2026ApJ...998..192C

Inferring stellar parameters and chemical abundances by forward modelling stellar spectra usually requires a spectral synthesis code, or an emulator constructed from a curated training set. In these situations continuum normalization is often implemented as a preprocessing step that is independent of stellar parameters. This leads to results that are biased, or inconsistent across signal-to-noise ratios (S/Ns). A more justified approach is to forward model spectra with all nuisances simultaneously, but in practice this can be an expensive or nonconvex optimization procedure. Here we describe a constrained linear model that can fit stellar absorption, telluric transmission, and the joint continuum-instrument response. Stellar absorption and telluric transmission are each modelled by factorizing a grid of rectified theoretical spectra into two nonnegative matrices with a chosen number of basis components. This model can represent all possible spectra using far fewer parameters than comparable data-driven models. The nonnegativity constraint ensures basis vectors are strictly additive, which limits rectified flux to less than or equal to unity, such that we can distinguish normalized spectra from the joint instrument-continuum response. The model requires no initial guess, and the linearity ensures that inference is convex, stable, and fast. This model allows us to reliably fit nuisances (e.g., tellurics, continuum), and is readily extensible to radial velocity and rotational broadening without any prior knowledge about the fundamental stellar properties. We demonstrate our method by fitting ESO/HARPS high-resolution echelle spectra of BAFGKM-type stars. With repeat observations of α Centauri A, we present results that are best in class: consistent across time to 0.2% at S/N ∼ 100, and to better than 0.5% at S/N ∼ 30.