Download Lecture 7 February 9

ASTR 1020 – February 9
.
Second Homework Due Today
Planetarium Next Tuesday Feb 14
First Exam Feb 21
Website
http://casa.colorado.edu/~wcash/APS1020/APS1020.html
Nature of Light
Light is a flux of particles called photons
Each photon is both a particle and a wave (a packet of waves)
250 years after Newton we still don’t understand it
Electromagnetic Theory (Maxwell’s Equations) 1860’s
Quantum Electrodynamics 1948 Feynman
Each photon has:
direction
wavelength
polarization
Light Waves
l
lambda is lower case Greek L
stands for length
Each photon is a sine wave moving at the speed of light
Wavelength is usually measure in Angstroms
1Å = 10-8cm =10-10m
about the diameter of an atom.
And 10Å = 1nm
Electric and Magnetic
Fields Sloshing Back
And Forth
Color
Wavelength Determines Color of Light
Color is the eye’s response to different wavelengths
Color is a physiological effect
A photon can have any wavelength
RED
YELLOW
VIOLET
7000Å
5500Å
4000Å
Electromagnetic Spectrum
visible is tiny chunk of em spectrum
Parts of EM Spectrum
Radio
Infrared
Visible
Ultraviolet
X-ray
Gamma-ray
l > 1mm (107A)
1mm> l > 10000A
10,000A > l > 3500A
3500A > l > 100A
100A > l > 0.1A
0.1A > l
Question
• What range of wavelength can the average
human eye see and what color is each side of
the spectrum?
A) 400nm-800nm, redder to bluer
B) 500nm-700nm, bluer to redder
C) 400nm-700nm, bluer to redder
D) 300nm-600nm, redder to bluer
E) None of the above
Answer
• What range of wavelength can the average human eye
see and what color is each side of the spectrum?
A) 400nm-800nm, redder to bluer
B) 500nm-700nm, bluer to redder
C) 400nm-700nm, bluer to redder
D) 300nm-600nm, redder to bluer
E) None of the above
Answer: C
Speed of Light
Speed of Light c = 3x108m/s
That’s a very odd statement
2 cars at 65mph
1 car at 130mph
Cover same distance in same amount of time
The Relative speeds are the same
Relativity
.8c
.8c
Clearly Approaching each other at 1.6c
NO!!!
v1  v2
v=
v1v2
1 2
c
per Einstein
v=
.8c  .8c 1.6c
=
= .975c
2
1  (.8)
1.64
v always less than c
if velocities << c, then v=v1+v2
(Concept of time and space changes)
Frequency
l
l
l
l
Moves l during each cycle
Frequency is the number of cycles per second,
n
Moves distance l for each of n cycles each second
ln = c
Greek “nu”
Frequency (2)
ln = c
3x108 m / s
l= =
= 1m
8
n 3x10 Hz
c
300MHz = 1m wavelength
3x108 m / s
14
n= =
=
6
x
10
Hz
10
l 5000 x10 m
c
Yellow Light = 600 trillion Hertz
Question
• An x-ray has a wavelength of 100Å
• (10nm, 1x10-8m). What is it's frequency, in
cycles per second? (aka Hertz)
• A. 3x1016
• B. 1.5x1016
• C. 3x1013
• D. 1.5x1013
Answer
• An x-ray has a wavelength of 100Å
(10nm, 1x10-8m). What is it's frequency, in
cycles per second? (aka Hertz)
• A. 3x1016
• B. 1.5x1016
• C. 3x1013
• D. 1.5x1013
• Answer: A. (3E8m/s)/(1E-8m)=3E16 Hz
Energy of a Photon
 = hn
h = 6.63x10-34 J s
Planck’s Constant
 = 6.6 x10 34 x6 x1014 = 4 x10 19 J
Sunlight is 104 W/m2
energy of yellow photon
Outside we have 1023 photons/m2/s hit us
Question
• How many times more energy is there in an
x-ray photon at 100A than the infrared light
photons emitted by every living human?
(Assuming 10,000nm wavelength of infrared
light).
• A. Ten times as powerful.
• B. A hundred times more powerful.
• C. A thousand times more powerful.
• D. 1x1012 (a trillion) times more powerful.
• E. 1x1015 (a quadrillion) times more powerful.
Answer
• How many times more energy is there in an
x-ray photon at 100A than the infrared light photons
emitted by every living human? (Assuming 10,000nm
wavelength of infrared light).
• A. Ten times as powerful.
• B. A hundred times more powerful.
• C. A thousand times more powerful.
• D. 1x1012 (a trillion) times more powerful.
• E. 1x1015 (a quadrillion) times more powerful.
• Answer: C. 10,000nm/10nm = 1000
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
l5 e hc lkT  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”
Question
A star with a temperature of 100,000K has
what color to the naked eye?
a) White
b) Yellow
c) Orange
d) Red
Wien’s Law
l peak
3x10
=
T
7
Å
(T in Kelvin)
As T rises, l drops
Bluer with temperature
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
Answer
• 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
• Answer: B. Since peak wavelength is a function of the
inverse of temperature, doubling the temp of a star
would cause it's peak wavelength to cut in half.
Stefan-Boltzman Law
L = AT
4
 = 5.67x108 W/m2/K4
A is area in m2
T in Kelvins
Example: The Sun
L = 5.7x10-8 x 4 x 3.14 x (7x108m)2 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
Answer
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 = 24
e) 32
Emission Lines
Electron Drops
Enrgy Lvl of H
Photon Escapes
Can Only Happen Between
Certain Pre-determined orbitals
Each Element Has Different Orbitals
So Each Element Has Different Lines
Spectrum of Hydrogen
Absorption Lines
Light moving through cold
gas can have photons removed.
Creates dark wavelengths
called absorption lines
Question
A star is viewed through a far away
hydrogen gas cloud, what kind of
spectrum can we expect to see?
A) Absorption only
B) Emission only
C) Continuum only
D) Emission and Continuum
E) Absorption and Continuum
Answer
A star is viewed through a far away
hydrogen gas cloud, what kind of
spectrum can we expect to see?
A) Absorption only
B) Emission only
C) Continuum only
D) Emission and Continuum
E) Absorption and Continuum
Stars Come in Different Colors
Stellar Temperature
Stars come in different sizes and temperatures.
Can the two be linked?
Question
You see three stars up in the sky. One is
bigger than the others and red, one is
yellow, and one is white. Which one
peaks at a higher frequency?
• A)Red
• B)Yellow
• C)White
• D)I need to know how far away they are
Question
You see three stars up in the sky. One is
bigger than the others and red, one is
yellow, and one is white. Which one
peaks at a higher frequency?
• A)Red
• B)Yellow
• C)White
• D)I need to know how far away they are
Stellar Classification
Full range of surface temperatures from 2000 to 40,000K
Spectral Classification is Based on Surface Temperature
Hottest
O
B
A
Oh Be A Fine
F
G
K M
Gal
Guy
{ } Kiss Me
Each Letter has ten subdivisions from 0 to 9
0 is hottest, 9 is coolest
Coolest
The Spectral Types
Stars of
Orion's Belt
>30,000
K
Lines of ionized helium, weak
hydrogen lines
<97 nm
(ultraviolet)*
B
Rigel
30,000
K10,000
K
Lines of neutral helium,
moderate hydrogen lines
97-290 nm
(ultraviolet)*
A
Sirius
10,000
K-7,500
K
Very strong hydrogen lines
290-390 nm
(violet)*
F
Polaris
7,500 K6,000 K
Moderate hydrogen lines,
moderate lines of ionized
calcium
390-480 nm
(blue)*
G
Sun, Alpha
Centauri A
6,000 K5,000 K
Weak hydrogen lines, strong
lines of ionized calcium
480-580 nm
(yellow)
K
Arcturus
5,000 K3,500 K
Lines of neutral and singly
ionized metals, some
molecules
580-830 nm
(red)
M
Betelgeuse,
Proxima
Centauri
<3,500
K
Molecular lines strong
>830 nm
(infrared)
O
*All stars above 6,000 K look more or less white to the human eye
because they emit plenty of radiation at all visible wavelengths.
Stellar Classification (2)
Sun
a Cen
Sirius
Antares
Rigel
G2
G2 + K5
A1
M1
B8
O5
B5
A5
F5
G5
K5
M5
40,000K
15,500
8500
6580
5520
4130
2800
Letters are odd due to confusion in sorting out temperature scale
between 1900 and 1920
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 l.
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 l to

ct  vt
cv
l
=l
= l 1 v
c
ct
c

The Doppler Formula


v
c
l = l0 1  
l l0  l V
=
=
l0
l0
c
v is positive if coming toward us
Wavelength l decreases from lab value
n v  v0 V
=
=
n0
v0
c
Frequency shifts up as source approaches
Doppler Examples
I run toward you with laser at 3m/s
c = 3x108m/s, l = 6328Å
v/c = 10-8
So l = l x v/c = 6328 x 10-8 = 6.3x10-5
l = 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
l = 400Å
l
400
v=c
= 300,000
= 18,284km / s
l0
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 l = 1cm
If you are going 65mph = 65 mi/hr x 1600m/mi / (3600 s/hr) = 30m/s
This creates a shift of l = 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.
Stellar Luminosity
By 1915 had lots of spectra and classifications
Had a few distances from parallax
Once distance was available, luminosity and Absolute Magnitude
could be calculated.
Herzsprung and Russel, working independently both plotted
absolute magnitude (luminosity) vs classification (temperature)
The H-R Diagram
Plot of Brightness vs Temperature
-5
Giants
Rigel
Capella
Brightness
0
Sirius
Procyon
Sun
+5
Main Sequence
a Cen B
White Dwarfs
+10
Sirius B
Prox Cen
+15
O
B
A
F
G
Spectral Type
K
M
The H-R Diagram
The Main Sequence
Stars Differ By:
Mass
Age
Composition
Nothing else!
And composition doesn’t vary
Age and Mass only.
Those on main sequence are all
burning H so age drops out.
MS is function of MASS only!!!
Full, Artistic H-R
As mass of
MS star increases,
both R and T
increase
increasing
size
AT4
T constant
on any vertical
line
Newly Formed Star
-5
Giants
Rigel
Capella
0
M
Sirius
Protostar
Procyon
Sun
+5
Main Sequence
Then sits while
burning H
a Cen B
White Dwarfs
+10
Sirius B
Prox Cen
+15
O
B
A
F
G
Spectral Type
K
Large,
Low T.
Settles down
to MS
M
MS Lifetime
What determines amount of time a star stays on Main Sequence?
Just like a kerosene heater: Amount of fuel and rate of burn.
More Mass = More Fuel
More Luminosity = Greater Burn Rate
We can scale from the Sun: M = 1M
L = 1L
Sun lasts 1010 years
M
MSLife = 10
L
10
M in solar masses
L in solar luminosities
Some Lifetimes
Sun
Sirius
Prox Cen
Rigel
Mass
Luminosity
Lifetime in Billion Years
1
2
.4
8
1
10
.001
10,000
10
2
4000
.008
Dinky little stars like Prox Cen will last trillions of years
Huge stars like Rigel are gone in a few million
There aren’t many large stars out there, because they don’t last.
10,000 O stars of the 100,000,000,000 Milky Way stars