ASTR 360 Problem Set 03

Problems

1. A different heavily reddened star 15 points

A star has E(B-V)=1.80 mag and R_V=3.1 (the diffuse-ISM average). Compute its A_V, and compute the flux dimming factor 10^(A_V/2.5) this extinction causes.

2. HD 200775's own extinction 15 points

Using HD 200775's own real published parameters (E(B-V)=0.53 mag, R_V=5.0), compute its A_V, and compare it to Cygnus OB2 No. 12's A_V computed in the lab. State which star suffers greater total visual extinction despite having a smaller color excess, and explain why in one sentence.

3. R_V misassumption error 15 points

If an observer incorrectly assumed the diffuse-ISM average R_V=3.1 for HD 200775 (rather than its real R_V=5.0) while using its real measured E(B-V)=0.53 mag, compute the resulting (incorrect) A_V and state the percent error relative to the correct A_V computed using the real R_V.

4. Dust emission peak shift 10 points

Using the modified-blackbody model at beta=2, compare the wavelength of peak emission for dust at 15 K versus dust at 50 K (both values used in the lecture's figure). State qualitatively (using Wien's-law-like reasoning) which is expected to peak at shorter wavelength and why, and name one real astronomical survey/telescope wavelength band well-suited to detecting the 50 K component that would be poorly suited for the 15 K component.

Due and Scope

Submit a complete derivation with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without a visible derivation receives partial credit at most, and quoting a lecture number without adapting it to this problem's specific inputs receives no credit for that step.

OpenStax Companion Reading

OpenStax Astronomy 2e (local extracted reference copy: references/openstax-astronomy-2e-extracted.txt) covers the interstellar medium in Chapter 20 ("Between the Stars: Gas and Dust in Space"): 20.1 The Interstellar Medium, 20.2 Interstellar Gas (including the 21 cm line and H II regions), 20.3 Cosmic Dust (extinction and reddening), 20.4 Cosmic Rays, 20.5 The Life Cycle of Cosmic Material, and 20.6 Interstellar Matter around the Sun. Chapter 20’s section numbering was cross-checked directly against its own embedded figure numbering this session (Figures 20.1 through 20.20 all appear under their matching section headers with no offset), so this citation is verified against the local extracted text rather than extrapolated by analogy. OpenStax’s treatment throughout Chapter 20 is descriptive and qualitative; nearly every quantitative derivation in this course (the 21 cm hyperfine radiative-transfer solution and HI column-density formula, the Jeans mass/length instability criterion, the free-fall collapse time, the Stromgren-sphere ionization-balance derivation, the Rankine-Hugoniot shock-jump conditions, and the cosmic-ray power-law spectrum) goes well beyond OpenStax Astronomy 2e’s introductory level; each lecture states explicitly where this course extends beyond the assigned reading.

References and Data Sources

Corresponding lecture slides and notes for this unit.
OpenStax Astronomy 2e (local extracted reference copy: references/openstax-astronomy-2e-extracted.txt) covers the interstellar medium in Chapter 20 ("Between the Stars: Gas and Dust in Space"): 20.1 The Interstellar Medium, 20.2 Interstellar Gas (including the 21 cm line and H II regions), 20.3 Cosmic Dust (extinction and reddening), 20.4 Cosmic Rays, 20.5 The Life Cycle of Cosmic Material, and 20.6 Interstellar Matter around the Sun. Chapter 20’s section numbering was cross-checked directly against its own embedded figure numbering this session (Figures 20.1 through 20.20 all appear under their matching section headers with no offset), so this citation is verified against the local extracted text rather than extrapolated by analogy. OpenStax’s treatment throughout Chapter 20 is descriptive and qualitative; nearly every quantitative derivation in this course (the 21 cm hyperfine radiative-transfer solution and HI column-density formula, the Jeans mass/length instability criterion, the free-fall collapse time, the Stromgren-sphere ionization-balance derivation, the Rankine-Hugoniot shock-jump conditions, and the cosmic-ray power-law spectrum) goes well beyond OpenStax Astronomy 2e’s introductory level; each lecture states explicitly where this course extends beyond the assigned reading.
Course datasets under materials/ASTR360/data/ where referenced above.