Extend this unit's three-way mass-estimator comparison to new hypothetical and real scenarios.
A hypothetical molecular clump has the same radius as OMC-1 (1.0 pc) but twice its density (2 x 1.0e+05 cm^-3). Compute its direct H2 mass and state the exact factor by which it exceeds OMC-1's own direct mass (derive this factor algebraically before computing the number, since density enters the mass linearly at fixed volume).
Using the X_CO conversion factor (X_CO=2.0e+20 cm^-2 (K km/s)^-1), compute the implied CO luminosity (in K km/s pc^2) for a cloud with H2 mass 5.0e3 Msun, and state whether this luminosity is larger or smaller than the value implied by Taurus's real mass.
Recompute Taurus's virial mass assuming its CO linewidth were instead 3.0 km/s (double the real published value, with the radius unchanged). Compute the factor by which the virial mass changes, and confirm it matches the M_vir ∝ sigma^2 scaling derived in the lecture.
Using your Taurus virial mass from the lab and Taurus's CO-derived mass, compute the ratio M_CO/M_vir, and using the same ratio computed for OMC-1 in the lab, state which cloud appears closer to virial balance and which appears more likely to be gravitationally unbound (M_vir substantially exceeding M_CO) or bound/contracting (M_CO substantially exceeding M_vir).
Submit a complete derivation with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without a visible derivation receives partial credit at most, and quoting a lecture number without adapting it to this problem's specific inputs receives no credit for that step.
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.
materials/ASTR360/data/ where referenced above.