PROBLEM SET 2

Astronomy 208

Distributed: 10/10/96 Due: 10/22/96

Problems 3-5 of this problem set relate to the articles discussed in class on 10/10/96 (Heiles, C. 1979, ApJ, 229, 533-544) and 10/17/96 (Bregman, J.N., Kelson, D.D. and Ashe, G.A. 1993, ApJ, 409, 682-690). In addition to having read these articles, you will need to understand the basic implications of McKee, C.F. and Ostriker, J.P. 1977 (ApJ, 218, 148-169), in order to complete the problems. You may also find http://www.cfa.harvard.edu/~agoodman/HI.html useful.

1.Show how ignoring stimulated emission in the formulation of Einstein coefficients is consistent with Wien's Law but not Planck's Law.

2. Predict, by presenting a plot of intensity versus frequency, and no more than two pages of writing, the full spectrum of radiation from a "mystery object" described by the illustration and table below. Note: we are just looking for the general idea, not incredibly detailed calculations.

Layer	Gas Temperature [K]	Dust Temperature [K]	Neutral Density [cm-3]	Electron Density [cm-3]	Composition
Zone A	50 K	30	104	1	Atomic Hydrogen mixed with dust
Zone B	1000 K	N/A	3 x 105	3 x 105	Hydrogen with virtually no dust

You may also assume:

• no magnetic field
• LTE between gas and all photons
• no shocks, but the existence of a reasonable "transition zone" between A & B, where gas goes from almost completely ionized to almost completely neutral, and dust exists in limited quantities. You can IGNORE emission from this zone in your answer.
• the object is not resolved, in that all the emission is always observed in one "beam" at any frequency

It is likely that you will need to make some small additional assumptions. Please be sure to state them carefully.

Extra credit: Comment on the viability and/or origin of an object like the one pictured.

3. After reading Heiles' article, what volume of the ISM would you expect to be filled with:

a.) shell wall structures?

b.) shell interiors?

You can assume any extrapolations necessary, just state your assumptions.

4. How does your answer to 4 compare with the relative volumes cold and hot gas predicted by the McKee & Ostriker (1977) model for the ISM?

5. Does the Bregman et al. (1993) article cause you to:

a.) change your answer to 3 a and b?

b.) give a different result for 4?

c.) Explain the reasoning Bregman et al. use to assert that

"the geometry of the interstellar medium is probably not described by an ensemble of clouds, either uniform, nonuniform (exponential), or of two-component type (the McKee-Ostriker ISM).," p. 689

Do you see any potential flaws in this reasoning? Can you suggest observational tests that would solidify or hurt Bregman et al.'s case?

References

Bregman, J.N., Kelson, D.D. and Ashe, G.A. 1993, Modeling the structure of H I in the galactic disk, ApJ, 409, 682-690.

Heiles, C. 1979, H I shells and supershells, ApJ, 229, 533-544.

McKee, C.F. and Ostriker, J.P. 1977, A theory of the interstellar medium - Three components regulated by supernova explosions in an inhomogeneous substrate, ApJ, 218, 148-169.