ULySS: A Full Spectrum Fitting Package

Aims. We provide an easy-to-use full-spectrum fitting package and explore its applications to (i) the determination of the stellar atmospheric parameters and (ii) the study of the history of stellar populations. Methods. We developed ULySS, a package to fit spectroscopic observations against a linear combination of non-linear model components convolved with a parametric line-of-sight velocity distribution. The minimization can be either local or global, and determines all the parameters in a single fit. We use chi2 maps, convergence maps and Monte-Carlo simulations to study the degeneracies, local minima and to estimate the errors. Results. We show the importance of determining the shape of the continuum simultaneously to the other parameters by including a multiplicative polynomial in the model (without prior pseudo-continuum determination, or rectification of the spectrum). We also stress the benefice of using an accurate line-spread function, depending on the wavelength, so that the line-shape of the models properly match the observation. For simple models, i. e., to measure the atmospheric parameters or the age/metallicity of a single-age stellar population, there is often a unique minimum, or when local minima exist they can unambiguously be recognized. For more complex models, Monte-Carlo simulations are required to assess the validity of the solution. Conclusions. The ULySS package is public, simple to use and flexible. The full spectrum fitting makes optimal usage of the signal.

💡 Research Summary

The paper presents ULySS (University of Lyon Spectroscopic analysis Software), a publicly available, Python‑based package for full‑spectrum fitting of astronomical data. ULySS fits an observed spectrum by convolving a linear combination of non‑linear model components with a parametric line‑of‑sight velocity distribution (LOSVD). The model components can represent individual stellar atmospheres (characterized by effective temperature, surface gravity, and metallicity) or simple stellar populations (SSPs) defined by age and metallicity. Linear coefficients weight each component, allowing the construction of composite populations or mixtures of stars and gas.

A central innovation of ULySS is the simultaneous treatment of the continuum shape. Instead of pre‑normalising the spectrum or estimating a pseudo‑continuum, a multiplicative polynomial of adjustable order is included directly in the model. This polynomial absorbs large‑scale flux variations caused by instrumental response, interstellar extinction, or imperfect flux calibration, thereby eliminating the need for ad‑hoc rectification steps. The authors demonstrate that fitting the continuum together with the physical parameters yields more reliable results, especially for low‑signal‑to‑noise data or spectra covering a wide wavelength range.

Another key aspect is the explicit handling of the line‑spread function (LSF). Because spectrographs often exhibit wavelength‑dependent resolution, ULySS allows the user to supply an LSF curve (or a set of LSFs) that is convolved with the model spectra before comparison with the data. By matching the model line shapes to the instrument’s actual performance, systematic biases in age, metallicity, or kinematic measurements are reduced dramatically.

Optimization proceeds by minimizing a χ² merit function that includes both the non‑linear physical parameters and the linear weights. By default ULySS employs the Levenberg‑Marquardt algorithm for local minimisation, but it also supports global search strategies such as simulated annealing or genetic algorithms for more complex parameter spaces. The software automatically generates χ² maps and convergence maps, which help the user visualise the topology of the solution space, identify possible local minima, and assess parameter degeneracies.

Error estimation is treated with a two‑tier approach. When the χ² surface exhibits a single, well‑behaved minimum, the covariance matrix from the local optimiser provides reliable 1σ uncertainties. For more intricate models—e.g., multi‑component SSP mixtures where several minima may exist—the authors recommend Monte‑Carlo simulations. By repeatedly adding realistic noise (consistent with the observed signal‑to‑noise ratio) and re‑fitting, one obtains a distribution of solutions that quantifies both random errors and systematic effects arising from parameter correlations.

The paper showcases three scientific applications.

1. Stellar atmospheric parameters – High‑resolution spectra of individual stars are fitted to retrieve T_eff, log g, and