On the gravitational content of molecular clouds and their cores

The gravitational term for clouds and cores entering in the virial theorem is usually assumed to be equal to the gravitational energy, since the contribution to the gravitational force from the mass distribution outside the volume of integration is assumed to be negligible. Such approximation may not be valid in the presence of an important external net potential. In the present work, we analyse the effect of an external gravitational field on the gravitational budget of a density structure. Our cases under analysis are (a) a giant molecular cloud (GMC) with different aspect ratios embedded within a galactic net potential, including the effects of gravity, shear and inertial forces, and (b) a molecular cloud (MC) core embedded within the gravitational potential of its parent MC. We find that for roundish GMCs, the tidal tearing due to the shear in the plane of the Galaxy is compensated by the tidal compression in the z-direction. The influence of the external effective potential on the total gravitational budget of these clouds is relatively small (up to similar to 15-25 per cent), although not necessarily negligible. However, for more filamentary GMCs, elongated on the plane of the Galaxy, the external effective potential can be dominant and can even overwhelm self-gravity, regardless of whether its main effect on the cloud is to disrupt it or compress it. This may explain the presence of some GMCs with few or no signs of massive star formation, such as the Taurus or the Maddalena's clouds. In the case of dense cores embedded in their parent MC, we found that the gravitational content due to the external field may be more important than the gravitational energy of the cores themselves. This effect works in the same direction as the gravitational energy, that is favouring the collapse of cores. We speculate on the implications of these results for star formation models, in particular that apparently nearly magnetically critical cores may actually be supercritical due to the effect of the external potential.