Shock generated vorticity in the interstellar medium and the origin of the stellar initial mass function

TL;DR

This paper proposes that shock waves in the interstellar medium naturally produce the observed log-normal density distribution and power-law tail in the stellar initial mass function, challenging the necessity of fully-developed turbulence.

Contribution

It demonstrates that shock interactions can generate the density PDFs and energy spectra observed in the ISM and IMF, offering a new explanation for their origins.

Findings

Curved shock waves produce log-normal density PDFs.

Interaction with spherical blast waves creates a power-law high-density tail.

Shock passages can achieve the Kolmogorov energy spectrum exponent.

Abstract

The main observational evidence for turbulence in the interstellar medium (ISM) and molecular clouds is the power-law energy spectrum for velocity fluctuations, E(k) \propto k^{\alpha}. The Kolmogorov scaling exponent, \alpha=-5/3, is typical. At the same time, the observed probability distribution function (PDF) of gas densities in both the ISM as well as in molecular clouds is a log-normal distribution, which is similar to the initial mass function (IMF) that describes the distribution of stellar masses. We examine the density and velocity structure of interstellar gas traversed by curved shock waves in the kinematic limit. We demonstrate mathematically that just a few passages of curved shock waves generically produces a log-normal density PDF. This explains the ubiquity of the log-normal PDF in many different numerical simulations. We also show that subsequent interaction with a spherical blast wave generates a power-law density distribution at high densities, qualitatively similar to the Salpeter power-law for the IMF. Finally, we show that a focused shock produces a downstream flow with energy spectrum exponent \alpha=-2. Subsequent shock passages reduce this slope, achieving \alpha \approx -5/3 after a few passages. Subsequent dissipation of energy piled up at the small scales will act to maintain the spectrum very near to the Kolomogorov value. Therefore, fully-developed turbulence may not be required to explain the observed energy spectrum and density PDF. We argue that the self-similar spherical blast wave arising from expanding HII regions or stellar winds from massive stars may ultimately be responsible for creating the high mass, power-law, tail in the IMF.