High Resolution IRAS Maps and IR Emission of M31 --- II. Diffuse Component and Interstellar Dust

Large-scale dust heating and cooling in the diffuse medium of M31 is studied using the HiRes IRAS maps in conjunction with UV, optical (UBV) and the HI maps. A dust heating/cooling model is developed based on a radiative transfer model which assumes a `Sandwich' configuration of dust and stars and takes fully into account the effect of scattering of dust grains. The model is applied to a complete sample of 'cells' (small areas of size $2'\times 2'$), generated from the above maps. The sample covers the M31 disk in the galactocentric radius range 2 --- 14 kpc, and includes only the cells for which the contribution of the discrete sources to the 60$\mu m$ surface brightness is negligible ($< 20$\%). This effectively excludes most of the bright arm regions from our analysis. We find that: (1) The mean optical depth (viewed from the inclination angle of 77$^\circ$) increases with radius from $\tau_V\sim 0.7$ at r=2kpc outwards, reaches a peak of ~1.6 near 10kpc, and stays quite flat out to 14kpc, where the signal falls below the 5sigma level. (2) A correlation between $\tau_V$ and HI surface density is suggested by the similarity between their radial profiles. Significant differences are found between the radial profiles of the H_2 gas (estimated from CO) and of the dust (from $\tau_V$), which are most probably due to the large uncertainty in the CO-to-H_2 conversion factor, and to the under-representation of H_2-rich regions in the sample of cells of diffuse regions. (3) The $\tau_V / N(HI)$ ratio decreases with increasing radius in the disk of M31, with an exponential law fit yielding an e-folding scale length of $9.6\pm 0.4$ kpc. (4) The optical depth adjusted for this gradient, $\tau_{V,c}$, is strongly and linearly correlated with N(HI) over one and a half order of magnitude of column density, indicating that at a given