Solar Structure and Scale Heights
H(chromosphere, T=2e+04 K, mu=1.0) = 602 km -- intermediate between the photospheric (134 km) and coronal (75,260 km) scale heights, consistent with the chromosphere's intermediate temperature and physical location.
| Criterion | Points |
|---|---|
| Correct scale-height arithmetic | 8 |
| Correct ordinal placement between photosphere and corona | 7 |
g = GM/(2R)^2 = g_sun/4 = 68.57 m/s^2. Since H ∝ 1/g at fixed T and mu, this star's scale height is 4 times the Sun's own photospheric scale height (535 km vs 134 km) -- larger, because its weaker surface gravity (same mass, larger radius) is less effective at compressing its atmosphere.
| Criterion | Points |
|---|---|
| Correct surface-gravity arithmetic | 7 |
| Correct factor-of-4 scale-height conclusion | 8 |
T_core/T_eff = 2,720. T_corona/T_eff = 259.9. The core ratio is far larger, as expected (fusion happens only in the core); the much smaller corona/photosphere ratio nonetheless represents a real, physically surprising temperature *increase* with distance from the surface, which the core-driven radiative cooling trend alone cannot explain -- requiring the non-radiative (magnetic) heating mechanism of Lecture 02.
| Criterion | Points |
|---|---|
| Correct ratio arithmetic for both | 5 |
| Correct physical explanation connecting to Lecture 02 | 5 |
r_cz = 0.71 x 695,700 km = 493,947 km. Volume fraction inside this radius = (0.71)^3 = 0.358, i.e., about 36% of the Sun's total volume lies inside the radiative-convective boundary, with the remaining ~64% forming the (much larger in volume, but much lower in density) convective envelope.
| Criterion | Points |
|---|---|
| Correct unit conversion to km | 5 |
| Correct volume-fraction (cube of radius fraction) arithmetic | 10 |
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 (Gauss vs Tesla, nT vs T, km/s vs m/s, hours vs seconds), for comparative-magnitude statements given in the wrong direction, and for level-1/level-2/level-3 data-provenance conflation (e.g., presenting the order-of-magnitude flare free-energy estimate as a precise measurement, or presenting a Carrington-Dst estimate as a directly measured historical value) -- these are the most common sources of mistakes in this course.