Lab 07: Capstone: Shocks, Cosmic Rays, and Magnetic Fields in Cassiopeia A

Apparatus and Setup

This capstone lab applies Lecture 13's shock-jump conditions and Lecture 14's cosmic-ray spectrum and magnetic-field scaling to the real Cassiopeia A supernova remnant, synthesizing this course's final unit into one real, multiwavelength object.

Materials and Data

Cassiopeia A: distance=3400 pc, age≈350 yr, shock velocity=5,000 km/s (Vink 2004 and subsequent Chandra proper-motion studies, level 2). Cosmic-ray PDG spectrum parametrization (Lecture 14). Crutcher (2012) molecular-cloud B-n scaling. Crab Nebula B field (Hester 2008, level 2).

Procedure

1. Compute Cassiopeia A's strong-shock compression ratio and post-shock (ion) temperature from its real shock velocity.
2. State the expected observed X-ray (electron) temperature range given incomplete electron-ion equilibration at fast collisionless shocks (Ghavamian, Laming & Rakowski 2007), and compute the ratio between your computed ion temperature and a representative observed electron temperature of kT=3 keV.
3. Using the PDG cosmic-ray flux parametrization, compute the flux at 100 GeV and at the knee energy (3x10^15 eV), and compute the ratio between them.
4. Using the Crutcher (2012) B-n relation, compute the predicted magnetic-field strength for gas at the OMC-1 core's density (from Unit 5) and compare it to the Galactic-average diffuse-ISM field strength.
5. Using the Crab Nebula's real published magnetic-field strength, compute the synchrotron critical frequency for an electron of Lorentz factor 1.0e6, and identify what part of the electromagnetic spectrum this frequency falls in.

Analysis and Uncertainty

Write a short (200-300 word) synthesis connecting Cassiopeia A's shock physics (Lecture 13) to the cosmic rays it is believed to accelerate and the magnetic field needed for that acceleration and for the resulting synchrotron emission (Lecture 14), explicitly naming which observed wavelength regime (X-ray, gamma-ray, radio) provides evidence for each piece of physics.

Deliverables

• All five computed quantities above with full derivations.
• The 200-300 word multiwavelength synthesis paragraph.

Assessment Criteria

• Correct shock-jump and cosmic-ray-flux arithmetic.
• Correct, non-overclaiming statement of the ion-vs-electron temperature discrepancy.
• A genuinely multiwavelength, specific (not generic) synthesis paragraph.

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.
• Cassiopeia A, cosmic-ray spectrum, Crutcher B-n relation, and Crab Nebula parameters: standard published, level 2; see materials/ASTR360/reference-log.md.
• Generated by materials/ASTR360/src/generate_astr360_content.py.