the Sun for
the listed main sequence types? What properties would not change
for non-main sequence stars?
O
G
M
Temperature*
Higher
Same
Lower
Mass
Higher
Same
Lower
Size
Larger
Same
Smaller
Blue
White
Red
Higher
Same
Red
Color*
Luminosity
23
Apparent Brightness
• The brightness an object appears to have.
• The further away the object, the dimmer it
looks
Luminosity
Apparent Brightness 
4 d 2
d = distance
24
Star A has a brightness of 1.0 μW/m2 and is known to be
4.0 ly away. Star B is 9.0 ly away and has a brightness of
3.0 μW/m2. How much more luminous is star B than star A?
A. 240×
B. 15×
C. 6.8×
D. 3.0×
25
Star A has a brightness of 1.0 μW/m2 and is known to be
4.0 ly away. Star B is 9.0 ly away and has a brightness of
3.0 μW/m2. How much more luminous is star B than star A?
A. 240×
B. 15×
C. 6.8×
D. 3.0×
L
B
2
4 d

LB 4 d BB

LA 4 d BA
2
B
2
A
LB  9.0 ly   3.0  W/m 


15
2
LA  4.0 ly  1.0  W/m 2 
2
2
26
Spectroscopic Parallax
• If luminosity and apparent brightness are
known, distance can be determined.
m  M  5log d  5
• It can be difficult to accurately measure
luminosity for one star
– Use spectra to get spectral type and class
• But, you can use a cluster of stars
• Distance to the cluster can be determined by
comparing the HR diagram of the cluster
with a template HR diagram
27
Spectroscopic Parallax
Observations
10000
Template
100
1
0.01
hot
O B A F G KM
cooler
0.0001
hot
O B A F G K M
cooler
28
Spectroscopic Parallax
10000
100
1
0.01
0.0001
hot
O B A F G K M
cooler
Now the vertical axis is on an absolute scale. We can read off the
luminosities of the stars, and from that, together with the apparent
brightness, we can determine the distance to the stars.
29
The Distance Ladder
•
•
•
•
See Extending Our Reach on p. 484
First rung: parallax
Second rung: spectroscopic parallax
Third rung: standard candles/inverse square
law
30
The Distance Ladder
We will be discussing the longer distance “rungs” of the ladder in subsequent lectures.
Figure 26.12, Freedman and Kaufmann,
7th ed. Universe, © 2005 W. H. Freeman & Company