# The dimensionality of stellar chemical space using spectra from the Apache Point Observatory Galactic Evolution Experiment

## TL;DR

This study demonstrates that stellar spectra contain high-dimensional information, with approximately 10 principal components needed to capture the chemical diversity of stars in the Milky Way, enabling spectral-based chemical tagging.

## Contribution

It introduces a model-independent spectral analysis method revealing the high dimensionality of stellar chemical space, advancing chemical tagging without relying on derived abundances.

## Key findings

- Approximately 10 principal components are needed to model spectra accurately.
- The chemical space has an estimated dimensionality of less than 10.
- Stars occupy a vast, finely sampled chemical space with about 10^{10} distinguishable cells.

## Abstract

Chemical tagging of stars based on their similar compositions can offer new insights about the star formation and dynamical history of the Milky Way. We investigate the feasibility of identifying groups of stars in chemical space by forgoing the use of model derived abundances in favour of direct analysis of spectra. This facilitates the propagation of measurement uncertainties and does not presuppose knowledge of which elements are important for distinguishing stars in chemical space. We use ~16,000 red-giant and red-clump H-band spectra from the Apache Point Observatory Galactic Evolution Experiment and perform polynomial fits to remove trends not due to abundance-ratio variations. Using expectation maximized principal component analysis, we find principal components with high signal in the wavelength regions most important for distinguishing between stars. Different subsamples of red-giant and red-clump stars are all consistent with needing about 10 principal components to accurately model the spectra above the level of the measurement uncertainties. The dimensionality of stellar chemical space that can be investigated in the H-band is therefore $\lesssim 10$. For APOGEE observations with typical signal-to-noise ratios of 100, the number of chemical space cells within which stars cannot be distinguished is approximately $10^{10\pm2} \times (5\pm 2)^{n-10}$ with $n$ the number of principal components. This high dimensionality and the fine-grained sampling of chemical space are a promising first step towards chemical tagging based on spectra alone.