Testing assumptions and predictions of star-formation theories
  (Abridged). We present numerical simulations of isothermal, MHD, supersonic
turbulence, designed to test various hypotheses frequently assumed in star
formation(SF) theories. We consider three simulations, each with a different
combination of physical size, rms sonic Mach number, and Jeans parameter, but
chosen as to give the same value of the virial parameter and to conform with
Larson's scaling relations. As in the non-magnetic case: we find no
simultaneously subsonic and super-Jeans structures in our MHD simulations. We
find that the fraction of small-scale super-Jeans structures increases when
self gravity is turned on, and that the production of gravitationally unstable
dense cores by turbulence alone is very low. This implies that self-gravity is
in general necessary not only to induce the collapse of Jeans-unstable cores,
but also to form them. We find that denser regions tend to have more negative
values of the velocity divergence, implying a net inwards flow towards the
regions' centers. We compare the results from our simulations with the
predictions from the recent SF theories by Krumholz & McKee, Padoan & Nordlund,
and Hennebelle & Chabrier, using the expressions recently provided by Federrath
& Klessen. We find that none of these theories reproduces the dependence of the
SFEff with Ms observed in our simulations in the MHD case. The SFEff predicted
by the theories ranges between half and one order of magnitude larger than what
we observe in the simulations in both the HD and the MHD cases. We conclude
that the type of flow used in simulations like the ones presented here and
assumed in recent SF theories, may not correctly represent the flow within
actual clouds, and that theories that assume it does may be missing a
fundamental aspect of the flow. We suggest that a more realistic regime may be
that of hierarchical gravitational collapse.
