Extend this unit's capstone tools to a second real supernova remnant and additional density/energy regimes.
Using Tycho's real published shock velocity (4,600 km/s), compute its post-shock ion temperature, and compare it to Cassiopeia A's (computed in the lab), stating which remnant's shock produces the hotter predicted plasma and by what percentage.
Using the steeper above-knee power-law index (3.1), compute the cosmic-ray flux at 10x the knee energy (3x10^16 eV) relative to the flux exactly at the knee, and compare the steepness of this decline to the flux decline over the same energy ratio using the below-knee index (2.7) instead.
Using the Crutcher (2012) B-n relation, compute the predicted magnetic-field strength for gas at Barnard 68's density (8.0e+04 cm^-3, from Unit 5), and compare it to the OMC-1 core's predicted field (computed in the lab), stating which core is predicted to have the stronger field and why, given the two cores' different densities.
Using the Crab Nebula's real magnetic field, compute the synchrotron critical frequency for a lower-energy electron with Lorentz factor 1.0e4 (rather than the lab's 1.0e6), and identify what part of the electromagnetic spectrum this frequency falls in, connecting your answer to the nu_c ∝ gamma^2 scaling.
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.