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

The Exammean 70.4, median 71.2Standard deviation 13.1

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

Earth vs White Dwarf

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!

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?

Escape Velocity

smxxx

xxxxR

GMVe /106104107

102107.622 6136

3011

Speed of light is 3x108 m/s, so escape velocity is .02c.

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

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!

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.

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 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.

Spectroscopy

Spectrum is plot of number of photons as a function of wavelengthTells us huge amounts about nature of object emitting light.

Thermal Radiation

1

125

2

kThc

e

hcI

Planck’s Law

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

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

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

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

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

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

Spectral Lines

• Electrons in atoms have electric potential energy

• Only specific energies allowed

• Different for each type of atom

Emission LinesElectron Drops

Photon Escapes

• Electron drops to lower energy level

• Emits photon

Absorption Lines

• Absorbs photon• Electron rises to higher

energy level

Electron rises

Photon Absorbed

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.

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

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

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

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.

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.

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 Usedin Astronomy

Stellar lines are broadened by star’s rotation.

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

Spectroscopic Binary