astr 1200 announcements website exams are at the back. please pick up. still have a calculator left
DESCRIPTION
White Dwarfs Held up by electron degeneracy About the size of the Earth R~5000km Mass Typically 0.8M Luminosity ~.001 L Degenerate Carbon Thin layer of “normal” HTRANSCRIPT
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ASTR 1200Announcements
Websitehttp://casa.colorado.edu/~wcash/APS1200/APS1200.html
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
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The Exammean 70.4, median 71.2Standard deviation 13.1
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White Dwarfs
• Held up by electron degeneracy• About the size of the Earth R~5000km• Mass Typically 0.8M
• Luminosity ~ .001 L
Degenerate Carbon
Thin layer of “normal” H
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Earth vs White Dwarf
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WD Density
ccgxxx
x
R
M /105.1)107(4
102
34
638
33
3
Water has a density of 1 g/ccLead 11 g/ccGold 19 g/cc
100,000 times density of gold!
NOT NORMAL MATTER!!
1 cubic centimeter masses one ton!
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Surface Gravity
2626
3011
2 /103)107(102107 smx
xxxx
RGMa
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?
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Escape Velocity
smxxx
xxxxR
GMVe /106104107
102107.622 6136
3011
Speed of light is 3x108 m/s, so escape velocity is .02c.
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Gravitational RedshiftEven light loses energy climbing out of this hole.
2mcR
GMm = 2x10-4
At 5000Å have 1Å shift to red
Looks like a 60km/s Doppler Shift
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Magnetic Field
30
RRBB o
When a star shrinks from 109m to 107m 1000 RR
So B increases from 1Gauss to a Million Gauss
A million Gauss can rip normal matter apart!
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Chandrasekhar LimitA peculiarity of Degeneracy Pressure is that it has a maximum mass.
Each electron added must find its own quantum state by having itsown 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.
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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.
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Immortal Stars
Regular stars need thermal pressure to balance gravity, and theyneed nuclear reactions to maintain the pressure, so the die when theyrun 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 theWhite 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.
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Spectroscopy
Spectrum is plot of number of photons as a function of wavelengthTells us huge amounts about nature of object emitting light.
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Thermal Radiation
1
125
2
kThc
e
hcI
Planck’s Law
Temperature Determines Where Spectrum Peaks
Position of Peak Determines Color
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Blue is Hotter than Red
Optically Thick, But hot
Sun almost “white hot”Burner “red hot”Desk “black hot”Ice Cube “black hot”
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Wien’s Law
Tx
peak
7103
As T rises, dropsBluer with temperature
Å (T in Kelvin)
T 300K 100,000A Earth5500 5500 Sun106 30 X-ray source
Hotter stars peak at bluer wavelengths
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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
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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
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Stefan-Boltzman Law
4ATL = 5.67x10-8 W/m2/K4
A is area in m2
T in Kelvins
Example: The Sun
L = (5.7x10-8 W/m2/K4 )x (6.2x1018 m2) x (5500K)4 = 4 x 1026 W
4x1026 Watts = 100 billion billion MegaWatts!!
A = 4πr2 = 4 x 3.14 x (7x108 m)2 = 6.2x1018 m2
L is luminosity in W
T = 5500 K
Hotter stars emit more energy per area
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Question
If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise?
a) 2b) 4c) 8d) 16e) 32
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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 doublesL2/L1 = (σA2T2
4)/(σA1T14) = (T2/T1)4
= 24 = 16 d.) 16
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Spectral Lines
• Electrons in atoms have electric potential energy
• Only specific energies allowed
• Different for each type of atom
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Emission LinesElectron Drops
Photon Escapes
• Electron drops to lower energy level
• Emits photon
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Absorption Lines
• Absorbs photon• Electron rises to higher
energy level
Electron rises
Photon Absorbed
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The Doppler ShiftAnother Powerful Tool
Frequency of light changes depending on velocity of source.
Similar to sound wave effectHigher pitch when vehicle approachesLower when it recedes.
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Spectral Shifts
Spectrum is identifiable asknown element, but lines appearshifted.
Measure the shift, and we getvelocity information!
Shift to blueward implies approachShift to redward implies departure
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The Doppler Shiftvt
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 cv
cvc
ctvtct
1
ct
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The Doppler Formula
cv10
cV
0
0
0
v is positive if coming toward us
Wavelength decreases from lab value
cV
vvv
0
0
0
Frequency shifts up as source approaches
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Doppler ExamplesI run toward you with laser at 3m/sc = 3x108m/s, = 6328Åv/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/sv/c = 6/300,000 = 2x10-5
100MHz becomes 100MHz + 108 x 2x10-5 = 100,002,000Hz if comingat you.
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Another Doppler Example
Star has known hydrogen line at 6563ÅDetect line at 6963Å
= 400Å
skmcv /284,186563400000,300
0
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.
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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!
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Example of How Its Usedin Astronomy
Stellar lines are broadened by star’s rotation.
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Binary Stars• 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 Binarylight 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 massCan be very distant (0.1pc) or touching
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Spectroscopic Binary