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  I  is max  at  max = 2.90 x 10 7 /T (Angstroms) (or  ’ max = 5.1 x 10 7 /T where ’ max is the wavelength at which I is max)  Class Problem: Calculate the wavelength at which I is maximum in the Sun and at which I is maximum in the Sun  Class Problem: What is the spectral type of a main sequence star in which I 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 =  T 4 or L = 4  R 2  T 4 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 Rayleigh-Jeans Approximation (at long wavelength) I = 2kT 2 /c 2 = 2kT/ 2 Wien Approximation – (at short wavelength) I = constant x 3 e (-constant x /T)

Class Problem The flux of M3’s IV-101 at the K-band is approximately 4.53 x 10 5 photons s –1 m –2  m -1. What would you expect the flux to be at 18  m? The star has a temperature of 4250K.

Using Planck’s Law Computational form: 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 -2 L Sun and an effective temperature Teff=3,200 K. What is the approximate density of this M dwarf? Calculate the effective temperature of a proto- stellar 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 M V =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?