Using new, homogeneous, long-slit spectroscopy in the wavelength range from ~0.35 to ~1micron, we study radial gradients of optical and near-infrared (NIR) IMF-sensitive features along the major axis of the bulge of M31, out to a galacto-centric distance of ~200 (~800pc). Based on state-of-the-art stellar population synthesis models with varying Na abundance ratio, we fit a number of spectral indices, from different chemical species (including TiOs, Ca, and Na indices), to constrain the low-mass (<0.5M_Sun) end slope (i.e. the fraction of low-mass stars) of the stellar IMF, as a function of galacto-centric distance. Outside a radial distance of ~10, we infer an IMF similar to a Milky-Way-like distribution, while at small galacto-centric distances, an IMF radial gradient is detected, with a mildly bottom-heavy IMF in the few inner arcsec. We are able to fit Na features (both NaD and NaI8190), without requiring extremely high Na abundance ratios. [Na/Fe] is ~0.4dex for most of the bulge, rising up to ~0.6dex in the innermost radial bins. Our results imply an overall, luminosity-weighted, IMF and mass-to-light ratio for the M31 bulge, consistent with those for a Milky-Way-like distribution, in contrast to results obtained, in general, for most massive early-type galaxies.
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