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We performed a numerical experiment designed for core formation in a self‐gravitating, magnetically supercritical, supersonically turbulent, isothermal cloud. A density probability distribution function (PDF) averaged over a converged turbulent state before turning self‐gravity on is well fitted with a lognormal distribution. However, after turning self‐gravity on, the volume fractions of density PDFs at a high density tail, compared with the lognormal distribution, increase as time goes on. In order to see the effect of self‐gravity on core formation rates, we compared the core formation rate per free‐fall time (CFR ff ) from the theory based on the lognormal distribution and the one from our numerical experiment. For our fiducial value of a critical density, 100, normalized with an initial value, the latter CFR ff  is about 30 times larger the former one. Therefore, self‐gravity plays an important role in significantly increasing CFR ff . This result implies that core (star) formation rates or core (stellar) mass functions predicted from theories based on the lognormal density PDF need some modifications. Our result of the increased volume fraction of density PDFs after turning self‐gravity on is consistent with power law like tails commonly observed at higher ends of visual extinction PDFs of active star‐forming clouds.

Enhanced core formation rate in a turbulent cloud by self‐gravity