Learning objectives
- fit a spectral index to a frequency-flux series and distinguish an optically thin synchrotron slope from a low-frequency turnover.
- 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/continuum_spectrum.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: FWHM = 30.03 arcmin; A_eff = 343.6 m^2.
Apparatus and procedure
- Read the CSV schema and plot log flux against log frequency, retaining measurement uncertainties.
- Fit S_nu proportional to nu^alpha using weighted least squares; compare a single power law with a broken/turnover model using residuals.
- Compute the synchrotron characteristic frequency for the supplied B and gamma values and compare its scale with the sampled band.
- Convolve a point-source and an extended-source sketch with the listed single-dish beam; explain beam dilution and flux conservation.
- Perturb each flux by its quoted uncertainty in 1000 seeded realizations and report the median alpha and central 68% interval.
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. |
Record fitted alpha, covariance, residual RMS, beam FWHM at each frequency, and model-selection caveat.
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 single power law is only a local empirical fit; curvature can reflect aging, absorption, or mixed components. 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/continuum_spectrum.csv, level 3. Real facility/survey context: reference log. No external image is used.