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Astr 421 Fall 2004

Galaxies Sylvain Veilleux

September 24, 2004 DUE: October 6, 2004


Problems 1 - 4.

Sparke & Gallagher, Problems 2.4, 2.5, 2.8, and 2.15

Problem 5.

The following question is about interstellar reddening in external galaxies. Let's consider two different situations.

Case 1: Stars are distributed uniformly throughout a thin layer of thickness D with a layer of absorbing material of optical depth $\tau_V$ between the stars and the observer ($\tau_V$ is the optical depth in the visual band).

Case 2: Same as Case 1, but now the absorbing medium is distributed uniformly with the stars.

Assume D is negligible compared to the distance to the observer, and the absorbing material obeys the so-called Whitford law with R $\equiv$ $A_V/E(B-V)$ = 3 where $E(B-V) \equiv A_B - A_V$ is called the ``color excess''.

The observer has measured integrated colors in U, B, and V for the slab of stars (seen face on), but these colors are naturally affected by reddening. Calculate the apparent value of R and S $\equiv$ $E(U-B)/E(B-V)$ for Cases 1 and 2 in the limits $\tau_V$ $\rightarrow$ 0 and $\tau_V$ $\rightarrow$ $\infty$.

Mention a couple of realistic situations in which this variation in R and S might actually occur.

Hint: Take a look at Section 3-11 of Mihalas & Binney (1981), attached with this problem sheet.

Note: The calculation is only academic since real dust grains have an albedo of about 50%, so they scatter much of the light rather than absorb it.

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Sylvain Veilleux 2004-09-24