Learning objectives
- estimate completeness, correct source surface density, infer an inner-Galaxy radius under a stated rotation model, and assess uncertainty.
- Propagate a statistical or calibration uncertainty and report a limitation.
- Preserve a reproducible record of inputs, transformations, and outputs.
Preparation, materials, and setup
Use Python 3 with the standard library (or a spreadsheet capable of regression and plotting), the supplied ../data/survey_injections.csv, and the relevant lecture notes. Record file name, row count, columns, units, and provenance level before editing. No facility observing time is assumed.
Dataset status: the supplied compact record is synthetic/instructor-provided (level 3), not an archived observation. Compare its analysis workflow with the real survey or observatory source cited in ../reference-log.md.
Computed check: corrected surface density = 71.43 deg^-2; Poisson-only uncertainty = 2.062 deg^-2.
Apparatus and procedure
- Partition injection/recovery rows by flux bin and sky tile; compute p_hat and binomial standard error for each stratum.
- Compute corrected surface density and Poisson uncertainty for the supplied detection count and usable area.
- Propagate completeness uncertainty using first-order derivatives and compare with Poisson-only uncertainty.
- Use the supplied l and v_LSR measurements with the stated flat-rotation parameters to compute Galactocentric radii.
- Load ../data/hi_kinematics_teaching.csv separately from the injection table and compute model-dependent Galactocentric radii from its longitude and v_LSR columns.
- Write a reproducible analysis note separating survey products, teaching records, model assumptions, and unresolved systematics.
- Use CDS catalog J/A+A/594/A116 and its ReadMe to select a listed 20-by-20-degree Galactic HI4PI FITS subcube nearest l=30 degrees, b=0 degrees. Record the actual file name, coordinates, FITS WCS, velocity convention, units, access date, and checksum; compare one real spectrum and a numerical N_HI integral with the supplied synthetic injection exercise.
Measurement record and uncertainty
| Record | Required entry |
|---|---|
| Input | File, release/source, units, masks or flags, and provenance level. |
| Model | Equation, parameter values, convention, and approximation. |
| Statistics | Fit covariance or counting error plus one calibration/selection/systematic term. |
| Validation | Independent recomputation, residual plot, and limiting-case check. |
Submit completeness plot, corrected-density calculation, kinematic radius table, and a one-page method/provenance note.
Deliverables and criteria
- Reproducible code or spreadsheet with inputs and units documented.
- One publication-quality labeled plot and a short interpretation (400-700 words).
- Uncertainty budget that separates random, common-mode, and model terms where relevant.
- Credit requires correct method, units, interpretation, provenance, and a limitation; a copied numeric result without an audit trail earns at most half credit.
Interpretive boundary
A completeness-corrected estimate remains conditional on injection realism, usable-area masks, and the adopted circular-rotation model. State explicitly which parts of your result are facts about this prepared teaching record and which are transferable inference methods.
References and provenance
Course teaching record: ../data/survey_injections.csv, level 3. Real facility/survey context: reference log. No external image is used.