README
This code is developed by Maria B. Stone.
October 17th, 2025
A minimal example notebook with code demonstrating Chebyshev polynomial fitting to correct star formation rate (SFR) values from one estimator to the baseline for another estimator.
This code was written for a research project (paper Stone et al. in review, ApJ) which looks into the star formation history parameters of low-redshift quasars. This research project utilized SFR data produced by CIGALE and MAGPHYS programs, and thus there was a need to bring everything to the same baseline.
In this paper, we have two SFR estimators: CIGALE-based and MAGPHYS-based. Both CIGALE and MAGPHYS are tools to model the spectral energy distribution of a galaxy. https://cigale.lam.fr/documentation/ https://www.iap.fr/magphys/
The quasar sample in this paper does not have reliable MAGPHYS estimates, only CIGALE-based estimates for SFR parameter. The control sample of galaxies has SFR estimates from both methods, on the other hand, so it is used to obtain a correction curve to bring the quasar sample value to MAGPHYS baseline. Thus, the Chebyshev fit correction for SFR is based on the data of a control sample of galaxies.
We first calculate the offsets between the two SFR values for each galaxy in the control sample,
offset = $\Delta$SFR = SFR${CIGALE}$ - SFR${MAGPHYS}$
All SFR values are expressed in log(10). The units of SFR are in solar masses per year.
We identified median offset values per dex of SFR$_{CIGALE}$ for control galaxies. The data regarding these median offset points for normal galaxies is saved in the file 'sfroffset.fits'.
The code demonstrates:
- How to construct a Chebyshev fit to median offsets for a control galaxy sample
- How to apply the correction to quasar host galaxies
- How to clip input values to the fit domain safely
- How to visualize in plots the fit results and the final histogram of corrected SFRs.
Open SFR_Chebyshev_fit.ipynb in Jupyter to reproduce the fits and figures.
Guidance on coding workflow and documentation provided by OpenAI’s ChatGPT (GPT-5).
If you use this example or its concepts, please cite:
Stone, M. (in review, ApJ), SFR Chebyshev Fit Example,
Zenodo: 10.5281/zenodo.17381579
SFR_Chebyshev_fit.ipynb— example Jupyter notebook with the fitting and correction stepssfroffset.fits— control sample offsetsquasar_subsample_sfrcigale.fits— quasar sample datafigure_fit_demo.pdf,figure_corrections.pdf,figure_histogram.pdf— visual outputsREADME.md— this documentation file