A Dual Power Law Distribution for the Stellar Initial Mass Function
  We introduce a new dual power law (DPL) probability distribution function for
the mass distribution of stellar and substellar objects at birth, otherwise
known as the initial mass function (IMF). The model contains both deterministic
and stochastic elements, and provides a unified framework within which to view
the formation of brown dwarfs and stars resulting from an accretion process
that starts from extremely low mass seeds. It does not depend upon a top down
scenario of collapsing (Jeans) masses or an initial lognormal or otherwise
IMF-like distribution of seed masses. Like the modified lognormal power law
(MLP) distribution, the DPL distribution has a power law at the high mass end,
as a result of exponential growth of mass coupled with equally likely stopping
of accretion at any time interval. Unlike the MLP, a power law decay also
appears at the low mass end of the IMF. This feature is closely connected to
the accretion stopping probability rising from an initially low value up to a
high value. This might be associated with physical effects of ejections
sometimes (i.e., rarely) stopping accretion at early times followed by outflow
driven accretion stopping at later times, with the transition happening at a
critical time (therefore mass). Comparing the DPL to empirical data, the
critical mass is close to the substellar mass limit, suggesting that the onset
of nuclear fusion plays an important role in the subsequent accretion history
of a young stellar object.
