Extend this unit's radiative-transfer and column-density tools to new spin temperatures, spectra, and sightlines.
Compute the hyperfine population ratio n1/n0 for gas at T_spin=500 K (intermediate between the CNM and WNM values used in the lecture), and state whether it is closer to the CNM's ratio or to the high-temperature limit of exactly 3.0.
A newly observed 21 cm spectral feature has a single Gaussian component with peak T_B=12.0 K and FWHM=6.0 km/s. Compute its HI column density in cm^-2, and state whether it is closer in order of magnitude to this course's representative CNM component or its representative WNM component.
Using only the given real Cygnus X-1 (N(H)=6.0e+21 cm^-2, Galactic latitude b=3.07 deg) and 3C 273 (N(HI)=1.79e+20 cm^-2, b=64.36 deg) values, compute the ratio of their column densities and connect the large difference to the two sightlines' different Galactic latitudes (without deriving a full Galactic HI disk model).
For CNM gas at T_spin=100 K, compute the brightness temperature predicted by the full radiative-transfer solution at tau=0.5 (no longer safely optically thin) and compare it to the optically thin approximation's prediction at the same tau. Compute the percent error the optically thin approximation makes at this tau, and state whether it over- or under-estimates the true brightness temperature.
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.