Properties of M31 I. Dust. Basic properties and a discussion about age-dependent dust heating

Aims. Observations acquired by the Spitzer Space Telescope and improvements to theoretical modeling of dust emission properties are used to discuss the distribution of dust and its characteristics in the closest neighbor spiral galaxy M31. These data are then used with GALEX FUV, NUV, and SDSS images to study the age dependence of the dust heating process. Methods. Spitzer IRAC/MIPS maps of M31 were matched together and compared to dust emission models allowing us to constrain the dust mass, the intensity of the mean radiation field, the abundance of polycyclic aromatic hydrocarbon (PAH) particles. The total infrared emission (TIR) was analyzed as a function of UV and optical colors and compared to predictions of models that consider age-dependent dust heating. Results. We demonstrate that cold-dust component emission dominates the infrared spectral energy distribution of M31. The mean intensity of the radiation field heating the dust is low (typically U < 2, where U = 1 is the value in the solar neighborhood). Because of a lack of submillimeter observations, the dust mass (M-dust) is only weakly constrained by the infrared spectrum, but we derived a lower limit of M-dust greater than or similar to 1.1 x 10(7) M-circle dot with a best-fit model value of M-dust = 7.6 x 10(7) M-circle dot, in good agreement with expectations from CO and HI measurements. Across the spiral-ring structure of M31, we show that a fraction > 3% of the total dust mass is in PAHs. UV and optical colors are correlated with the total infrared to far ultraviolet (TIR/FUV) ratios in similar to 670 pc-sized regions over the disk of M31, although deviating from the relationship between infrared excess and ultraviolet spectral slope (referred as IRX-beta relationship) for starburst galaxies. In particular, redder regions have lower values of the TIR/FUV ratio for a fixed color. Considering the predictions of models that account for the dust-heating age dependence, we found that in 83% of the regions analyzed across the 10 kpc ring, more than 50% of the energy absorbed by the dust is rediated at lambda > 4000 angstrom and that dust in M31 appears mainly heated by populations a few Gyr old even across the star-forming ring. We also found that the attenuation varies radially peaking close to 10 kpc and decreases more rapidly with radius in the inner regions of M31 than in the outer regions in agreement with previous studies. We finally derived the attenuation map of M31 at 6 ''/px resolution (similar to 100 pc/px along the plane of M31). Conclusions.