Abstract
The present paper extends our previous theory of the stellar initial
mass function (IMF) by including the time-dependence, and by including
the impact of magnetic field. The predicted mass spectra are similar to
the time independent ones with slightly shallower slopes at large masses
and peak locations shifted toward smaller masses by a factor of a few.
Assuming that star-forming clumps follow Larson type relations, we
obtain core mass functions in good agreement with the observationally
derived IMF, in particular when taking into account the thermodynamics
of the gas. The time-dependent theory directly yields an analytical
expression for the star formation rate (SFR) at cloud scales. The SFR
values agree well with the observational determinations of various
Galactic molecular clouds. Furthermore, we show that the SFR does not
simply depend linearly on density, as sometimes claimed in the
literature, but depends also strongly on the clump mass/size, which
yields the observed scatter. We stress, however, that any SFR
theory depends, explicitly or implicitly, on very uncertain assumptions
like clump boundaries or the mass of the most massive stars that can
form in a given clump, making the final determinations uncertain by a
factor of a few. Finally, we derive a fully time-dependent model for the
IMF by considering a clump, or a distribution of clumps accreting at a
constant rate and thus whose physical properties evolve with time. In
spite of its simplicity, this model reproduces reasonably well various
features observed in numerical simulations of converging flows. Based on
this general theory, we present a paradigm for star formation and the
IMF.
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