ASTR 1020 – January 28 Second Homework Due Thursday (Feb 9) Next Observatory opportunity tomorrow (Feb 8) @ 7pm Planetarium on Feb 14 First Exam Feb 21 Today: Stars Website http://casa.colorado.edu/~wcash/APS1020/APS1020.html

Stars are grouped in Galaxies Sun and all the stars we see are part of the 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

Distances to the Stars Closest Star, Proxima Centauri is 4.2x1016m away. (Alpha Cen ~4.3x1016m) Need a more convenient unit

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.

Question There’s a big black hole in the Center of the Milky Way at a distance of 3x1020m. How long does it take for its light to reach us? A) 3years B) 30 years C) 300 years D) 3000 years E) 30,000 years

Answer There’s a big black hole in the Center of the Milky Way at a distance of 3x1020m. How long does it take for its light to reach us? A) 3years B) 30 years C) 300 years D) 3000 years E) 30,000 years

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? Takes about a hundred million years to circumnavigate the galaxy

Star Names Arabic Names Constellations 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 Can Take Many Years Use Old Photographic Plates 1900

Parallax I year cycle

The Parsec 1 parsec 360 degrees in circle 60 arcminutes per degree 1AU 1 arcsecond 360 degrees in circle 60 arcminutes per degree 60 arcseconds per arcminute 200,000AU = 1 parsec = 3x1016m parsec ---- parallax second

Question Based on the definition of a parsec , if star A has a parallax of 0.5 arcseconds and star B has a parallax of 0.75 arcseconds which one is farther from the Earth? A. Star B is farther away because it has a higher parallax B. Star A is farther away because it has a lower parallax C. All stars are the same distance away from the Earth D. It is impossible to tell from this information.

Answer Based on the definition of a parsec , if star A has a parallax of 0.5 arcseconds and star B has a parallax of 0.75 arcseconds which one is farther from the Earth? A. Star B is farther away because it has a higher parallax B. Star A is farther away because it has a lower parallax C. All stars are the same distance away from the Earth D. It is impossible to tell from this information.

Measure Parallax distance to a star in parsecs = 1/(parallax in arcseconds) e.g. measure .04” parallax, then distance is 25pc Measuring Parallax was first successful way to measure distances to stars after centuries of trying Took high speed photography in 1890’s to do it.

Question The parallax of an observed star is 0.1 arcseconds, how many light years is it away from Earth? a. 1 light year b. 3 light years c. 10 light years d. 30 light years e. 75 light years

Question The parallax of an observed star is 0.1 arcseconds, how many light years is it away from Earth? a. 1 light year b. 3 light years c. 10 light years d. 30 light years (10parsecs) e. 75 light years

Brightness Around the sky stars vary in brightness and in color. Brightness is the result of two factors 1. Intrinsic Luminosity 2. Distance Each Sphere has area A=4d2 d Brightness is Star Emits N photons per second 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

Question If the distance between Earth and the Sun were cut in half, how much brighter would the sun appear in our sky? a. 2x brighter b. 4x brighter c. 8x brighter d. 16x brighter

Answer If the distance between Earth and the Sun were cut in half, how much brighter would the sun appear in our sky? a. 2x brighter b. 4x brighter c. 8x brighter d. 16x brighter Brightness is a function of the inverse square of distance, so if distance was cut by half it would get brighter by 4x=1/(.5)2

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: Start with Vega m=1 Polaris 2.51x fainter m=2 2.5x fainter than Polaris m=3 2.5x fainter than that m=4 etc

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

Question 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? 2.51 20 400 10,000 100,000,000

Answer 5magnitudes difference is a factor of 100. By what factor do the fluxes differ between two stars of 20 magnitudes difference 2.51 20 400 10,000 100,000,000 20 magnitudes is four factors of 102, which is 108

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