Constructing Polynomial Spectral Models for Stars

TL;DR

This paper introduces polynomial spectral models (PSMs) that efficiently approximate stellar spectra across multiple parameters, enabling fast, simultaneous fitting of complex models to observed spectra, significantly reducing computational costs.

Contribution

The paper presents a novel polynomial spectral modeling approach that requires far fewer calculations than traditional grid methods, allowing efficient multi-parameter stellar spectral fitting.

Findings

A quadratic PSM can approximate spectra within 10^{-3} flux accuracy.

The PSM recovers stellar abundances within ~0.02 dex rms.

The method enables rapid, simultaneous fitting of complex stellar models.

Abstract

Stellar spectra depend on the stellar parameters and on dozens of photospheric elemental abundances. Simultaneous fitting of these $\mathcal{N}\sim 10-40$ model labels to observed spectra has been deemed unfeasible, because the number of ab initio spectral model grid calculations scales exponentially with $\mathcal{N}$. We suggest instead the construction of a polynomial spectral model (PSM) of order $\mathcal{O}$ for the model flux at each wavelength. Building this approximation requires a minimum of only ${\mathcal{N}+\mathcal{O}\choose\mathcal{O}}$ calculations: e.g. a quadratic spectral model ($\mathcal{O}=2$) to fit $\mathcal{N}=20$ labels simultaneously, can be constructed from as few as $231$ ab initio spectral model calculations; in practice, a somewhat larger number ($\sim 300-1000$) of randomly chosen models lead to a better performing PSM. Such a PSM can be a good approximation only over a portion of label space, which will vary case by case. Yet, taking the APOGEE survey as an example, a single quadratic PSM provides a remarkably good approximation to the exact ab initio spectral models across much of this survey: for random labels within that survey the PSM approximates the flux to within $10^{-3}$, and recovers the abundances to within $\sim 0.02$ dex rms of the exact models. This enormous speed-up enables the simultaneous many-label fitting of spectra with computationally expensive ab initio models for stellar spectra, such as non-LTE models. A PSM also enables the simultaneous fitting of observational parameters, such as the spectrum's continuum or line-spread function.