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

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.