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Spitzer Space Telescope and Herschel Space Observatory imaging of M31 is used, with a physical dust model, to construct maps of dust surface density, dust-to-gas ratio, starlight heating intensity, and polycyclic aromatic hydrocarbon (PAH) abundance, out to R ≈ 25 kpc. The global dust mass is M d = 5.4 × 10 7 M ☉ , the global dust/H mass ratio is M d / M H = 0.0081, and the global PAH abundance is 〈 q PAH 〉 = 0.039. The dust surface density has an inner ring at R = 5.6 kpc, a maximum at R = 11.2 kpc, and an outer ring at R ≈ 15.1 kpc. The dust/gas ratio varies from M d / M H ≈ 0.026 at the center to ∼0.0027 at R ≈ 25 kpc. From the dust/gas ratio, we estimate the interstellar medium metallicity to vary by a factor ∼10, from Z / Z ☉ ≈ 3 at R = 0 to ∼0.3 at R = 25 kpc. The dust heating rate parameter 〈 U 〉 peaks at the center, with 〈 U 〉 ≈ 35, declining to 〈 U 〉 ≈ 0.25 at R = 20 kpc. Within the central kiloparsec, the starlight heating intensity inferred from the dust modeling is close to what is estimated from the stars in the bulge. The PAH abundance reaches a peak q PAH ≈ 0.045 at R ≈ 11.2 kpc. When allowance is made for the different spectrum of the bulge stars, q PAH for the dust in the central kiloparsec is similar to the overall value of q PAH in the disk. The silicate–graphite–PAH dust model used here is generally able to reproduce the observed dust spectral energy distribution across M31, but overpredicts 500 μm emission at R ≈ 2–6 kpc, suggesting that at R = 2–6 kpc, the dust opacity varies more steeply with frequency (with β ≈ 2.3 between 200 and 600 μm) than in the model.
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