ASTR 330 Problem Set 06: The Chandrasekhar Mass for a Helium-Core White Dwarf

OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 22.1-22.2.

Problems

1. Helium-core Chandrasekhar mass 20 points

Compute the Chandrasekhar mass for a pure-helium-core white dwarf (μ_e = 2.0, essentially identical to the carbon-oxygen case since helium-4 also has two nucleons per electron), and compare it to the carbon-oxygen value (1.4351 M⊙, Lab 06).

2. Hypothetical higher mu_e 15 points

Compute the Chandrasekhar mass for a hypothetical composition with μ_e = 2.2 (somewhat more neutron-rich than carbon-oxygen), and state whether it is larger or smaller than the carbon-oxygen value, consistent with the M_Ch ∝ μ_e⁻² scaling.

3. Sirius B, revisited 15 points

Using your Problem 1 helium-core Chandrasekhar mass, recompute Sirius B's mass (1.018 M⊙) as a percentage of this (slightly different) limit, and compare to the 70.9% found in Lab 06 using the carbon-oxygen value.

4. PSR J0348+0432’s white dwarf companion 20 points

PSR J0348+0432's white dwarf companion has a measured mass of 0.172 M⊙ (live-verified this session). Compute this mass as a percentage of the carbon-oxygen Chandrasekhar mass, and state whether this is consistent with its continued existence as a stable white dwarf.

Due and Scope

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 Companion Reading

OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 22.1-22.2.

References and Data Sources