Constructing Polynomial Spectral Models for Stars

Hans-Walter Rix; Yuan-Sen Ting; Charlie Conroy; David W. Hogg

doi:10.3847/2041-8205/826/2/L25

paper

Constructing Polynomial Spectral Models for Stars

arXiv:1603.06574 · doi:10.3847/2041-8205/826/2/L25

Abstract

Stellar spectra depend on the stellar parameters and on dozens of photospheric elemental abundances. Simultaneous fitting of these $N \sim 10 - 40$ model labels to observed spectra has been deemed unfeasible, because the number of ab initio spectral model grid calculations scales exponentially with $N$ . We suggest instead the construction of a polynomial spectral model (PSM) of order $O$ for the model flux at each wavelength. Building this approximation requires a minimum of only $(O N + O)$ calculations: e.g. a quadratic spectral model ( $O = 2$ ) to fit $N = 20$ 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 $1 0^{- 3}$ , 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.

4 pages, 2 figures, ApJL (Accepted for publication- 2016 May 9)

Constructing Polynomial Spectral Models for Stars

Abstract

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