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We present a detailed study of how the Star Formation Rate (SFR) relates tothe interstellar medium (ISM) of M31 at ~140pc scales. The SFR is calculatedusing the far-ultraviolet and 24um emission, corrected for the old stellarpopulation in M31. We find a global value for the SFR of 0.25+/-0.05Msun/yr andcompare this with the SFR found using the total far-infrared (FIR) luminosity.There is general agreement in regions where young stars dominate the dustheating. Atomic hydrogen (HI) and molecular gas (traced by carbon monoxide, CO)or the dust mass is used to trace the total gas in the ISM. We show that theglobal surface densities of SFR and gas mass place M31 amongst a set of low-SFRgalaxies in the plot of Kennicutt (1998b). The relationship between SFR and gassurface density is tested in six radial annuli across M31, assuming a power lawrelationship with index, N. The star formation law using total gas traced by HIand CO gives a global index of N=2.03+/-0.04, with a significant variation withradius; the highest values are observed in the 10kpc ring. We suggest that thisslope is due to HI turning molecular at ~10Msun/pc2. When looking at H2regions, we measure a higher mean SFR suggesting a better spatial correlationbetween H2 and SF. We find N~0.6 with consistent results throughout the disk -this is at the low end of values found in previous work and argues against asuperlinear SF law on small scales.

Herschel Exploitation of Local Galaxy Andromeda (HELGA) III: The Star Formation Law in M31