2025MNRAS.542..669G

We describe a novel framework to model galaxy spectra with two cospatial stellar populations, such as may represent a bulge and bar or thick and thin disc, and apply it to APOGEE spectra in the inner $\sim$2 kpc of M31, as well as to stacked spectra representative of the northern and southern parts of M31's disc ($R\sim 4\!-\!7$ kpc). We use a new unWISE-based photometric decomposition of M31 that includes a Sérsic bulge, bar, and exponential disc. This informs our full-spectrum fitting with A-LIST spectral templates to derive the radial velocity, velocity dispersion, metallicity, and $\alpha$ abundance for both components in each spectrum. In the bulge, one component exhibits little net rotation, high velocity dispersion ($\sim$170 km s$^{-1}$), an average [M/H] = 0.07, and average [$\alpha$/M] = 0.29, while the second component shows structured rotation, lower velocity dispersion ($\sim$121 km s$^{-1}$), and similar average abundances. We also constrain the abundance gradients for each of these components. We tentatively associate the first component with the classical bulge and the second with the bar. In the north disc we identify two distinct components: the first with hotter kinematics, lower metallicity, and higher $\alpha$ abundance than the second ([M/H] = 0.1 and 0.39, [$\alpha$/M] = 0.29 and 0.07). These discs appear comparable to the Milky Way's 'thick' and 'thin' discs, providing the first evidence that M31's inner disc has a similar chemodynamical structure. Such multipopulation analysis is crucial to constrain galaxy evolution models that strive to recreate the complex stellar populations found in the Milky Way.