The dust in M31

We have analysed Herschel observations of M31, using the PPMAP procedure. The resolution of PPMAP images is sufficient (similar to 31 pc on M31) that we can analyse far-IR dust emission on the scale of giant molecular clouds. By comparing PPMAP estimates of the far-IR emission optical depth at 300 mu m (tau(300)), and the near-IR extinction optical depth at 1.1 mu m (tau(1.1)) obtained from the reddening of RedGiant Branch (RGB) stars, we showthat the ratio R-tau(obs.) equivalent to tau(1.1)/tau(300) falls in the range 500 less than or similar to R-tau(obs.) less than or similar to 1500. Such low values are incompatible with many commonly used theoretical dustmodels, which predict values of R-kappa(model) equivalent to kappa(1.1)/kappa(300) (where kappa is the dust opacity coefficient) in the range 2500 less than or similar to R-kappa(model) less than or similar to 4000. That is, unless a large fraction, greater than or similar to 60 per cent, of the dust emitting at 300 mu m is in such compact sources that they are unlikely to intercept the lines of sight to a distributed population like RGB stars. This is not a new result: variants obtained using different observations and/or different wavelengths have already been reported by other studies. We present two analytic arguments for why it is unlikely that greater than or similar to 60 per cent of the emitting dust is in sufficiently compact sources. Therefore it may be necessary to explore the possibility that the discrepancy between observed values of R-tau(obs.) and theoretical values of R-kappa(model) is due to limitations in existing dust models. PPMAP also allows us to derive optical-depth weighted mean values for the emissivity index, beta equivalent to -dln (kappa(lambda))/dln (lambda), and the dust temperature, T, denoted (beta) over bar and (T) over bar. We show that, in M31, R-tau(obs.) is anticorrelated with (beta) over bar according to R-tau(obs.) similar or equal to 2042(+/- 24) - 557(+/- 10) (beta) over bar. If confirmed, this provides a challenging constraint on the nature of interstellar dust in M31.