### Lecture 7

```ASTR 1200
Announcements
Second problem set due
Lecture Notes going up on the website
First Exam October 7
Website
Summary: Sun as a Star
• Formed from cloud 4.6x109 years ago
• Collapsed to present size
– stabilized by nuclear reactions
•
•
•
•
•
•
•
Emits 4x1026 W
Runs on proton-proton chain and CNO cycle
Now 20% brighter
Turbulent upper envelope
Magnetic Fields from Differential Rotation
Sunspots, Corona, Solar Wind
Activity Cycle 11 years
Stars are grouped in Galaxies
• Sun and all the stars we see are part of
Milky Way Galaxy
• We all orbit a common center
• Sun is 3x1020m from center of MW
You are here
Each star orbits
center
Disk Stability Again
The Light Year
Light Travels at 300,000km/s (186,000miles/s = 3x108m/s)
That’s one foot per nanosecond
One Year is 3.15x107 seconds long
In one year light travels 3.15x107x3x108 = 1016m
This is the definition of a light year. Prox Cen is at 4ly.
The Parsec
Astronomers use the parsec as a measure of distance
1pc = 3ly
1pc = 3x1016m
Origin of parsec comes from method of measuring
distance
Each Star Orbits the Center
How Long does that Take?
r3
P  2
GM
P  6.28
3x10 
20 3
6.7 x10 11 x 2 x10 42
30 x10 60
 6. 3
 6.3 2.5 x10 29
31
13 x10
P  6.3 25x1028  6.3x5x1014  3x1015 sec
3x1015 sec
8
P

10
years
7
3x10 s / yr
Takes about a hundred million years to circumnavigate the galaxy
2r 2 x1021 m
v

 6 x105 m / s  600km / s
15
P
3x10 s
Star Names
• Arabic Names
– Antares, Capella, Mira, etc.
• Constellations
a Orionis, b Cygni, … then 49 Ori, 50 Ori, etc.
• Catalogues HD80591, SAO 733421, etc
• RA and Dec – just position in the sky
Proper Motion
2003
All stars move
Nearby stars move faster
Appear to move against fixed field
1900
Can Take Many Years
Use Old Photographic Plates
Parallax
I year cycle
The Parsec
1 parsec
1AU
1 arcsecond
360 degrees in circle
60 arcminutes per degree
60 arcseconds per arcminute
200,000AU = 1 parsec = 3x1016m
parsec ---- parallax second
Brightness
Around the sky stars vary in brightness and in color.
Brightness is the result of two factors
1. Intrinsic Luminosity
2. Distance
d
Each Sphere has
area A=4pd2
Brightness is
Star Emits N photons
per second
N
B
4d 2
photons/m2/s
Brightness (2)
Brightness e.g. 10-12 Watts/m2
Simple and easy to understand
If your eye is 10-4m2, then it collects 10-16W
4 stars at 10-12W/m2 together have 4x10-12W/m2
But this would be too easy for astronomers.
We use a brightness system invented by Ptolemy in the 400’s
The Magnitude System
Ptolemy Broke Stars into 5 magnitude groups
m=1 the brightest, m=5 the faintest
In 1700’s it was found this was a logarithmic scale, as that is how
the naked eye responds. Also, faintest were about 100x fainter than
brightest.
Break the factor of 100 into 5 equal factors:
Polaris 2.51x fainter
2.5x fainter than Polaris
2.5x fainter than that
etc
m=1
m=2
m=3
m=4
1mag  5 100  2.51
Magnitudes (2)
Every 5 magnitudes is a factor of 100
m=5 is 100 times fainter than m=0
m=10 is 100x100 =10,000 times fainter than m=0
m=15 is (100)3 = 1million times fainter than m=0
Sun
m=-26.5
Full Moon
m=-13
Venus
m=-4
Sirius
m=-1.5
Vega
m=1
Polaris
m=2
Faintest Visible m=6
Faintest Detected m=28
Works only in the visible.
Really inconvenient in modern astronomy because we
observe across the spectrum from radio to gamma rays.
Absolute Magnitude
The magnitude a star would have were it at 10pc
We see a star of magnitude m=10 at 100 pc.
What would be its magnitude (M) if it were at 10 pc instead of 100pc?
At 10 times closer the star would be 100x brighter = 5 magnitudes
M = 10-5 = 5
M  m  5 log10 d  5
M  10  5 log100 5  10  10  5  5
Clicker
A 5 magnitude difference means a factor of
100 in flux. By what factor do the fluxes
differ between two stars of 20
magnitudes difference?
a) 2.51
b) 20
c) 400
d) 10,000
e) 100,000,000
5magnitudes difference is a factor of 100. By
what factor do the fluxes differ between
two stars of 20 magnitudes difference
a) 2.51
b) 20
c) 400
d) 10,000
20 magnitudes is four factors of 10 ,
which is 10
e) 100,000,000
2
8
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
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
Clicker
• 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
• 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
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 5000x10 m
c
Yellow Light = 600 trillion Herz
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
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
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.
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: 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.
Planck’s Law
I
2
2hc
1
l5 ehc 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
7
3x10

T
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
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: 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
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 = 24
e) 32
Emission Lines
Electron Drops
Energy Levels 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
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
Stars Come in Different Colors
Stellar Temperature
Stars come in different sizes and temperatures.
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
F
G
K
Gal
Kiss Me
Guy
{ }
Oh Be A Fine
Each Letter has ten subdivisions from 0 to 9
0 is hottest, 9 is coolest
M
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
```