1. The Rosette Nebula
R_s(Rosette)=20.30 pc versus observed 10 pc, a percent difference of 103.0%, versus Orion's 59.2% from the lab -- the Rosette's discrepancy is larger in this course's simplified single-density model, plausibly because large, evolved, lower-density H II regions like the Rosette have had more time to develop non-uniform density structure (e.g., a central cavity swept clear by stellar winds) that the idealized uniform-density Stromgren model does not capture.
| Criterion | Points |
|---|
| Correct Rosette Stromgren-radius arithmetic | 6 |
| Correct percent-difference comparison to Orion | 5 |
| Reasoned, non-generic physical explanation | 4 |
2. Ionizing photon rate needed for a target radius
Solving R_s formula for Q_H at R_s=0.6 pc gives Q_H=2.48e+48 photons/s, smaller than theta1 Ori C's real published Q_H (1.0e+49 photons/s) -- consistent with Orion being at least partly density-bounded (some ionizing photons escape or are absorbed by dust rather than all going into ionizing gas within the observed radius) rather than purely ionization-bounded.
| Criterion | Points |
|---|
| Correct algebraic inversion for Q_H | 7 |
| Correct, reasoned ionization-vs-density-bounded interpretation | 8 |
3. Recombination-line ratio sanity check
An observed Halpha/Hbeta ratio of 4.0, above the theoretical case B value of 2.86, implies significant internal dust extinction along that specific sightline through the nebula; this diagnostic depends only on the relative line fluxes at fixed atomic physics (Te), independent of the separate ionization-balance (Q_H, n_e) calculation used to derive the Stromgren radius.
| Criterion | Points |
|---|
| Correct extinction interpretation | 5 |
| Correct independence reasoning | 5 |
4. Electron density sensitivity
R_s(n_e=1200)=0.602 pc, a factor of 0.630 relative to the original (0.96 pc) -- consistent with the R_s ∝ n_e^(-2/3) scaling, since doubling n_e should scale R_s by 2^(-2/3)=0.630.
| Criterion | Points |
|---|
| Correct Stromgren-radius recomputation | 7 |
| Correct confirmation of the n_e^(-2/3) scaling factor | 8 |