1. Sirius B's mass fraction of the Chandrasekhar limit
1.018 / 1.4 = 72.7% of the Chandrasekhar limit. Remaining mass before reaching the limit: 1.4 − 1.018 = 0.382 M☉.
| Criterion | Points |
|---|---|
| Correct percentage | 8 |
| Correct remaining-mass calculation | 7 |
Worked Solutions
2. Hypothetical white dwarf density and mass
V = (4/3)π(4.174e+06)³ = 3.047e+20 m³. M = ρV = 2.703e+09 × 3.047e+20 = 8.236e+29 kg = 0.414 M☉, which is below the Chandrasekhar limit.
| Criterion | Points |
|---|---|
| Correct volume | 5 |
| Correct mass | 5 |
| Correct Chandrasekhar comparison | 5 |
3. Neutron star spin-up from angular momentum conservation
I ∝ R², so P_final = P_initial × (R_final/R_initial)² = 25 days × (12/12,000)² = 25 × (0.001)² = 2.50e-05 days = 2.1600 s.
| Criterion | Points |
|---|---|
| Correct R ratio squared | 8 |
| Correct final period with unit conversion | 7 |
4. Textbook problem: Type Ia vs. Type II progenitors
Full-credit answers should state: Type Ia progenitors are white dwarfs in binary systems that accrete mass (or merge with a companion white dwarf) and approach the Chandrasekhar limit, triggering runaway carbon fusion that disrupts the entire star with no remnant left behind and a strikingly uniform peak luminosity (useful as a standard candle). Type II progenitors are massive stars (>8 M☉) whose iron core cannot release further fusion energy, undergoing catastrophic core collapse that typically leaves a neutron star (or black hole) remnant and is often accompanied by a burst of neutrinos.
| Criterion | Points |
|---|---|
| Correct Type Ia mechanism and remnant | 8 |
| Correct Type II mechanism and remnant | 7 |
Grading Notes
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.