The precise definition of the lower mass limit of red supergiant stars (RSGs) is an open question in astrophysics and does not attract much attention. Here, we assemble a spectroscopic evolved cool star sample with 6602 targets, including RSGs, asymptotic giant branch stars, and red giant branch stars, in the Large Magellanic Cloud based on Gaia DR3 and Sloan Digital Sky Survey IV/APOGEE-2. The reference spectrum of each stellar population is built according to the quantile range of relative intensity (1% ∼ 99%). Five different methods, e.g., χ 2, cosine similarity, machine learning (ML), equivalent width, and line ratio, are used in order to separate different stellar populations. ML and χ 2 provide the best and relatively consistent prediction of a certain population. The derived lower limit of the RSG population is able to reach the K s -band tip of the red giant branch (K s ≈12.0 mag), indicating a luminosity as low as about 103.5 L ⊙, which corresponds to a stellar radius of only about 100 R ⊙. Given the mass–luminosity relation of L/L⊙=f(M/M⊙)3 with f ≈ 15.5 ± 3 and taking into account the mass loss of faint RSGs up to now, the minimal initial mass of the RSG population would be about 6.1 ± 0.4 M ⊙, which is much lower than the traditional threshold of 8 M ⊙ for the massive stars. This is the first spectroscopic evidence, indicating that the lower mass limit of the RSG population is around 6 M ⊙. However, the destinies of such faint RSGs are still elusive and may have a large impact on stellar evolutionary and supernova models.
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