Star Formation, the ISM, and Post-Main-Sequence Evolution
Cloud A (cold, dense) is far more likely to be collapsing: low temperature reduces thermal pressure support, and high density increases self-gravity per unit volume, both favoring collapse. Cloud B's higher temperature and much lower density place it firmly in typical diffuse-ISM territory, stable against collapse.
| Criterion | Points |
|---|---|
| Correct qualitative direction (Cloud A collapses) | 8 |
| Correct physical reasoning citing both T and n | 7 |
t(6 M☉) = 10 × 6^-2.5 = 0.1134 Gyr. t(2 M☉) = 10 × 2^-2.5 = 1.7678 Gyr. Ratio t(2)/t(6) = 15.59.
| Criterion | Points |
|---|---|
| Correct 6 M☉ lifetime | 5 |
| Correct 2 M☉ lifetime | 5 |
| Correct ratio | 5 |
t = 10 Gyr × 5^-2.5 = 0.1789 Gyr = 178.9 Myr.
| Criterion | Points |
|---|---|
| Correct formula applied | 8 |
| Correct final age in Myr | 7 |
From L = M^3.5 = 10⁴, M = (10⁴)^(1/3.5) = 13.89 M☉. Age = 10 Gyr × (13.89)^-2.5 = 13.9 Myr.
| Criterion | Points |
|---|---|
| Correct mass from luminosity | 8 |
| Correct implied cluster age | 7 |
Award full marks for correct method, units, and a numeric result consistent with the arithmetic shown (allow reasonable rounding). Verify the student re-derives the number rather than quoting it from the lecture without adapting it to the problem's specific inputs.