ASTR 474 Problem Set 05: Radiative Transfer and Approximation Validity

Objectives and instructions

Practice computational reasoning, quantitative analysis, validation, and scientific communication for lectures 07-08.

Use SI or explicitly stated astronomical units consistently; show conversions and significant figures.
Cite all data, software, and adapted code. Distinguish supplied measured data from synthetic records.
Include runnable code and record environment, command, and seed where used.
Collaboration on concepts is permitted; each submitted derivation, code, and interpretation must be the student's own and contributors must be named.

Revisions and resubmissions are encouraged to improve mastery and grade under the course policy.

Problem 5.1

Solve dI/dtau=S-I for constant S and boundary I0; show the steps and verify the tau=1 value against the generated record.

Deliver: derivation or code, units/conventions, a reproducible result, uncertainty or validation evidence, and a short physical interpretation.

Problem 5.2

At tau=0.1 and tau=5, compare the first-order thin approximation with the exact solution. State absolute and relative errors and choose a tau domain for a 1% relative-error requirement using a denser computed scan.

Deliver: derivation or code, units/conventions, a reproducible result, uncertainty or validation evidence, and a short physical interpretation.

Problem 5.3

Explain why a grey constant-source slab cannot by itself model a non-LTE scattering atmosphere. Identify which physical terms would change the source function or closure.

Deliver: derivation or code, units/conventions, a reproducible result, uncertainty or validation evidence, and a short physical interpretation.

Reproducibility check

Use this generated reference result as one consistency check, not as a substitute for showing reasoning: For the first-order thin approximation, relative intensity error is 0.000122 at tau=0.01 and 2.88 at tau=5; the tolerance defines whether either is acceptable.

No textbook exercise is adopted for this course; problems are original and cite the primary software/data sources in the reference log.

Submission

Submit a readable PDF report, source code, environment/version record, and any generated tables/figures. The assignment is complete only when another student can rerun the command and identify the inputs and validation test.