Cloud fragmentation cascades and feedback: on reconciling an unfettered inertial range with a low star formation rate

Molecular cloud complexes exhibit both (i) an unfettered Larson-type spectrum over much of their dynamic range, whilst (ii) still producing a much lower star-formation rate than were this cascade to remain unfettered all the way down to star-forming scales. Here we explain the compatibility of these attributes with minimalist considerations of a mass-conserving fragmentation cascade, combined with estimates of stellar feedback. Of importance is that the amount of feedback needed to abate fragmentation and truncate the complex decreases with decreasing scale. The scale at which the feedback momentum matches the free-fall momentum marks a transition scale below most of the cascade is truncated and the molecular cloud complex dissipated. For a $10^6M_\odot$ GMC complex starting with radius of $\sim 50$pc, the combined feedback from young stellar objects, supernovae, radiation, and stellar winds for a GMC cloud complex can truncate the cascade within an outer free-fall time but only after the cascade reaches parsec scales.