  The formation mechanism of massive stars remains one of the main open
problems in astrophysics, in particular the relationship between the mass of
the most massive stars, and that of the cores in which they form. Numerical
simulations of the formation and evolution of large molecular clouds, within
which dense cores and stars form self-consistently, show in general that the
cores' masses increase in time, and also that the most massive stars tend to
appear later (by a few to several Myr) than lower-mass stars. Here we present
an idealized model that incorporates accretion onto the cores as well as onto
the stars, in which the core's mass growth is regulated by a ``gravitational
choking'' mechanism that does not involve any form of support. This process is
of purely gravitational origin, and causes some of the mass accreted onto the
core to stagnate there, rather than being transferred to the central stars.
Thus, the simultaneous mass growth of the core and of the stellar mass can be
computed. In addition, we estimate the mass of the most massive allowed star
before its photoionizing radiation is capable of overcoming the accretion flow
onto the core. This model constitutes a proof-of-concept for the simultaneous
growth of the gas reservoir and the stellar mass, the delay in the formation of
massive stars observed in cloud-scale numerical simulations, the need for
massive, dense cores in order to form massive stars, and the observed
correlation between the mass of the most massive star and the mass of the
cluster it resides in. Also, our model implies that by the time massive stars
begin to form in a core, a number of low-mass stars are expected to have
already formed.
