1. A different heavily reddened star
A_V = 3.1 x 1.80 = 5.58 mag, giving a flux dimming factor of 10^(5.58/2.5) = 170.61.
| Criterion | Points |
|---|---|
| Correct A_V arithmetic | 7 |
| Correct dimming-factor arithmetic | 8 |
Worked Solutions
2. HD 200775's own extinction
A_V(HD 200775) = 2.65 mag, versus A_V(Cyg OB2-12) = 9.30 mag -- Cygnus OB2 No. 12 suffers substantially greater total extinction despite the comparison depending on both E(B-V) and R_V together (A_V=R_V E(B-V)); Cyg OB2-12's much larger E(B-V) more than compensates for HD 200775's larger R_V.
| Criterion | Points |
|---|---|
| Correct A_V arithmetic for HD 200775 | 7 |
| Correct comparative statement in the right direction | 8 |
3. R_V misassumption error
Incorrect A_V (using R_V=3.1) = 3.1 x 0.53 = 1.64 mag, versus the correct A_V (using R_V=5.0) = 2.65 mag -- a percent error of 38.0%, a substantial systematic underestimate from assuming the diffuse-ISM R_V for this anomalous dense-cloud sightline.
| Criterion | Points |
|---|---|
| Correct incorrect-R_V A_V arithmetic | 7 |
| Correct percent-error computation and direction (underestimate) | 8 |
4. Dust emission peak shift
The 50 K component peaks at shorter wavelength than the 15 K component (Wien's-law-like behavior even for a modified blackbody); a far-infrared instrument like Herschel/PACS (70-160 micron) is well-suited to the warmer 50 K component but would miss much of the emission from the colder 15 K component, better captured at longer submillimeter wavelengths (e.g., Herschel/SPIRE or ALMA).
| Criterion | Points |
|---|---|
| Correct qualitative peak-shift direction | 5 |
| Correct, reasoned wavelength-regime example | 5 |
Grading Notes
Award full marks for correct method, units, and a numeric result consistent with the arithmetic shown (allow reasonable rounding). Verify that the student re-derives the number for this problem's specific inputs rather than quoting a lecture example without adaptation. Watch specifically for unit-conversion errors (cm^-3 vs m^-3, pc vs m, K km/s integrals), for comparative-magnitude statements given in the wrong direction, and for level-1/level-2/level-3 data-provenance conflation (e.g., presenting the illustrative synthetic HI spectrum shape as an exact measurement of a specific real sightline) -- these are the most common sources of mistakes in this course.