A possible observational bias in the estimation of the virial parameter in virialized clumps

The dynamics of massive clumps, the environment where massive stars originate, is still unclear. Many theories predict that these regions are in a state of near-virial equilibrium, or near energy equi-partition, while others predict that clumps are in a sub-virial state. Observationally, the majority of the massive clumps are in a sub-virial state with a clear anti-correlation between the virial parameter α_vir and the mass of the clumps M_c, which suggests that the more massive objects are also the more gravitationally bound. Although this trend is observed at all scales, from massive clouds down to star-forming cores, theories do not predict it. In this work we show how, starting from virialized clumps, an observational bias is introduced in the specific case where the kinetic and the gravitational energies are estimated in different volumes within clumps and how it can contribute to the spurious α_vir-M_c anti-correlation in these data. As a result, the observed effective virial parameter α_eff < α_vir, and in some circumstances it might not be representative of the virial state of the observed clumps.