Radio-FIR correlations within M 31

We present a study of the relationship between the surface brightness of the radio continuum emission and the FIR emission within M 31, based on radio maps at four wavelengths (73 cm, 20 cm, 11 cm and 6 cm) and the HIRES-FIR maps at 60 mu m and 100 mu m. For a common resolution of 5' we decomposed the radio emission into a thermal and a nonthermal radio continuum map at lambda 20 cm, and the FIR emission into emission from warm (27 K) and cool (19 K) dust. The good angular resolutions of the maps (5', 3' and 2') allowed the use of rigorous statistical methods to determine the slopes of the correlations. We obtained the following results: 1. In the region 30' < R < 90', at all three resolutions corresponding to 1 x 5 kpc down to 0.4 x 2 kpc in the plane of M 31, the total radio emission is significantly correlated with the total FIR emission, even after correction for the general radial decrease. In the latter case, the slope of the lambda 20 cm-radio/total-FIR relation is unity. Also in the inner disk (R < 30') of M 31 the total radio emission at lambda 20 cm correlates significantly with total FIR emission after radial correction; the slope is also unity in spite of the fact that in the inner disk the dust temperatures are quite different from those in the outer disk. 2. After radial correction significant correlations exist in the outer disk on a scale of a few kpc between thermal radio and warm dust emission as well as between nonthermal radio and cool dust emission, with slopes of 1.17 +/- 0.13 and 0.80 +/- 0.09, respectively. The thermal-radio/warm-dust correlation is expected from the common dependence of the two emissions on the massive ionizing stars. However, the nonthermal-radio/cool-dust correlation cannot be explained by a common dependence on the energy sources, because the heating of the cool dust is dominated by the ISRF. Instead, we propose that this correlation arises because of a coupling of the magnetic field to the gas which is mixed with the cool dust. This 'magnetic field-gas coupling' model can explain the slope less than or equal to 1 of the nonthermal-radio/cool-dust correlation if energy equipartition between cosmic-ray electrons and magnetic fields is not valid on scales less than or equal to 2 kpc.