1	Astro 1050 Wed. Sep. 25, 2002 Today: Finish Chapter 6 –Starlight and Atoms Review
2	Planck and other Formulae Planck formula gives intensity of light at each wavelength It is complicated. We’ll use two simpler formulae which can be derived from it. Wien’s law tells us what wavelength has maximum intensity Stefan-Boltzmann law tells us total radiated energy per unit area
3	Example of Wien’s law What is wavelength at which you glow? Room T = 300 K so This wavelength is about 20 times longer than what your eye can see. Camera in class operated at 7-14 μm. What is temperature of the sun – which has maximum intensity at roughly 0.5 mm?
4	Example of the Stefan-Boltzmann law Suppose a brown-out causes the temperature of a lamp filament to drop to 0.9 of its original value. By what factor does the light output of the lamp drop? Using the Stefan-Boltzmann law (with the numerical value of s) we could have calculated how big (in m²) a light filament would have to be to emit 100 W of light, at any given temperature. We could also use it to find the size of a star, if we know how much light energy that star emitted
5	Kirchoff’s laws Hot solids emit continuous spectra Hot gasses try to do this, but can only emit discrete wavelengths Cold gasses try to absorb these same discrete wavelengths In stars we see absorption lines – what does that tell us? Stars have “atmospheres” of gasses Stars must be colder on the outside, hotter on the inside
6	Funny?!
7	Hydrogen Lines Energy absorbed/emitted depends on upper and lower levels Higher energy levels are close together Above a certain energy, electron can escape (ionization) Series of lines named for bottom level To get absorption, lower level must be occupied Depends upon temperature of atoms To get emission, upper level must be occupied Can get down-ward cascade through many levels
8	Which levels will be occupied? The higher the temperature, the higher the typical level Collisions can knock electrons to higher levels, if moving atoms have enough kinetic energy At T ~ 300 K (room T) almost all H in ground state (n=1) At T ~ 10,000 K many H are in first excited state (n=2) At T ~ 15,000 K many H are ionized Because you have highest n=2 population at ~10,000K you also have highest Balmer line strength there. This gives us another way to estimate temperatures of stars
9	Sense larger T range using many atoms Different atoms hold on to electrons with different force Use weakly held electrons to sense low temperatures (Fe, Ca, TiO) TiO molecule is destroyed above 4000K Ca has lost 1 electron by ~5000K, but still has others to give lines Use moderately held electrons to sense middle temperatures (H) Below 6000 K most H electrons in lowest state – can’t cause Balmer lines Above 15,000K most H electrons completely lost (ionized) Use tightly held electrons to sense high temperatures (He, ionized He) Below 10,000K most He electrons in ground state – just like H, no visible absorption lines Above 15,000K most H has lost one electron, but still has a second one to cause absorptions
10	Classification of stars O B A F G K M scheme Originally in order of H strength – A,B,etc Above order is for decreasing temperature Standard mnemonic: Oh, Be A Fine Girl (Guy), Kiss Me Use numbers for finer divisions: A0, A1, ... A9, F0, F1, ... F9, G0, G1, ...
11	Composition of Stars Somewhat complicated – we must correct for temperature effects Regular pattern: More of the simplest atoms: H, then He, ... Subtle patterns later – related to nuclear fusion in stars
12	Doppler effect Effect similar in light and sound Waves compressed with source moving toward you Sound pitch is higher, light wavelength is smaller (bluer) Waves stretched with source moving away from you Sound pitch is lower, light wavelength is longer (reder) v = velocity of source c = velocity of light (or sound) l = apparent wavelength of light l_o = original wavelength of light
13	Doppler effect examples Car with horn blowing, moving away from you at 70 MPH. Speed of sound is ~700 MPH = 1000 ft/sec Original horn pitch is 200 cycles/sec Þ l_o ~ 5 ft Star moving toward you at 200 km/sec = 2.0´10⁵ m/s Speed of light c = 3.00 ´ 10⁸ m/s Original Ha l_o= 0.65647 mm
14	Review Topics (chapters 1-6) Chapter 1 – Scales of the Cosmos Relative sizes, distances, Earth to Universe Scientific Notation Units (e.g., Light Years) Don’t memorize numbers but do have a feel for these topics
15	Review Topics (chapters 1-6) Chapter 2 – The Sky Constellations Brightness of Stars (Magnitude Scale) Celestial Sphere Precession In general, motion of stars in sky from any position on Earth from understanding the tilt and rotation of Earth
16	Review Topics (chapters 1-6) Chapter 3 – Cycles of the Sky The Seasons Path of Sun as a function of season Phases of the Moon Tidal Forces Eclipses Small Angle Formula
17	Review Topics (chapters 1-6) Chapter 4 – Cycles of the Sky Greek view of Universe (and why!) Copernican Revolution (Sun in Center) Tycho, Kepler and Kepler’s Laws Galileo’s Telescopic Observations Newton’s Laws of Motion/Gravity
18	Review Topics (chapters 1-6) Chapter 5 – Astronomical Tools Electromagnetic Radiation/Energy Spectrum Resolution of Telescopes Ground vs. Space Telescopes Telescopes at different wavelengths Spectrographs and light spectra
19	Review Topics (chapters 1-6) Chapter 6 – Atoms and Starlight Properties of Atoms Black Body Radiation Application to Spectra of Stars Kirchhoff’s Laws Emission/Absorption Lines Spectral classes/temperatures Doppler Effect