ASTR 470 PS 05: Compactness and neutron-star radius

Objectives

Derive and apply a high-energy astrophysics model.
Use units, approximations, and uncertainty explicitly.
Interpret a real system or verified mission specification without overclaiming.
Communicate a reproducible analysis and limitation.

Instructions

Submit four complete responses, code or reproducible pseudocode, one labeled figure/table, and a provenance note. Report SI units before converting to astronomical units. Arithmetic slips receive partial credit only when the model and units are correct. Revisions with a change log are encouraged.

Problem 1

Derive the governing relation used in Lectures 06-07. Apply it to the supplied neutron_star_models.csv; show dimensions, intermediate values, and one limiting-case check.

Problem 2

Use neutron_star_models.csv to make a labeled plot or comparison table. Test this specific alternative: compare mass-radius models with compactness and redshift observables. Explain which conclusion changes and which remains robust.

Problem 3

A skeptical reviewer says: 'Compactness and neutron-star radius proves the source physics directly.' Write a 250-word response separating observed, calibrated, inferred, and model-dependent claims. Use two concrete entries from the data record.

Problem 4

Transfer problem: design a follow-up measurement using a named instrument or archive. Specify band/energy or timing requirement, expected signal, background/systematic risk, and a decision rule. Cite the exact source anchor: NICER About page and OpenStax 24.1..

Computed reference check

r_L approximately 0.36034 pc The estimate uses pc approximately equal to E/c and shows why Galactic magnetic fields erase arrival directions.

Exact practice anchors: OpenStax Astronomy 2e, Sections 23.4, 24.5, 24.6, 27.1, or 20.4 as appropriate; see references/source-indexes/openstax-astronomy-2e-problem-index.md for indexed exercise wording. Human spot-check against the adopted edition is required.

Deliverables

100 points: derivation and units 30, data/model analysis 30, critique and evidence 20, transfer design 20.