CfA OIR Division Lunch Talks
Wednesday, April 15, 2015, 11:00 am, Pratt Conference Room

An Analytic Explanation of the Stellar Initial Mass Function
from the Theory of Spatial Networks

Andrei Klishin (MIT)

The distribution of stars by mass or the stellar initial mass function (IMF) that has been intensively studied in the Milky Way and other galaxies is the key property regulating star formation and galaxy evolution. The mass function of prestellar dense cores (DCMF) is an IMF precursor that has a similar shape, a broken power law with a sharp decline at low masses, but offset to higher masses. Results from numerical simulations of star formation qualitatively resemble an observed IMF/DCMF, however, most analytic IMF theories critically depend on the empirically chosen input spectrum of mass fluctuations which evolve into dense cores and, subsequently, stars. Here we propose an analytic approach by representing a system of dense cores accreting gas from the surrounding diffuse interstellar medium (ISM) as a spatial network growing by preferential attachment and assuming that the ISM density has a self-similar fractal distribution following the Kolmogorov turbulence theory. We obtain a scale free power law with the exponent that is not related to the input fluctuation mass spectrum but depends only on the fractal distribution dimensionalities of infalling gas (Dp) and turbulent ISM (Dm = 2.35). It can be as steep as 3.24 (uniform volume density Dp = 3) and becomes Salpeter ( = 2.35) for Dp = 2.5 that corresponds to a variety of Brownian processes in physics. Our theory reproduces the observed DCMF shape over three orders of magnitude in mass, and it rules out a low mass star dominated bottom-heavy IMF shape unless the same steep slope holds at the higher masses.