Lab 04: CME Transit Time and the Parker Wind's Numerical Solution

Apparatus and Setup

This lab computes both the naive constant-speed and a simple drag-based transit-time estimate for the real 6 September 2017 CME (Lecture 07), then reproduces Lecture 08's numerical transonic Parker-wind solve at several radii.

Materials and Data

CME LASCO speed: 1571 km/s (level 2). Ambient slow solar wind speed: 400 km/s (level 2, OMNI climatology). Coronal temperature: 1.5e+06 K, mu=0.60. Parker critical radius: r_c=4.62 R_sun (computed in Lecture 08).

Procedure

1. Compute the naive constant-speed travel time (1 AU/v_CME) and confirm it matches Lecture 07's stated value.
2. Using the drag-based deceleration functional form from Lecture 07's figure (exponential relaxation toward the ambient wind speed with a 15-hour time constant), numerically integrate or evaluate the CME's distance vs time and estimate the arrival time at 1 AU; compare it to the real observed ~36-hour transit time.
3. Numerically solve the Parker transonic wind equation (bisection on the physical branch, as in Lecture 08) for u=v/c_s at r/r_c=0.5, 1.0, 2.0, and 47 (1 AU), and tabulate v in km/s at each radius.
4. Confirm that u=1.0 (v=c_s) exactly at r/r_c=1.0, the defining property of the critical point.

Analysis and Uncertainty

Discuss why the drag-based model's specific functional form (and its 15-hour time constant) is an illustrative, level-3 choice calibrated only to roughly reproduce the real observed transit time, not a first-principles solution of the full drag-force differential equation, which would require knowing the ambient solar wind's density profile in detail.

Deliverables

• The naive and drag-based transit-time estimates compared to the real observed value.
• The four-radius Parker-wind speed table with the critical-point check.

Assessment Criteria

• Correct naive travel-time arithmetic.
• Correct numerical root-finding for the Parker wind equation at all four radii.
• Correctly confirmed critical-point property (u=1 at r=r_c).

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.
• CME speed and solar wind climatology: standard published, level 2; see materials/ASTR370/reference-log.md.
• Generated by materials/ASTR370/src/generate_astr370_content.py.