Physics 611 Problem Assignment #1

Physics 611 Problem Assignment #1
Astrophysics(Stellar Atmospheres) Due: Wednesday, September 13, 2006

FLUXES EXPRESSED IN MANY WAYS

(1) A certain mysterious cosmic object has a perfectly flat spectrum over a wide spectral
range. Its monochromatic energy flux is given by

1.00 ergs s-1 cm-3 0.10 Å £ λ £ 10.0 m
Fλ = {
0 λ < 0.10 Å or λ > 10.0 m


(a) Find a general expression for Fν [erg s-1 cm-2 Hz-1], the monochromatic flux (per unit
frequency interval).

(b) Numerically evaluate Fν at λ = 0.10 Å and λ = 10.0 m.

(d) Numerically evaluate Nλ at λ = 0.10 Å and λ = 10.0 m.

(e) Find a general expression for Nν [photons s-1 cm-2 Hz-1], the monochromatic photon flux
(per unit frequency interval).

(f) Numerically evaluate Nν at λ = 0.10 Å and λ = 10.0 m.

(g) About how often does a photon from this source with a wavelength λ, within a window
of width Dλ= 0.1λ0, pass through a 1.00 cm2 patch which is normal to the line-of-sight,
for λ0 = 0.10 Å? For λ0 = 10.0 m? (Assume in each case that the window barely lies
entirely within the spectral range where the flux is non-zero, i.e., the windows range
from 0.10 Å to 0.11 Å and from 9.0 m to 10.0 m.)

(2) The intensity of radiation associated with a black body of temperature T is given by the
Planck function

Iν(θ,φ) = Bν(T) = (2hν3/c2) / (ehν/kT -1).

For a general black body and for a black body the temperature of the sun, T = 5780 K, find
(a) an expression for and the value of λν,max, the wavelength at which Iν(θ,φ) peaks, and

(b) an expression for and the value of λλ,max, the wavelength at which Iλ(θ,φ) peaks.

(c) In elementary astronomy textbooks (e.g., in Universe by Freedman and Kaufmann, the
currently used text in Ph 127) Wien's Law is often expressed λmax= 0.0029/T where T is
the temperature of a star in kelvins and λmax is the wavelength of maximum emission in
meters. In this expression does λmax represent Iν,max(θ,φ) or Iλ,max(θ,φ)?

Hint: Two solutions of the equation x(a) = a(1-e-x) are x(3) = 2.821439 and x(5) = 4.965114, correct to seven significant figures.