PROBLEM SET 2

Astronomy 208

Distributed: 10/12/00 Due: 10/31/00

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

2. a. 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

30 K

20

104

1

Atomic Hydrogen mixed with dust

Zone B

8000 K

N/A

102

105

Hydrogen with virtually no dust

You may also assume:

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

2. b. Comment on the viability and/or origin of an object like the one pictured. Could this object really exist? How, where?

3. a. Bohlin, Savage & Drake's (1978) measurements of a gas-to-dust ratio rely on the optical color excess (E(B-V)) for the stars along the lines of sight included in their study. That color excess is often turned into a visual extinction using the relation AV=3.1 E(B-V). Explain the origin of that relation, and its limitations.

3. b. The dust extinction measurements in Alves, Lada & Lada 1999 rely on the near-infrared (J,H,K) stellar colors presented in Alves et al. 1998. These measurements give more reliable estimates of extinction than do optical colors. Explain why.

3. c. (Grossly) estimate what the reduction in scatter might have been in Bohlin, Savage & Drake's Figure 2, based on your comparison of optical and near-infrared color-excess methods for determining extinction. Comment on whether you think this reduction in scatter would have mattered to Bohlin, Savage & Drake's main results. Then, comment on how it might matter in a study of high-extinction regions, like rho-Oph.

Good References for Problem 3: General reference on dust: Whittet, 1992. Review on extinction laws: Mathis 1990.