Apparatus and Setup
This lab reproduces Lecture 07's three-way OMC-1 mass comparison (direct, CO-derived, virial) and extends it to the real, quiescent Taurus Molecular Cloud, applying Lecture 08's Larson-law virial-mass estimator to both.
Materials and Data
| Cloud | Distance (pc) | Radius (pc) | n(H2) (cm^-3) | T (K) | CO FWHM (km/s) |
|---|---|---|---|---|---|
| Orion Molecular Cloud (OMC-1) | 414 | 1.0 | 1.0e+05 | 25 | 3.0 |
| Taurus Molecular Cloud | 140 | 6.0 | 3.0e+02 | 10 | 1.5 |
Standard published values, level 2 (Genzel & Stutzki 1989 for OMC-1; Goldsmith et al. 2008 for Taurus). X_CO=2.0e+20 cm^-2 (K km/s)^-1 (Bolatto, Wolfire & Leroy 2013).
Procedure
- For Taurus, compute the direct (density x volume) H2 mass, exactly as Lecture 07 did for OMC-1.
- For Taurus, compute the CO-derived mass via the X_CO conversion, following Lecture 07's method.
- For Taurus, compute the virial mass using Lecture 08's M_vir=5 sigma^2 R/G estimator, with sigma=FWHM/2.355.
- Tabulate all three mass estimates for both Orion and Taurus side by side, and discuss which cloud shows better agreement among its three independent estimates, and why (Taurus's more quiescent, less turbulent nature is a reasonable hypothesis to test against the numbers).
Analysis and Uncertainty
Using Larson's sigma ∝ R^0.5 relation, explain why Taurus's larger radius but much narrower linewidth than OMC-1 illustrates the size-linewidth relation's role in setting virial mass, and identify which single measurement (radius or linewidth) you would most want an independent, higher-precision check on if the two clouds' virial-to-CO mass ratios disagreed substantially.
Deliverables
- Taurus's direct, CO-derived, and virial mass estimates with full derivations.
- The four-cloud (Orion + Taurus, three methods each) mass comparison table.
- A short discussion of which cloud's three estimates agree best and why.
Assessment Criteria
- Correct direct-mass volume/density arithmetic for Taurus.
- Correct X_CO conversion arithmetic for Taurus.
- Correct virial-mass arithmetic (including the sigma=FWHM/2.355 conversion) for Taurus.
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 Molecular Cloud and Taurus Molecular Cloud parameters: standard published, level 2; see
materials/ASTR360/reference-log.md. - Generated by
materials/ASTR360/src/generate_astr360_content.py.