ASTR 1200 Announcements

Second problem set due Lecture Notes going up on the website First Exam October 7 Website http://casa.colorado.edu/~wcash/APS1200/APS1200.html

Summary: Sun as a Star

• Formed from cloud 4.6x10

9 years ago • Collapsed to present size – stabilized by nuclear reactions • Emits 4x10 26 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 3x10 20 m 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 = 3x10 8 m/s) That’s one foot per nanosecond One Year is 3.15x10

7 seconds long In one year light travels 3.15x10

7 x3x10 8 = 10 16 m 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 = 3x10 16 m

Origin of parsec comes from method of measuring distance

Each Star Orbits the Center

How Long does that Take?

P

 2 

r

3

GM P

 6 .

28 6 .

7  3

x

10 20

x

10  11

x

2  3

x

10 42  6 .

3 30

x

10 60 13

x

10 31  6 .

3 2 .

5

x

10 29

P

 6 .

3 25

x

10 28  6 .

3

x

5

x

10 14  3

x

10 15 sec

P

 3

x

10 15 sec 3

x

10 7

s

/

yr

 10 8

years

Takes about a hundred million years to circumnavigate the galaxy

v

 2 

r P

 2

x

10 21

m

3

x

10 15

s

 6

x

10 5

m

/

s

 600

km

/

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

1900

Proper Motion

2003 All stars move Nearby stars move faster Appear to move against fixed field Can Take Many Years Use Old Photographic Plates

Parallax

I year cycle

The Parsec

1 parsec 1AU 200,000AU = 1 parsec = 3x10 16 m 1 arcsecond 360 degrees in circle 60 arcminutes per degree 60 arcseconds per arcminute 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=4pd 2 Star Emits N photons per second Brightness is

B



N

4 

d

2 photons/m 2 /s

Brightness (2)

Brightness e.g. 10 -12 Watts/m 2 Simple and easy to understand If your eye is 10 -4 m 2 , then it collects 10 -16 W 4 stars at 10 -12 W/m 2 together have 4x10 -12 W/m 2 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. 1

mag

 5 100  2 .

51 Break the factor of 100 into 5 equal factors: Start with Vega Polaris 2.51x fainter 2.5x fainter than Polaris 2.5x fainter than that etc m=1 m=2 m=3 m=4

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 Full Moon Venus Sirius Vega m=-26.5

m=-13 m=-4 m=-1.5

m=1 Polaris Faintest Visible m=2 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 log 10

d

 5

M

 10  5 log 100  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

Answer

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 e) 100,000,000 20 magnitudes is four factors of 10 2 , which is 10 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 1 Å = 10 -8 cm =10 -10 m about the diameter of an atom.

And 10 Å = 1 nm

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 (10 7 A) 1 mm > l > 10000A 10,000A > l > 3500A 3500A > l 100A > l 0.1A > l > 100A > 0.1A

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

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 = 3x10 8 m/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!!!

v

 1

v

1  

v

2

v

1

v

2

c

2

v

 .

8

c

1   .

8

c

(.

8 ) 2  1 .

6

c

1 .

64  .

975

c

v always less than c per Einstein if velocities << c, then v=v 1 +v 2 (Concept of time and space changes)

l

Frequency

l l l Moves l during each cycle Frequency is the number of cycles per second, n Greek “nu” Moves distance l for each of n ln  cycles each second

c

ln 

c

Frequency (2)

l  n

c

 3

x

10 8

m

/

s

3

x

10 8

Hz

 1

m

300MHz = 1m wavelength n 

c

l  3

x

10 8

m

/

s

5000

x

10  10

m

 6

x

10 14

Hz

Yellow Light = 600 trillion Herz

Question

• An x-ray has a wavelength of 100Å • (10nm, 1x10 -8 m). What is it's frequency, in cycles per second? (aka Hertz) • A. 3x10 16 • B. 1.5x10

16 • C. 3x10 13 • D. 1.5x10

13

Question

• An x-ray has a wavelength of 100Å (10nm, 1x10 -8 m). What is it's frequency, in cycles per second? (aka Hertz) • A. 3x10 16 • B. 1.5x10

16 • C. 3x10 13 • D. 1.5x10

13 • Answer: A. (3E8m/s)/(1E-8m)=3E16 Hz

Energy of a Photon

 

h

n h = 6.63x10

-34 J s Planck’s Constant   6 .

6

x

10  34

x

6

x

10 14  4

x

10  19

J

Sunlight is 10 4 W/m 2 energy of yellow photon Outside we have 10 23 photons/m 2 /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. 1x10 12 • E. 1x10 15 (a trillion) times more powerful.

(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. 1x10 12 (a trillion) times more powerful.

• E. 1x10 15 (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

 2

hc

2 l 5 1

e hc

l

kT

 1 Temperature Determines Where Spectrum Peaks Position of Peak Determines Color

Blue is Hotter than Red

Optically Thick, But hot Sun Burner almost “white hot” “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

 3

x

10 7

T

Å As T rises, l drops Bluer with temperature 300K 5500 10 6 100,000A 5500 30 (T in Kelvin) 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/m 2 /K 4 A is area in m 2 T in Kelvins Example: The Sun L = 5.7x10

-8 x 4 x 3.14 x (7x10 8 m) 2 x (5500K) 4 = 4 x 10 26 W 4x10 26 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 = 2 4 e) 32

Electron Drops

Emission Lines

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.

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 F

Oh Be A Fine Gal { } Guy Kiss Me

G K M

Coolest Each Letter has ten subdivisions from 0 to 9 0 is hottest, 9 is coolest

The Spectral Types

O B A F G K M Stars of Orion's Belt Rigel Sirius Polaris Sun, Alpha Centauri A Arcturus Betelgeuse, Proxima Centauri >30,000 K 30,000 K 10,000 K 10,000 K-7,500 K 7,500 K 6,000 K 6,000 K 5,000 K 5,000 K 3,500 K Lines of ionized helium, weak hydrogen lines Lines of neutral helium, moderate hydrogen lines Very strong hydrogen lines Moderate hydrogen lines, moderate lines of ionized calcium Weak hydrogen lines, strong lines of ionized calcium Lines of neutral and singly ionized metals, some molecules <3,500 K Molecular lines strong *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.

<97 nm (ultraviolet)* 97-290 nm (ultraviolet)* 290-390 nm (violet)* 390-480 nm (blue)* 480-580 nm (yellow) 580-830 nm (red) >830 nm (infrared)

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