Capstone Synthesis: Radiative and Dynamical Cross-Checks for Sirius AB
Sirius A: L_SB = 25.75 L⊙ vs. published 25.4 L⊙ (agreement 1.4%). Sirius B: L_SB = 0.0231 L⊙ vs. published 0.0245 L⊙ (agreement 5.8%).
| Criterion | Points |
|---|---|
| Correct Sirius A calculation and agreement | 12 |
| Correct Sirius B calculation and agreement | 13 |
Percent agreement = 0.1% (restated from Problem Set 04).
| Criterion | Points |
|---|---|
| Correct restatement/consistency with PS04 | 15 |
L_Edd(Sirius A, 2.063 M⊙) = 6.78e+04 L⊙; actual/Eddington = 3.75e-02%. L_Edd(Sirius B, 1.018 M⊙) = 3.34e+04 L⊙; actual/Eddington = 7.33e-05%. Both are minuscule fractions, confirming radiation pressure is negligible for both stars.
| Criterion | Points |
|---|---|
| Correct Eddington-luminosity arithmetic for both stars | 12 |
| Correct percentage-of-Eddington calculation for both | 8 |
Full credit requires: (a) an explicit numeric comparison of the two agreement percentages with a plausible reason for any difference (e.g., different sensitivity to measurement uncertainty in R vs. in P and a); (b) a correct statement that Sirius B's degenerate-matter structure does not undermine the purely radiative (surface-emission) Stefan-Boltzmann argument, which depends only on the emitting surface's R and T, not on what supports the star's interior; (c) a correct conclusion that both stars' actual luminosities are far below their Eddington limits, so radiation pressure is negligible in the hydrostatic balance of both, consistent with Lecture 05's ideal-gas treatment.
| Criterion | Points |
|---|---|
| Correct point (a) | 7 |
| Correct point (b) | 7 |
| Correct point (c) | 6 |
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 (AU/m, years/seconds, km/Mpc, Msun/kg) -- these are the most common source of order-of-magnitude mistakes in this course.