ASTR 230 Problem Set 04: White Dwarfs, Supernovae, and Neutron Stars

Problem set for Unit 4.

Problems

1. Sirius B's mass fraction of the Chandrasekhar limit 15 points

Sirius B has a measured mass of 1.018 M☉. Express this as a percentage of the Chandrasekhar limit (1.4 M☉), and state how much additional mass (in M☉) Sirius B could accrete before reaching that limit.

2. Hypothetical white dwarf density and mass 15 points

Using Sirius B's density (2.703e+09 kg/m³, from Lab 04) as typical of a carbon-oxygen white dwarf, compute the mass of a hypothetical white dwarf with radius 0.006 R☉. State whether this mass is below or above the Chandrasekhar limit.

3. Neutron star spin-up from angular momentum conservation 15 points

A massive-star core with radius 1.2 × 10⁴ km rotates once every 25 days before collapse. It collapses to a neutron star of radius 12 km. Using I ∝ R² and conservation of angular momentum, compute the neutron star's rotation period in seconds.

4. Textbook problem: Type Ia vs. Type II progenitors 15 points

OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 23, Review Questions (death of low-mass vs. massive stars): in 150-250 words, contrast the progenitor systems and observational signatures that distinguish a Type Ia from a Type II supernova, using this course's Lecture 08 vocabulary (accretion, Chandrasekhar limit, iron core, core collapse).

Due and Scope

Submit a clear solution with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without visible work receives partial credit at most.

OpenStax Companion Reading

OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 23.1 (white dwarfs) and Chapter 23.2-23.4 (supernovae, neutron stars, pulsars).

References and Data Sources