Learning objectives
- convert frequency to radio velocity, fit a Gaussian line, integrate brightness temperature, and derive an optically thin H I column.
- 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/hi_spectrum_teaching.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: N_HI = 1.75e+21 cm^-2; integral = 960 K km/s.
Apparatus and procedure
- Use the exact rest frequency and radio convention to create a velocity axis; verify sign with a receding-source test.
- Fit a Gaussian plus constant baseline to the supplied spectrum and inspect fit residuals near line wings.
- Numerically integrate T_B dv using the channel spacing, then compare with the analytic Gaussian area.
- Apply the thin H I column-density conversion and perturb baseline and line amplitude to estimate systematic sensitivity.
- State why this teaching spectrum cannot establish real optical depth or Galactic structure.
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 the velocity spectrum, fit parameters and covariance, integrated brightness, N_HI, and a concise assumptions table.
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
The optically thin N_HI is proportional to integrated brightness; a baseline error across a broad line can dominate the formal fit uncertainty. 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/hi_spectrum_teaching.csv, level 3. Real facility/survey context: reference log. No external image is used.