A constrained linear model for continuum normalization of stellar spectra

TL;DR

This paper introduces a constrained linear model for continuum normalization in stellar spectra that efficiently fits multiple nuisances simultaneously, improving consistency and accuracy without requiring initial guesses.

Contribution

The proposed model factorizes theoretical spectra into basis components, enabling fast, convex inference that jointly models stellar absorption, telluric transmission, and continuum effects.

Findings

Achieves 0.2% consistency across time for high S/N spectra

Performs better than existing methods at lower S/N levels

Demonstrates robustness on ESO/HARPS spectra of various star types

Abstract

Inferring stellar parameters and chemical abundances by forward modeling 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 pre-processing step that is independent of stellar parameters. This leads to results that are biased, or inconsistent across signal-to-noise ratios. A more justified approach is to forward model spectra with all nuisances simultaneously, but in practice this can be an expensive or non-convex optimization procedure. Here we describe a constrained linear model that can fit stellar absorption, telluric transmission, the joint continuum-instrument response. Stellar absorption and telluric transmission are each modeled by factorizing a grid of rectified theoretical spectra into two non-negative matrices with a chosen number of basis components. This model characterizes all possible spectra in many fewer parameters than comparable data-driven models. The non-negativity 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 $\alpha$-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.