ASTR 410 Problem Set 04 Solutions: Chemical Evolution of the Galactic Disk and Dark Matter Halos and the Local Mass Budget: quantitative reasoning

Instructor solution key

Scoring overview

Problems 1–4 are worth 25 points each. Award credit for correct reasoning, units, reproducibility, and interpretation; separate arithmetic slips from conceptual errors.

Problem 1

Expected approach: define the observable and model, substitute the shared constants or CSV values, preserve units, and test the stated assumption. Accept algebraically equivalent derivations when the physical interpretation is correct.

Key: The closed-box estimate is Z=y ln(1/mu) = 0.021.

Problem 2

Expected approach: define the observable and model, substitute the shared constants or CSV values, preserve units, and test the stated assumption. Accept algebraically equivalent derivations when the physical interpretation is correct.

Key: The result must include a labeled plot, a sensitivity comparison, and a provenance statement. A numerical answer without those elements is incomplete.

Problem 3

Expected approach: define the observable and model, substitute the shared constants or CSV values, preserve units, and test the stated assumption. Accept algebraically equivalent derivations when the physical interpretation is correct.

Key: The result must include a labeled plot, a sensitivity comparison, and a provenance statement. A numerical answer without those elements is incomplete.

Problem 4

Expected approach: define the observable and model, substitute the shared constants or CSV values, preserve units, and test the stated assumption. Accept algebraically equivalent derivations when the physical interpretation is correct.

Key: The result must include a labeled plot, a sensitivity comparison, and a provenance statement. A numerical answer without those elements is incomplete.

Common errors