We use new Herschel multi-band imaging of the Andromeda galaxy to analyze how dust heating occurs in the central regions of galaxy spheroids that are essentially devoid of young stars. We construct a dust temperature map of M31 through fitting modified blackbody SEDs to the Herschel data, and find that the temperature within 2 kpc rises strongly from the mean value in the disk of 17 pm 1K to sim35K at the centre. UV to near-IR imaging of the central few kpc shows directly the absence of young stellar populations, delineates the radial profile of the stellar density, and demonstrates that even the near-UV dust extinction is optically thin in M31s bulge. This allows the direct calculation of the stellar radiation heating in the bulge, Uast(r), as a function of radius. The increasing temperature profile in the centre matches that expected from the stellar heating, i.e. that the dust heating and cooling rates track each other over nearly two orders of magnitude in Uast. The modelled dust heating is in excess of the observed dust temperatures, suggesting that it is more than sufficient to explain the observed IR emission. Together with the wavelength dependent absorption cross section of the dust, this demonstrates directly that it is the optical, not UV, radiation that sets the heating rate. This analysis shows that neither young stellar populations nor stellar near-UV radiation are necessary to heat dust to warm temperatures in galaxy spheroids. Rather, it is the high densities of Gyr-old stellar populations that provide a sufficiently strong diffuse radiation field to heat the dust. To the extent which these results pertain to the tenuous dust found in the centres of early-type galaxies remains yet to be explored.
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