The dust in M31

We have analysed Herschel observations of M31, using the PPMAP procedure. The resolution of PPMAP images is sufficient (∼ 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 μ m (τ_{{300}}), and the near-IR extinction optical depth at 1.1 μ m (τ_{{1.1}}) obtained from the reddening of Red Giant Branch (RGB) stars, we show that the ratio R^{ obs.}_τ ≡ τ_{{1.1}}/τ_{{300}} falls in the range 500≲ R^{ obs.}_τ ≲ 1500. Such low values are incompatible with many commonly used theoretical dust models, which predict values of R^{ model}_κ ≡ κ _{{1.1}}/κ_{{300}} (where κ is the dust opacity coefficient) in the range 2500≲ R^{ model}_κ ≲ 4000. That is, unless a large fraction, ≳ 60{{ per cent}}, of the dust emitting at 300 μ 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 ≳ 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^{ obs.}_τ and theoretical values of R^{ model}_κ is due to limitations in existing dust models. PPMAP also allows us to derive optical-depth weighted mean values for the emissivity index, β ≡ -dln (κ_λ)/dln (λ), and the dust temperature, T, denoted {\bar{β }} and {\bar{T}}. We show that, in M31, R^{ obs.}_τis anticorrelated with {\bar{β }} according to R^{ obs.}_τ ≃ 2042(± 24)-557(± 10){\bar{β }}. If confirmed, this provides a challenging constraint on the nature of interstellar dust in M31.