ASTR 1200
Announcements
Exams are at the back. Please pick up.
Still have a calculator left at the exam.
Problem Sets 3 and 4 posted. Due next week.
Today will review equations of light and do Doppler
Shift. (Necessary for PS3)
Second exam will be October 30
Website
http://casa.colorado.edu/~wcash/APS1200/APS1200.html
The Exam
mean 70.4, median 71.2
Standard deviation 13.1
White Dwarfs
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Held up by electron degeneracy
About the size of the Earth R~5000km
Mass Typically 0.8M
Luminosity ~ .001 L
Thin layer of “normal” H
Degenerate Carbon
Earth vs White Dwarf
WD Density
2 x1033
6


 1.5 x10 g / cc
8 3
4 3 4 x(7 x10 )
R
3
M
Water has a density of 1 g/cc
Lead 11 g/cc
Gold 19 g/cc
100,000 times density of gold!
NOT NORMAL MATTER!!
1 cubic centimeter masses one ton!
Surface Gravity
GM 7 x1011 x2 x1030
6
2
a 2 
 3x10 m / s
6 2
R
(7 x10 )
This is 300,000 gees
If you weigh 150lbs on Earth, you would weigh
45 million pounds on a White Dwarf!
What would happen to you and your spaceship?
Escape Velocity
2GM
2 x6.7 x10 11 x 2 x1030
13
6
Ve 


4
x
10

6
x
10
m/ s
6
R
7 x10
Speed of light is 3x108 m/s, so escape velocity is .02c.
Gravitational Redshift
Even light loses energy climbing out of this hole.
GMm
2
 mc
R
 = 2x10-4
At 5000Å have 1Å shift to red
Looks like a 60km/s Doppler Shift
Magnetic Field
 R0 
B  Bo  
 R
3
When a star shrinks from 109m to 107m
R0
 100
R
So B increases from 1Gauss to a Million Gauss
A million Gauss can rip normal matter apart!
Chandrasekhar Limit
A peculiarity of Degeneracy Pressure is that it has a maximum mass.
Each electron added must find its own quantum state by having its
own velocity.
But what happens when the next electron has to go faster than light?
The Chandrasekhar Limit for a White Dwarf is 1.4M
No White Dwarf Can have more than 1.4M
Otherwise it will groan and collapse under its own weight.
We’ll come back to this later.
WDs are Common
Every star with less than 5M will end up as a White Dwarf
Most stars with mass above 1.3M have reached end of MS life.
White Dwarfs are VERY common ~ 10% of all stars
Closest is only 2.7pc away. (Sirius B)
Will become increasing common as universe ages.
Immortal Stars
Regular stars need thermal pressure to balance gravity, and they
need nuclear reactions to maintain the pressure, so the die when they
run out of fuel.
Not so White Dwarfs. They are as stable as a rock. Literally.
A quadrillion years in the future all the stars will be gone, but the
White Dwarfs will still be here.
Their glow is fossil energy left from their youth as a regular star.
Might die in 1031 years if protons prove to be unstable themselves.
That’s 10,000,000,000,000,000,000,000,000,000,000 years!
Really don’t know if universe will still be here.
Spectroscopy
Spectrum is plot of number of photons as a function of wavelength
Tells us huge amounts about nature of object emitting light.
Thermal Radiation
Planck’s Law
I
2hc 2
1
5 e hc kT  1
Temperature Determines Where Spectrum Peaks
Position of Peak Determines Color
Blue is Hotter than Red
Optically Thick, But hot
Sun
almost “white hot”
Burner “red hot”
Desk
“black hot”
Ice Cube “black hot”
Wien’s Law
Hotter stars peak at bluer wavelengths
 peak
3x10

T
7
Å
(T in Kelvin)
As T rises,  drops
Bluer with temperature
T
300K
5500
106

100,000A
5500
30
Earth
Sun
X-ray source
Question
• How many times smaller would the peak
wavelength be for a star twice as hot as
the Sun? (Remember the sun is 5500K)
• A. Twice as long
• B. Half as long
• C. Four times as long
• D. A fourth as long
Question
• How many times smaller would the peak wavelength be
for a star twice as hot as the Sun? (Remember the sun is
5500K)
λ = (3x107 Å K)/T
Tsun = 5500K
Tstar = 11000K
λstar/λsun = ((3x107 Å K)/Tstar)/ ((3x107 Å K)/Tsun)
= Tsun /Tstar
= 5500K /11000K = 1/2
B. Half as long
Stefan-Boltzman Law
Hotter stars emit more energy per area
L  AT
4
 = 5.67x10-8 W/m2/K4
A is area in m2
T in Kelvins
L is luminosity in W
Example: The Sun
A = 4πr2 = 4 x 3.14 x (7x108 m)2 = 6.2x1018 m2
T = 5500 K
L = (5.7x10-8 W/m2/K4 )x (6.2x1018 m2) x (5500K)4 = 4 x 1026 W
4x1026 Watts = 100 billion billion MegaWatts!!
Question
If you were to double the temperature of the
Sun without changing its radius, by what
factor would its luminosity rise?
a) 2
b) 4
c) 8
d) 16
e) 32
Question
If you were to double the temperature of the
Sun without changing its radius, by what
factor would its luminosity rise?
L = σAT4
A stays the same (radius doesn’t change)
T doubles
L2/L1 = (σA2T24)/(σA1T14) = (T2/T1)4
d.) 16
4
= 2 = 16
Spectral Lines
• Electrons in atoms
have electric
potential energy
• Only specific
energies allowed
• Different for each
type of atom
Emission Lines
• Electron drops to
lower energy level
• Emits photon
Electron Drops
Photon Escapes
Absorption Lines
• Absorbs photon
• Electron rises to higher
energy level
Electron rises
Photon Absorbed
The Doppler Shift
Another Powerful Tool
Frequency of light changes depending on velocity of source.
Similar to sound wave effect
Higher pitch when vehicle approaches
Lower when it recedes.
Spectral Shifts
Spectrum is identifiable as
known element, but lines appear
shifted.
Measure the shift, and we get
velocity information!
Shift to blueward implies approach
Shift to redward implies departure
The Doppler Shift
vt
ct
Observer
D
During t seconds, source emits n waves of wavelength .
They move ct during that time.
But source also moves vt during that time.
So the n waves are scrunched into ct-vt instead of the usual ct
Thus the wavelength is reduced from  to

ct  vt
cv


  1 v
c
ct
c

The Doppler Formula


v
c
  0 1  
 0   V


0
0
c
v is positive if coming toward us
Wavelength  decreases from lab value
 v  v0 V


0
v0
c
Frequency shifts up as source approaches
Doppler Examples
I run toward you with laser at 3m/s
c = 3x108m/s,  = 6328Å
v/c = 10-8
So    x v/c = 6328 x 10-8 = 6.3x10-5
 = 6328.000063Å ---- That’s why we can’t sense a change
Shuttle orbits at 6km/s
v/c = 6/300,000 = 2x10-5
100MHz becomes 100MHz + 108 x 2x10-5 = 100,002,000Hz if coming
at you.
Another Doppler Example
Star has known hydrogen line at 6563Å
Detect line at 6963Å
 = 400Å

400
vc
 300,000
 18,284km / s
0
6563
Star is receding at 18,000km/s !!
In some cases astronomers can detect shifts as small as one part in a million.
That implies detection of motion as small as 300m/s.
What about that #@&! radar gun?
Cop uses radar which typically operates near  = 1cm
If you are going 65mph = 65 mi/hr x 1600m/mi / (3600 s/hr) = 30m/s
This creates a shift of  = 30/3x108 = 10-7 in the wavelength
1cm shifts to .9999999 cm. Not much.
To say you were 5mph over the limit needs to measure one part in 100million!
Example of How Its Used
in Astronomy
Stellar lines are broadened by star’s rotation.
Binary Stars
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Optical Double
appear close together but aren’t really binary
Visual Binary
orbiting, but we can see them both
Astrometric Binary proper motion wiggles to show orbit
Spectrum Binary
spectra of two stars of different type
Spectroscopic Binary Doppler shift shows orbital motion
Eclipsing Binary
light varies
Half of all stars are in binaries….
Binary stars are formed at birth.
Both components will have same age and composition.
Can vary in mass
Can be very distant (0.1pc) or touching
Spectroscopic Binary