Physics 427
Introduction to Astrophysics
Problem Assignment #8
Due: Wednesday, October 9, 2013
STELLAR MAGNITUDES, COLOR INDICES AND INTERSTELLAR REDDENING
(1) Assume that an eclipsing binary of parallax π = 0.031" has identical G2 V components with Mv =
4.79. Find the apparent magnitude of the system during (a) total eclipse, (b) no eclipse.
(2) A spectroscopic binary consists of components with the following properties:
Component Spectral Type
A
B
A0 V
F0 V
Mv
0.70
2.80
(B-V) (U-B)
0.00
0.30
0.00
0.02
Find: (a) LU,F0 / LU,A0, (b) LB,F0 / LB,A0, (c) LV,F0 / LV,A0, (d) (B-V)system, and (e) (U-B)system.
(3) Assume that U = B = V = 0.00 for the following flux densities:
Band λeff [Å]
U
B
V
3585
4382
5502
Fν [erg cm-2 s-1 Hz-1]
1.79 × 10-20
4.13 × 10-20
3.81 × 10-20
Find (U-B) and (B-V) for stars with the following energy distributions:
(a) Fν = constant,
(b) Fν  ν-2,
(c) a black body with T = ,
(d) a black body with T = 21000 K.
Hint: Use Planck's Law for parts (c) and (d), and the fact that the flux Fν will be proportional to the
black body intensity, Bν(T).
Bν(T) = (2hν3/c2) / (ehν/kT - 1).
(4) Suppose that the reddening law in a particular direction is given by Δmλ  λ-α. Taking the effective
wavelengths of the U, B, and V filters to be λ3600Å, λ4400Å, and λ5500Å respectively and assuming
that the U, B, and V magnitudes can be represented by monochromatic magnitudes at their effective
wavelengths, find:
(a) an expression for R = AV / EB-V, the ratio of total to differential absorption,
(b) the values of α for which R = 3.0, 3.1, and 3.2,
(c) an expression for the ratio EU-B / EB-V,
(d) the value of α for which EU-B / EB-V = 0.72.
(e) In reality EU-B / EB-V = C1 + C2 EB-V . Why is the actual value of C2 not zero?
(f) If R = 3.2 for the model of this problem, find the value of the constant k such that Q =
(U-B) - k(B-V) is reddening free.