Oct. 11, Review: BB radiation enables measure of both stellar temperature T, and surface flux, F s The shift of the peak λ, to have a maximum flux (brightness) at wavelength λ max, allows the BB spectrum temperature to be directly measured since Wien’s Law relates the two: λ max = /T (for λ max in meters) or λ max = 2.95 x 10 6 /T (for λ max in nm, more usual unit) So Sun, with surface temp. T = 5500K, has λ max = 540nm The energy flux of the BB source (as measured per unit area on its surface) is proportional to the temperature T to 4 th power, by the Stefan-Boltzmann Law: F s = σ T 4 where σ = 5.7 x W/(m 2 - K 4 ) where K is the temperature in degrees Kelvin (note: σ = 5.7 x erg/(cm 2 - sec - K 4 ) if you use cm units instead or m for R and erg/sec instead of W) The total energy flux emitted from a BB source of radius R is its luminosity: L = 4πR 2 F s = 4πR 2 σ T 4 The total energy flux detected from a BB source with luminosity L at distance d is F = L / 4πd 2 (this is the inverse square law for light) NOTE: must distinguish surface flux, F s, from detected flux which we will call F

Oct. 11, How can we “scale” from Sun to T & R for stars? The wonders of BB radiation (so simple!) allow us to do direct “measurements” of stellar temperature, T, (on surface of a star) and the radius, R, of that stellar surface (= radius of star): –Measure star color (by using filters; discuss next week…) to first estimate λ max and thus T from Wien law –Use known (from parallax) distance of star and inverse square law to estimate luminosity, L, from measured flux, F –Use Stefan-Boltzmann law to estimate R from L and T Practice this with examples as in Box 5-2 in Text… You don’t need to “know” the constants (e.g. σ); just use RATIOS and the fundamental L ~ R 2 T 4 relation to scale from the values for the Sun

Oct. 11, On to spectra of light from the elements A given element (Hydrogen, Helium…. Iron) is composed of atoms with a well defined structure: nucleus (protons+neutrons) surrounded by a “cloud” of orbiting electrons in fixed orbits at discrete energy levels n = 1, 2, etc. as shown for H below: Electrons can only “Jump” from one n value to another and either lose (if n decreases) or gain (if n increases) energy. That energy loss/gain produces spectral lines in emission (energy given from electron to light) or absorption (energy given from the light to the electron) Energy levels in H Atom for Bohr model

Oct. 11, Spectral lines provide composition of Stars Each element (H…. Fe… U) has unique spectral lines since electron orbits differ since total electron number differs Light from the stars (Sun, Vega, etc.) show spectral lines primarily in absorption (dark lines) due to light from “hot” surface (BB continuum) shining up through “cooler” overlying stellar atmosphere. Corona (outermost “atmosphere”) of the Sun, visible in solar eclipse, shows spectral lines in emission since hot gas not shining through cool gas and since no BB continuum (corona is beyond edge of Sun) Demonstrate today in class with “Tower of Light” for spectra of H, He, Ne (emission line sources since hot gas in tube gives energy to electrons that then “drop” down to give back energy as light)