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 \approx 25 { kpc } .
The global dust mass is M _ { d } = 5.4 \times 10 ^ { 7 } M _ { \odot } , the global dust/H mass ratio is M _ { d } / M _ { H } = 0.0081 , and the global PAH abundance is \langle q _ { PAH } \rangle = 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 \approx 15.1 { kpc } .
The dust/gas ratio varies from M _ { d } / M _ { H } \approx 0.026 at the center to \sim 0.0027 at R \approx 25 { kpc } .
From the dust/gas ratio , we estimate the interstellar mediu ( ISM ) metallicity to vary by a factor \sim 10 , from Z / Z _ { \odot } \approx 3 at R = 0 to \sim 0.3 at R = 25 { kpc } .
The dust heating rate parameter \langle U \rangle peaks at the center , with \langle U \rangle \approx 35 , declining to \langle U \rangle \approx 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 } \approx 0.045 at R \approx 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 \micron emission at R \approx 2 – 6 { kpc } , suggesting that at R = 2 – 6 { kpc } , the dust opacity varies more steeply with frequency ( with \beta \approx 2.3 between 200 and 600 \micron ) than in the model .