The ALMaQUEST Survey: V. The non-universality of kpc-scale star formation relations and the factors that drive them

Using a sample of ~15,000 kpc-scale star-forming spaxels in 28 galaxies drawn from the ALMA-MaNGA QUEnching and STar formation (ALMaQUEST) survey, we investigate the galaxy-to-galaxy variation of the `resolved' Schmidt-Kennicutt relation (rSK; Sigma_H2 - Sigma_SFR), the `resolved' star forming main sequence (rSFMS; Sigma_* - Sigma_SFR) and the `resolved' molecular gas main sequence (rMGMS; Sigma_* - Sigma_H2). The rSK relation, rSFMS and rMGMS all show significant galaxy-to-galaxy variation in both shape and normalization, indicating that none of these relations is universal between galaxies. The rSFMS shows the largest galaxy-to-galaxy variation and the rMGMS the least. By defining an `offset' from the average relations, we compute a Delta_rSK, Delta_rSFMS, Delta_rMGMS for each galaxy, to investigate correlations with global properties. We find the following correlations with at least 2 sigma significance: the rSK is lower (i.e. lower star formation efficiency) in galaxies with higher M_*, larger Sersic index and lower specific SFR (sSFR); the rSFMS is lower (i.e. lower sSFR) in galaxies with higher M_* and larger Sersic index; the rMGMS is lower (i.e. lower gas fraction) in galaxies with lower sSFR. In the ensemble of all 15,000 data points, the rSK relation and rMGMS show equally tight scatters and strong correlation coefficients, compared with a larger scatter and weaker correlation in the rSFMS. Moreover, whilst there is no correlation between Delta_rSK and Delta_rMGMS in the sample, the offset of a galaxy's rSFMS does correlate with both of the other two offsets. Our results therefore indicate that the rSK and rMGMS are independent relations, whereas the rSFMS is a result of their combination.