Molecular gas and star formation are known to be related by a power law in galaxies at kpc scales. It has been found recently, however, that this law breaks down at the scale of giant molecular clouds (GMCs), around 100 parsecs. This is thought to occur because at this scale, the individual properties of GMCs such as their evolutionary stage become more important. On the other hand, it is clear that star formation from molecular gas involves many other physical parameters, such as interstellar dust, interstellar radiation field, and dense gas, among other possibilities. In order to explain the complex and time dependent nature of these intertwined parameters, we have attempted a multi-parameter analysis towards various parameters in GMCs in the nearby spiral galaxy, M33, using data from the NRO45m, ASTE telescopes and the literature.
Our analysis resulted in confirming that indeed the power law relation between molecular gas and star formation does break down at the GMC scales, but that dust and star formation correlate well, and that including the interstellar radiation field and dense gas results in two well defined planes in 3-D space. If these "fundamental" planes are a general property of galaxies, it has the potential of becoming the crossing point of Galactic and extragalactic studies.