Accelerated Fitting of Stellar Spectra

Abstract

Stellar spectra are often modeled and fitted by interpolating within a rectilinear grid of synthetic spectra to derive the stars' labels: stellar parameters and elemental abundances. However, the number of synthetic spectra needed for a rectilinear grid grows exponentially with the label space dimensions, precluding the simultaneous and selfconsistent fitting of more than a few elemental abundances. Shortcuts such as fitting subsets of labels separately can introduce unknown systematics and do not produce correct error covariances in the derived labels. In this paper we present a new approach-Convex Hull Adaptive Tessellation (CHAT)-which includes several new ideas for inexpensively generating a sufficient stellar synthetic library, using linear algebra and the concept of an adaptive, data-driven grid. A convex hull approximates the region where the data lie in the label space. A variety of tests with mock data sets demonstrate that CHAT can reduce the number of required synthetic model calculations by three orders of magnitude in an eight-dimensional label space. The reduction will be even larger for higher dimensional label spaces. In CHAT the computational effort increases only linearly with the number of labels that are fit simultaneously. Around each of these grid points in the label space an approximate synthetic spectrum can be generated through linear expansion using a set of "gradient spectra" that represent flux derivatives at every wavelength point with respect to all labels. These techniques provide new opportunities to fit the full stellar spectra from large surveys with 15-30 labels simultaneously.

Signatures of unresolved binaries in stellar spectra: implications for spectral fitting

“…To efficiently calculate the synthetic spectrum at an arbitrary point in label space (as is required during fitting) we interpolate between nearby models at each wavelength pixel using a neural network. This approach, which makes it possible to self-consistently fit for many stellar labels simultaneously, is similar to that developed in Ting et al (2016b) and Rix et al (2016). It was introduced in Ting et al (2017a) and will be fully explained in Ting et al (2017c, in prep).…”

Blind chemical tagging with DBSCAN: prospects for spectroscopic surveys

“…• abundances (from Table 1): -conservative -from Holtzman et al (2015) -optimistic -from Leung & Bovy (2019) -theoretical -from Ting et al (2016) We begin by explaining our parameter choices to create an APOGEE-like survey, followed by a description of our parameter choice for DBSCAN. We summarize the results of our assessment statistics before describing the recovery fraction in more detail.…”

“…Uncertainties used to add normally distributed noise to cluster member abundances around the chosen centre. Conservative from Holtzman et al (2015), optimistic from Leung & Bovy (2019), and theoretical from Ting et al (2016). element conservative optimistic theoretical…”

“…• theoretical : Member abundances selected with spread around cluster centre corresponding to theoretical uncertainties at the Cramer-Rao bound computed in Ting et al (2016). Considered together, the three possible choices of abundances for each star constitute three abundance spaces on which we perform chemical tagging.…”

Analysis of Stellar Spectra from LAMOST DR5 with Generative Spectrum Networks

“…The error information they generate is most relevant to the internal errors of each method or the dispersion of the difference between their results and that of external counterparts. Simple linear interpolation could not precisely characterize the complex relationship between flux and stellar parameters until Rix et al (2016); Ting et al (2016Ting et al ( , 2018 put forward a polynomial spectral model and the Payne method, that are both based on the training of a mathematical model using ab initio spectral model grids. These approaches benefit from artificial neural networks because they are effective at fitting complex non-linear relations.…”