Download the data before interpreting a fit
Use the public real-data archive linked below and extract it into an empty directory. It contains the original 74880-byte HD 48682 FITS image, unchanged REASONS fit notes, six transcribed measured flux detections, five Python files and eight expected outputs. The provenance file records exact source versions and SHA 256 hashes. The restored image comes from Zenodo 12583396 v0.0 under CC BY 4.0; the separately published numerical photometry retains its own attribution.
Despite its filename, the FITS file is an image, not a visibility table. Its continuum reference is 229.4830981104 gigahertz, whereas RESTFRQ records 230.538 gigahertz. The scripts preserve both. They mask 4799 nonfinite edge pixels, retain the negative right-ascension increment, and use the actual elliptical restoring beam. These details affect a physical prediction and are not housekeeping to discard.
The selected photometry is the paper’s own PACS reduction at 70,100 and 160 micrometres, together with published 250,350 and 850 micrometre detections. Alternate reductions of the same PACS observations are not counted twice. Upper limits whose confidence convention has not been verified, and correlated synthetic Spitzer spectral bins, are omitted. The 2020 erratum concerns observing and calibration description; this exercise does not repeat that pipeline.
Reading: Matrà · REASONS archive 12583396, version v0.0, CC BY 4.0 · Hengst et al. 2020 · HD 48682, Tables 1–2 · Hengst et al. 2020 · published erratum
Run the flat folder
Start with the tutorial’s seven independent checks. They test the finite Planck integral, mass integration, radiative equilibrium, actual beam normalization and image/SED flux closure. Then run the analysis and compare its outputs with the supplied expected directory. The same flat package has been rerun with CPython 3.9.6 and 3.13.11 without network access.
The analysis evaluates 448 conditional families. Dust occupies three annuli at 0.9,1.0 and 1.1 times trial radius with fixed mass fractions. Twenty-four logarithmic size bins preserve the chosen number-law mass integrals; each grain and annulus solves radiative equilibrium. The same population makes the six-band spectrum and the SMA-frequency image. A fixed stellar blackbody, with radius derived from the stated luminosity and temperature, contributes to both.
There is deliberately no planet parameter in this fit. The dynamical Lab is a separate synthetic experiment around its own star. A successful radiative annulus fit cannot be relabeled as a fit of the Lab planet to HD 48682. The package also records unverified delivered primary-beam response, omitted calibration covariance and the coarse geometry grid.
Reading: Matrà · REASONS archive 12583396, version v0.0, CC BY 4.0 · Hengst et al. 2020 · HD 48682, Tables 1–2
Derive the one parameter that is solved exactly
At each grid point, predict dust flux per reference mass and add the fixed stellar contribution. Only the nonnegative dust mass amplitude is optimized continuously. Differentiate the weighted residual sum with respect to amplitude; its linear derivative gives a ratio of weighted products. If that ratio is negative, the constrained optimum is the zero boundary.
Photometry uses reciprocal reported variance. The image uses every second finite pixel within 15 arcseconds, with an outer-annulus robust noise scale and a sampled-area-to-beam-area factor. This prevents grossly treating oversampling as independent information, but does not supply the full CLEAN covariance. Save spectrum and image scores separately. Their sum ranks conditional examples; it is not a calibrated probability or confidence interval.
Reading:
Read the alternatives, not only the first row
The saved grid selects a 40 astronomical-unit family with minimum grain radius 5 micrometres and optical exponent two. Its combined diagnostic score is 14.3188. A 25 astronomical-unit family with 15 micrometre minimum grains scores 14.3248. A 60 astronomical-unit family with 0.2 micrometre grains and exponent one scores 16.1689. Those are very different physical assumptions with nearby rankings in this restricted calculation.
Read conditional-profile.csv and geometry-profile.csv alongside model-sed.csv. Check which alternatives lie at grid boundaries, and inspect the input fit notes stating weak orientation and width constraints. Do not convert the smallest score into a unique belt radius or planet mass. Expanding the grid can move its minimum; changing grain composition can change it again.
The restricted blackbody alternative is optimized over a continuous 0.5–160 AU radius interval. A coarse lower grid edge of 15 AU would exclude its best radius. It reaches a spectrum score of 28.7303 near 6.715 astronomical units. This is worse than the flexible grain spectrum within the stated error convention, but the comparison is still conditional on a simplified emission model and unmodeled calibration correlations.
Reading:
Make one controlled change and keep the record
First change the minimum grain radius while keeping the geometric family fixed. Explain how its temperature and long-wave efficiency change before reading the new mass amplitude. Then change the image inclination without changing the optically thin total dust spectrum. If the integrated model flux changes simply because it was projected, inspect field losses and normalization.
For a numerical check, the selected family is recomputed with 48 size bins and fourfold finer quadrature. The saved band changes are below 0.234 percent; quadrature alone changes them by less than 0.00731 percent. These bounds validate this selected radiative calculation, not every possible optical law or the stochastic Lab dynamics.
A useful transfer exercise is to remove the image term and compare the radius profile. State which ambiguity the image actually reduces, and which remains. Keep a table of changed assumptions, separate score contributions and residuals. That record is more informative than a single best-fit illustration.
Reading: