Constructing Polynomial Spectral Models for Stars
Abstract
Stellar spectra depend on the stellar parameters and on dozens of photospheric elemental abundances. Simultaneous fitting of these { N } ∼ 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 ≤ft(≥nfrac{}{}{0em}{}{{ N }+{ O }}{{ O }}\right) 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 (∼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 ∼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.
- Publication:
-
The Astrophysical Journal
- Pub Date:
- August 2016
- DOI:
- 10.3847/2041-8205/826/2/L25
- arXiv:
- arXiv:1603.06574
- Bibcode:
- 2016ApJ...826L..25R
- Keywords:
-
- methods: data analysis;
- stars: abundances;
- stars: atmospheres;
- techniques: spectroscopic;
- Astrophysics - Solar and Stellar Astrophysics
- E-Print:
- 4 pages, 2 figures, ApJL (Accepted for publication- 2016 May 9)