The dust in M31

We have analysed Herschel observations of M31, using the ppmap procedure. The resolution of ppmap images is sufficient ($\sim 31\, {\rm pc}$ 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 $300\, \mu {\rm m}\, (\tau _{{300}})$, and the near-IR extinction optical depth at $1.1\, \mu {\rm m}\, (\tau _{{1.1}})$ obtained from the reddening of Red Giant Branch (RGB) stars, we show that the ratio ${\cal R}^{\mathrm{ obs.}}_\tau \equiv \tau _{{1.1}}/\tau _{{300}}$ falls in the range $500\lesssim {\cal R}^{\mathrm{ obs.}}_\tau \lesssim 1500$. Such low values are incompatible with many commonly used theoretical dust models, which predict values of ${\cal R}^{\mathrm{ model}}_\kappa \equiv \kappa _{{1.1}}/\kappa _{{300}}$ (where κ is the dust opacity coefficient) in the range $2500\lesssim {\cal R}^{\mathrm{ model}}_\kappa \lesssim 4000$. That is, unless a large fraction, $\gtrsim 60{{\ \rm per\ cent}}$, of the dust emitting at $300\, \mu {\rm m}$ 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 $\gtrsim 60{{\ \rm per\ cent}}$ 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 ${\cal R}^{\mathrm{ obs.}}_\tau$ and theoretical values of ${\cal R}^{\mathrm{ model}}_\kappa$ 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 (κλ)/dln (λ), and the dust temperature, T, denoted ${\bar{\beta }}$ and ${\bar{T}}$. We show that, in M31, ${\cal R}^{\mathrm{ obs.}}_\tau$ is anticorrelated with ${\bar{\beta }}$ according to ${\cal R}^{\mathrm{ obs.}}_\tau \simeq 2042(\pm 24)-557(\pm 10){\bar{\beta }}$. If confirmed, this provides a challenging constraint on the nature of interstellar dust in M31.