Transcript Document

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 3
1
In  2
c e hn / kT  1
• 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 ) 
1.19x1027 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?