Massive 70 micron quiet clumps II: non-thermal motions driven by gravity in massive star formation?

The dynamic activity in massive star forming regions prior to the formation of bright protostars is still not fully investigated. In this work we present observations of HCO+ J=1-0 and N2H+ J=1-0 made with the IRAM 30m telescope towards a sample of 16 Herschel-identified massive 70 micron quiet clumps associated with infrared dark clouds. The clumps span a mass range from 300 M_sun to 2000 M_sun. The N2H+ data show that the regions have significant non-thermal motions with velocity dispersion between 0.28 km s^-1 and 1.5 km s^-1, corresponding to Mach numbers between 2.6 and 11.5. The majority of the 70 micron quiet clumps have asymmetric HCO+ line profiles, indicative of significant dynamical activity. We show that there is a correlation between the degree of line asymmetry and the surface density Sigma of the clumps, with clumps of Sigma>=0.1 g cm^-2 having more asymmetric line profiles, and so are more dynamically active, than clumps with lower Sigma. We explore the relationship between velocity dispersion, radius and Sigma and show how it can be interpreted as a relationship between an acceleration generated by the gravitational field a_G, and the measured kinetic acceleration, a_k, consistent with the majority of the non-thermal motions originating from self-gravity. Finally, we consider the role of external pressure and magnetic fields in the interplay of forces.