Lab 06: The Stromgren Sphere: The Orion Nebula

Apparatus and Setup

This lab computes the Stromgren radius for the Orion Nebula in full, compares it to the nebula's real observed size, and applies real Orion Nebula spectroscopic diagnostics (Te, n_e) to justify the input parameters used.

Materials and Data

theta1 Orionis C: spectral type O7V, T_eff≈39,000 K, Q_H=1.0e+49 photons/s (Vacca, Garmany & Shull 1996; Martins, Schaerer & Hillier 2005, standard published, level 2). Orion Nebula: n_e=600 cm^-3, Te=10,000 K (Baldwin et al. 1991; Osterbrock & Ferland 2006, level 2), observed radius≈0.6 pc, distance=414 pc (Menten et al. 2007).

Procedure

1. Using the case B recombination coefficient at Te=10,000 K, compute the Stromgren radius from Q_H and n_e.
2. Compare your computed Stromgren radius to the nebula's real observed radius, and compute the percent difference.
3. Discuss, quantitatively where possible, at least two real physical reasons for the discrepancy (e.g., non-uniform density with a lower average density than the quoted representative n_e over the nebula's full extent, density-bounded rather than ionization-bounded geometry, or contributions from additional fainter ionizing stars in the Trapezium cluster beyond theta1 Ori C alone).
4. Compute the recombination timescale and confirm it is astronomically short compared to theta1 Ori C's stellar lifetime, justifying the equilibrium assumption.

Analysis and Uncertainty

Explain why a factor-of-order-unity discrepancy between the idealized Stromgren radius and a real nebula's observed size should be considered an expected, honest limitation of the idealized model rather than a computational error, and identify what additional observation (e.g., a resolved density map) would let you test which of your proposed explanations in Step 3 dominates.

Deliverables

• The computed Stromgren radius with full derivation.
• The percent-difference comparison to the observed radius.
• At least two specific, physically reasoned explanations for the discrepancy.
• The recombination-timescale equilibrium justification.

Assessment Criteria

• Correct Stromgren-radius arithmetic with correct alpha_B and unit handling (cm, then converted to pc).
• Correctly computed percent difference.
• At least two specific, non-generic physical explanations for the model-observation discrepancy.

References and Provenance

• OpenStax Astronomy 2e (local extracted reference copy: references/openstax-astronomy-2e-extracted.txt) covers the interstellar medium in Chapter 20 ("Between the Stars: Gas and Dust in Space"): 20.1 The Interstellar Medium, 20.2 Interstellar Gas (including the 21 cm line and H II regions), 20.3 Cosmic Dust (extinction and reddening), 20.4 Cosmic Rays, 20.5 The Life Cycle of Cosmic Material, and 20.6 Interstellar Matter around the Sun. Chapter 20’s section numbering was cross-checked directly against its own embedded figure numbering this session (Figures 20.1 through 20.20 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. OpenStax’s treatment throughout Chapter 20 is descriptive and qualitative; nearly every quantitative derivation in this course (the 21 cm hyperfine radiative-transfer solution and HI column-density formula, the Jeans mass/length instability criterion, the free-fall collapse time, the Stromgren-sphere ionization-balance derivation, the Rankine-Hugoniot shock-jump conditions, and the cosmic-ray power-law spectrum) goes well beyond OpenStax Astronomy 2e’s introductory level; each lecture states explicitly where this course extends beyond the assigned reading.
• Orion Nebula and theta1 Orionis C parameters: standard published, level 2; see materials/ASTR360/reference-log.md.
• Generated by materials/ASTR360/src/generate_astr360_content.py.