Explaining the stellar initial mass function with the theory of spatial networks

TL;DR

This paper introduces a novel network science-based model for the stellar initial mass function, explaining its power-law shape through fractal properties of the interstellar medium and core accretion dynamics.

Contribution

It presents a new theoretical framework combining network growth and turbulence theory to predict the stellar initial mass function without relying on empirical fluctuation spectra.

Findings

Reproduces observed IMF over three decades in mass

Predicts power-law core mass function from fractal ISM properties

Rules out bottom-heavy IMF in single star-forming regions

Abstract

The distributions of stars and prestellar cores by mass (initial and dense core mass functions, IMF/DCMF) are among the key factors regulating star formation and are the subject of detailed theoretical and observational studies. Results from numerical simulations of star formation qualitatively resemble an observed mass function, a scale-free power law with a sharp decline at low masses. However, most analytic IMF theories critically depend on the empirically chosen input spectrum of mass fluctuations which evolve into dense cores and, subsequently, stars, and on the scaling relation between the amplitude and mass of a fluctuation. Here we propose a new approach exploiting the techniques from the field of network science. We represent a system of dense cores accreting gas from the surrounding diffuse interstellar medium (ISM) as a spatial network growing by preferential attachment and assume that the ISM density has a self-similar fractal distribution following the Kolmogorov turbulence theory. We effectively combine gravoturbulent and competitive accretion approaches and predict the accretion rate to be proportional to the dense core mass: $dM/dt \propto M$. Then we describe the dense core growth and demonstrate that the power-law core mass function emerges independently of the initial distribution of density fluctuations by mass. Our model yields a power law solely defined by the fractal dimensionalities of the ISM and accreting gas. With a proper choice of the low-mass cut-off, it reproduces observations over three decades in mass. We also rule out a low-mass star dominated "bottom-heavy" IMF in a single star-forming region.