Conditions for core collapse for different total numbers of cores (columns) and PDF slopes. Top: function m∕m_J (Eq. (24)) projected on the plain “core density vs. cloud mass”. Lines denote the condition m∕m_J = 1; the domains of unstable cores for the three exemplary values of q are shown with arrows. An isothermal Jeans mass within the cloud M_{J, c} for T = 30 K is adopted. Bottom: mass–density relationship for cores (Eq. (8)) where the mass is given in units of the total mass of the cloud. The density contrast in the cloud is fixed at (ρ₀ ∕ρ_c)= 10³.