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 RED 7000Å YELLOW 5500Å VIOLET 4000Å 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 7000Å YELLOW 5500Å VIOLET 4000Å

Electromagnetic Spectrum visible is tiny chunk of em spectrum

Parts of EM Spectrum Radio l > 1mm (107A) Infrared 1mm> l > 10000A Visible 10,000A > l > 3500A Ultraviolet 3500A > l > 100A X-ray 100A > l > 0.1A Gamma-ray 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 NO!!! .8c .8c Clearly Approaching each other at 1.6c v always less than c if velocities << c, then v=v1+v2 per Einstein (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 Greek “nu” Moves distance l for each of n cycles each second

Frequency (2) 300MHz = 1m wavelength 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 h = 6.63x10-34 J s Planck’s Constant energy of yellow photon Sunlight is 104 W/m2 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 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? White Yellow Orange Red

Wien’s Law Å As T rises, l drops Bluer with temperature (T in Kelvin) 300K 100,000A Earth 5500 5500 Sun 106 30 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 s = 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? 2 4 8 16 32

Answer If you were to double the temperature of the Sun without changing its radius, by what factor would its luminosity rise? 2 4 8 16 = 24 32

Emission Lines Electron Drops Energy Levels of H Photon Escapes Can Only Happen Between Certain Pre-determined orbitals Spectrum of Hydrogen Each Element Has Different Orbitals So Each Element Has Different Lines

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 F G K M Coolest { Gal } Oh Be A Fine Kiss Me Guy Each Letter has ten subdivisions from 0 to 9 0 is hottest, 9 is coolest

The Spectral Types O Stars of Orion's Belt >30,000 K Lines of ionized helium, weak hydrogen lines <97 nm (ultraviolet)* B Rigel 30,000 K-10,000 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 K-6,000 K Moderate hydrogen lines, moderate lines of ionized calcium 390-480 nm (blue)* G Sun, Alpha Centauri A 6,000 K-5,000 K Weak hydrogen lines, strong lines of ionized calcium 480-580 nm (yellow) K Arcturus 5,000 K-3,500 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) *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 G2 a Cen G2 + K5 Sirius A1 Antares M1 Rigel B8 O5 40,000K B5 15,500 A5 8500 F5 6580 G5 5520 K5 4130 M5 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

The Doppler Formula v is positive if coming toward us Wavelength l decreases from lab value 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 dl = 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 dl = 400Å 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 dl = 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 The H-R Diagram 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

The H-R Diagram Plot of Brightness vs Temperature -5 Rigel Giants Capella Sirius Brightness Procyon Sun Main Sequence +5 a Cen B White Dwarfs +10 Sirius B Prox Cen +15 O B A F G K M Spectral Type

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 sAT4 T constant on any vertical line

Newly Formed Star M Spectral Type O +10 +5 -5 +15 B A F G K Protostar +15 B A F G K Sun Sirius a Cen B Prox Cen Procyon Rigel Capella Sirius B Main Sequence Giants White Dwarfs Protostar Large, Low T. Settles down to MS Then sits while burning H

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 in solar masses L in solar luminosities

Some Lifetimes Mass Luminosity Lifetime in Billion Years Sun 1 1 10 Sirius 2 10 2 Prox Cen .4 .001 4000 Rigel 8 10,000 .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