Apparatus and Setup
This is a computational lab (no telescope required) that builds this unit's hydrostatic scale-height calculation for the photosphere and corona from Lectures 01-02's real solar structure parameters, and extends it to predict the coronal density falloff with height.
Materials and Data
| Layer | T (K) | mu | Scale height H |
|---|---|---|---|
| Photosphere | 5772 | 1.30 | 134 km |
| Corona | 1.5e+06 | 0.60 | 75,260 km |
T_eff and standard solar-model core parameters (T_core=1.57e+07 K, rho_core=1.5e+05 kg/m^3) are standard published values, level 2 (see ../reference-log.md). g_sun=GM_sun/R_sun^2=274.3 m/s^2 is computed directly from IAU nominal M_sun, R_sun.
Procedure
- Recompute g_sun=GM_sun/R_sun^2 from the given constants and confirm it matches the value above.
- Recompute the photospheric scale height H=kT/(mu m_H g) and confirm it matches Lecture 01's stated value.
- Recompute the coronal scale height at T_corona=1.5e+06 K, mu=0.60, and compute the ratio H_corona/H_photosphere.
- Using the coronal base density (n=1e+08 cm^-3, standard published quiet-Sun value) and an isothermal exponential falloff with the coronal scale height, estimate the coronal density at a height of one solar radius above the photosphere, and compare it (order of magnitude) to the base density.
Analysis and Uncertainty
Discuss why an isothermal, single-scale-height model is a simplification for the real corona (whose temperature and composition vary with height and position, and which is not in a strict static hydrostatic state at all per Lecture 08's Parker wind argument), and state explicitly that this lab's density estimate should be read as an order-of-magnitude illustration of the scale-height concept, not a precise coronal density model.
Deliverables
- Recomputed g_sun, H_photosphere, H_corona with full derivations.
- The H_corona/H_photosphere ratio.
- The estimated coronal density at one solar radius above the photosphere and a discussion of the model's limitations.
Assessment Criteria
- Correct g_sun arithmetic from G, M_sun, R_sun.
- Correct scale-height arithmetic for both layers with correct units (km).
- Honest, non-overclaiming discussion of the isothermal density-falloff model's limitations.
References and Provenance
- OpenStax Astronomy 2e (local extracted reference copy: references/openstax-astronomy-2e-extracted.txt) covers the Sun in Chapter 15 ("The Sun: A Garden-Variety Star"): 15.1 The Structure and Composition of the Sun, 15.2 The Solar Cycle, and 15.3 Solar Activity above the Photosphere. Chapter 15’s section numbering was cross-checked directly against its own embedded figure numbering this session (Figures 15.1 through 15.24 all appear under their matching section headers with no offset), so this citation is verified against the local extracted text rather than extrapolated by analogy from a prior course. OpenStax’s treatment throughout Chapter 15 is descriptive and qualitative; nearly every quantitative derivation in this course (the hydrostatic solar-atmosphere/scale-height argument, the sunspot magnetic-pressure balance, the Parker solar-wind critical-point argument and its numerical transonic solution, flare free-energy budgets, the Chapman-Ferraro magnetopause standoff distance, and the Dessler-Parker-Sckopke ring-current/Dst relation) goes well beyond OpenStax Astronomy 2e’s introductory level; each lecture states explicitly where this course extends beyond the assigned reading.
- Solar structure parameters: IAU nominal values and standard solar model (Bahcall et al.), level 2; see
materials/ASTR370/reference-log.md. - Generated by
materials/ASTR370/src/generate_astr370_content.py.