Gravity as the main driver of non-thermal motions in massive star formation

The origin of non-thermal motions in massive star forming regions can be ascribed to turbulence acting against the gravitational collapse, or to the self-gravity itself driving the rapid global collapse. The dependence between velocity dispersion, radius and clouds surface density found by Heyer et al. (2009), $\sigma/R^{1/2}\propto \Sigma^{1/2}$, has been interpreted in terms of global collapse of clouds. In this work we demonstrate that this relation is an expression of a more general relation between accelerations. We introduce the gravo-turbulent acceleration, a$_k$, which describe the non-thermal motions in each region, and the acceleration generated by the gravitational field a$_G$, which is proportional to $\Sigma$. We also introduce a new coefficient, the force partition coefficient $\alpha_{for}$ which is equivalent to the virial parameter but does not distinguish between collapsing and non-collapsing regions. In this work we use the a$_k$ - a$_G$ formalism in the analysis of a new sample of 16 massive starless clumps (MSCls) combined with data from the literature. We show that a$_k$ and a$_G$ are not independent. The non-thermal motions in each region can originate from both local turbulence and self-gravity but overall the data in the a$_k$ vs. a$_G$ diagram demonstrate that the majority of the non-thermal motions originate from self-gravity. We further show that all the MSCls with $\Sigma\geq 0.1$ g cm$^{-2}$ show signs of infall motions, a strong indication that the denser regions are the first to collapse. Finally, we include in the formalism the contribution of an external pressure and the magnetic fields.