Apparatus and Setup
This lab computes the order-of-magnitude free-energy estimate for a range of assumed active-region field strengths and volumes (Lecture 05), then reconstructs the real published timeline of the 2017-09-06 X9.3 flare case study (Lecture 06).
Materials and Data
| Quantity | Value | Provenance |
|---|---|---|
| GOES class | X9.3 | standard published, level 2 |
| Peak flux | 9.3e-04 W/m^2 | standard published, level 2 |
| CME LASCO speed | 1571 km/s | standard published (CDAW catalog), level 2 |
| Storm Dst minimum | -142 nT | standard published (Kyoto WDC/NOAA), level 2 |
| Observed CME transit time | ~36 hours | standard published range, level 2 |
Representative AR volume (area=1.5e+18 m^2, height scale=1.0e+07 m) is an order-of-magnitude, level 3 estimate, explicitly disclosed (see ../reference-log.md).
Procedure
- Compute the free-energy estimate E_free=(B^2/2 mu0)V for the given sunspot field strength and AR volume, and confirm it matches Lecture 05's stated value.
- Recompute E_free for two additional AR volume estimates (half and double the given volume), holding B fixed, and tabulate all three.
- Compute the light travel time from the Sun to Earth (1 AU/c) in minutes, and compare it to the real observed CME transit time in hours, expressing the ratio between the two timescales.
- Compute the GOES-class-to-flux ratio between the X9.3 flare and a hypothetical M5.0 flare, and state how many M5.0-equivalent peak fluxes would be needed to match the X9.3 flare's peak flux.
Analysis and Uncertainty
Discuss why doubling the assumed AR volume exactly doubles the free-energy estimate (a direct consequence of the linear volume dependence in E_free=(B^2/2 mu0)V), and why this makes the volume assumption the single largest source of uncertainty in this order-of-magnitude estimate.
Deliverables
- The three-volume free-energy table.
- The light-travel-time vs CME-transit-time ratio.
- The X9.3-to-M5.0 flux ratio.
Assessment Criteria
- Correct free-energy arithmetic for all three volumes.
- Correct light-travel-time computation and ratio.
- Correct GOES-class flux ratio arithmetic.
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.
- AR12673/X9.3 flare and storm values: standard published, level 2; AR volume: order-of-magnitude, level 3; see
materials/ASTR370/reference-log.md. - Generated by
materials/ASTR370/src/generate_astr370_content.py.