The tensile strength of dust aggregates consisting of small elastic grains: constraints on the size of condensates in protoplanetary discs

A consensus view on the formation of planetesimals is now exposed to a threat, since recent numerical studies on the mechanical properties of dust aggregates tend to dispute the conceptual picture that submicrometer-sized grains conglomerate into planetesimals in protoplanetary discs. With the advent of precise laboratory experiments and extensive computer simulations on the interaction between elastic spheres comprising dust aggregates, we revisit a model for the tensile strength of dust aggregates consisting of small elastic grains. In the framework of contact mechanics and fracture mechanics, we examine outcomes of computer simulations and laboratory experiments on the tensile strength of dust aggregates. We provide a novel analytical formula that explicitly incorporates the volume effect on the tensile strength, namely, the dependence of tensile strength on the volume of dust aggregates. We find that our model for the tensile strength of dust aggregates well reproduces results of computer simulations and laboratory experiments, if appropriate values are adopted for the elastic parameters used in the model. Moreover, the model with dust aggregates of submicrometer-sized grains is in good harmony with the tensile strength of cometary dust and meteoroids derived from astronomical observations. Therefore, we reaffirm the commonly believed idea that the formation of planetesimals begins with conglomeration of submicrometer-sized grains condensed in protoplanetary discs.