Using the Oxford Short Wavelength Integral Field specTrograph (SWIFT), we investigate radial variations of several initial mass function (IMF) dependent absorption features in M31 and M32. We obtain high signal-to-noise spectra at six pointings along the major axis of M31 out to ~ 700 (2.7 kpc) and a single pointing of the central 10 pc for M32. In M31 the sodium NaI {lambda}8190 index shows a flat equivalent width profile at ~ 0.4 {AA} through the majority of the bulge, with a strong gradient up to 0.8 {AA} in the central 10 (38 pc); the Wing-Ford FeH {lambda}9916 index is measured to be constant at 0.4 {AA} for all radii; and calcium triplet CaT {lambda}8498, 8542, 8662 shows a gradual increase through the bulge towards the centre. M32 displays flat profiles for all three indices, with FeH at ~ 0.5 {AA}, very high CaT at ~ 0.8 {AA} and low NaI at ~ 0.1 {AA}. We analyse these data using stellar population models. We find that M31 is well described on all scales by a Chabrier IMF, with a gradient in sodium enhancement of [Na/Fe] ~ +0.3 dex in the outer bulge, rising within the central 10 to perhaps [Na/Fe] ~ +1.0 dex in the nuclear region. We find M32 is described by a Chabrier IMF and young stellar age in line with other studies. Models show that CaT is much more sensitive to metallicity and [{alpha}/Fe] than to IMF. We note that the centres of M31 and M32 have very high stellar densities and yet we measure Chabrier IMFs in these regions.
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