Constructing Polynomial Spectral Models for Stars [SSA]

http://arxiv.org/abs/1603.06574


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), which can then 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 to ab initio spectral models only over a limited portion of label space, which will vary case by case. Yet, taking the APOGEE survey as an example, we found that one 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. We suggest that 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.

Read this paper on arXiv…

H. Rix, Y. Ting, C. Conroy, et. al.
Wed, 23 Mar 16
22/73

Comments: 4 pages, 2 figures, submitted to ApJL