Lab 07: Capstone: PSR J0348+0432 and the Physics of Core Collapse

Apparatus and Setup

This capstone lab applies this course's full compact-object toolkit (the Chandrasekhar mass, Lecture 12; the core-collapse energy budget, Lecture 13) to PSR J0348+0432, a real pulsar-white-dwarf binary whose relativistic orbital parameters and component masses were live-verified this session via a direct web fetch (see ../reference-log.md).

Materials and Data

Procedure

1. Compute the neutron star's mass and the white dwarf companion's mass each as a fraction (percent) of the Chandrasekhar mass derived in Lab 06, and classify each object accordingly.
2. Compute the neutron star's mean density from its measured mass and radius, and express it as a fraction of standard nuclear saturation density (2.3e+17 kg/m³).
3. Using the generalized Kepler's third law (ASTR 310, Lecture 08), P² = 4π²a³/[G(m1+m2)], verify that the system's measured orbital period and semimajor axis are consistent with the sum of the neutron star and white dwarf masses given in the data table (convert all units to SI first).
4. Using the core-collapse binding-energy estimate ΔE ≈ (3/5)GM²(1/R_remnant − 1/R_core) for a 1.4 M⊙ core collapsing from a 3000 km progenitor radius to the neutron star's measured radius, compute the total energy released, and state what percentage of that energy is carried away by channels other than visible kinetic energy and light (using the standard published 1e+44 J visible-energy value).

Analysis and Uncertainty

Write a short (150-250 word) synthesis connecting this lab's four results: why the neutron star's mass and density together confirm it cannot be a white dwarf, why the companion's mass confirms it can be one, and why the energy budget in step 4 shows the visible supernova was only a small fraction of the total event.

Deliverables

• Both Chandrasekhar-mass-fraction classifications with supporting arithmetic.
• The neutron-star density and nuclear-density-fraction calculation.
• The Kepler's-third-law consistency check with full unit conversions.
• The binding-energy budget calculation and percentage breakdown.
• The written synthesis paragraph.

Assessment Criteria

• Correct Chandrasekhar-mass-fraction arithmetic and classification for both objects.
• Correct density and nuclear-density-fraction arithmetic.
• Correct Kepler's-third-law unit conversions and consistency check.
• Correct binding-energy arithmetic and an honestly characterized (not understated) neutrino-energy-fraction percentage.
• Synthesis paragraph correctly integrates all four results rather than restating them separately.

References and Provenance

• OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 22.3-22.5.
• PSR J0348+0432 masses, radius, and orbital parameters: live-verified this session via a direct web fetch of Wikipedia's "PSR J0348+0432" article, citing Antoniadis et al. (2013), Science 340, 1233232; see materials/ASTR330/reference-log.md.
• Generated by materials/ASTR330/src/generate_astr330_content.py.