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 (κ_λ)/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. [ABSTRACT FROM AUTHOR]