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Black Bodies • Wien’s Law – Peak intensity • Stefan-Boltzman Law – Luminosity • Planck’s Law – Energy Distribution – Rayleigh-Jeans approximation – Wien approximation Wien’s Law – Peak Intensity Il is max at lmax = 2.90 x 10 7/T (Angstroms) (or l’max = 5.1 x 107/T where l’max is the wavelength at which In is max) Class Problem: Calculate the wavelength at which In is maximum in the Sun and at which Il is maximum in the Sun Class Problem: What is the spectral type of a main sequence star in which Il is maximum at H-alpha? A giant star? Class Problem: What is the peak wavelength of an 05 star at 35000K (if it were radiating as a black body!)? Luminosity – Stefan Boltzman Law • F = sT4 or L = 4p R2 sT4 • Class Problem: What is the approximate absolute magnitude of a DA white dwarf with an effective temperature of 12,000, remembering that its radius is about the same as that of the Earth? Planck’s Law 2hn 1 In 2 c e hn / kT 1 3 • Rayleigh-Jeans Approximation (at long wavelength) In = 2kTn2/c2 = 2kT/l2 • Wien Approximation – (at short wavelength) In = constant x n3 e (-constant x n /T) Class Problem • The flux of M3’s IV-101 at the K-band is approximately 4.53 x 105 photons s–1 m–2 mm-1. What would you expect the flux to be at 18 mm? The star has a temperature of 4250K. Using Planck’s Law Computational form: Bl (T ) 1.19 x10 27 l5 1.44 x108 / lT e 1 For cgs units with wavelength in Angstroms Class Problems • You are studying a binary star comprised of an B8V star at Teff = 12,000 K and a K2III giant at Teff = 4500 K. The two stars are of nearly equal V magnitude. What is the ratio of their fluxes at 2 microns? • In an eclipsing binary system, comprised of a B5V star at Teff = 16,000K and an F0III star at Teff = 7000K, the two stars are known to have nearly equal diameters. How deep will the primary and secondary eclipses be at 1.6 microns? Class Problems • Calculate the radius of an M dwarf having a luminosity L=10-2LSun and an effective temperature Teff=3,200 K. What is the approximate density of this M dwarf? • Calculate the effective temperature of a protostellar object with a luminosity 50 times greater than the Sun and a diameter of 3” at a distance of 200 pc. Class Problems • You want to detect the faint star of an unresolved binary system comprising a B5V star and an M0V companion. What wavelength regime would you choose to try to detect the M0V star? What is the ratio of the flux from the B star to the flux from the M star at that wavelength? • You want to detect the faint star of an an unresolved binary system comprising a K0III giant and a DA white dwarf with a temperature of 12,000 K (and MV=10.7). What wavelength regime would you choose to try to detect the white dwarf? What is the ratio of the flux from the white dwarf to the flux from the K giant at that wavelength?