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

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^α. The Kolmogorov scaling exponent, α=-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 α=-2. Subsequent shock passages reduce this slope, achieving α\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.

26 pages, 5 figures, accepted for publication in the Astrophysical Journal

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Cited by in corpus (21)

• The SILCC (SImulating the LifeCycle of molecular Clouds) project: I. Chemical evolution of the supernova-driven ISM
• Turbulent molecular clouds
• The Big Problems in Star Formation: the Star Formation Rate, Stellar Clustering, and the Initial Mass Function
• The stellar and sub-stellar IMF of simple and composite populations
• Formation of Massive Molecular Cloud Cores by Cloud-cloud Collision
• Formation of Turbulent and Magnetized Molecular Clouds via Accretion Flows of HI Clouds
• Turbulent Gas in Lensed Planck-selected Starbursts at redshifts 1-3.5
• Ionization compression impact on dense gas distribution and star formation, Probability density functions around H ii regions as seen by Herschel
• Vorticity, Shocks and Magnetic Fields in Subsonic, ICM-like Turbulence
• X-ray variation statistics and wind clumping in Vela X-1
• The IMF of stellar clusters: effects of accretion and feedback
• Magnetic field amplification by shocks in galaxy clusters: application to radio relics
• The clumpy absorber in the high-mass X-ray binary Vela X-1
• The Efficiency of Magnetic Field Amplification at Shocks by Turbulence
• Shock interactions, turbulence, and the origin of the stellar mass spectrum
• Numerical simulations of supernova remnants in turbulent molecular clouds
• Squeezed between shells? On the origin of the Lupus I molecular cloud. APEX/LABOCA, Herschel, and Planck observations
• Turbulence generation by a shock wave interacting with a random density inhomogeneity field
• Lagrangian statistics of a shock-driven turbulent dynamo in decaying turbulence
• The effect of tidal forces on the Jeans instability criterion in star-forming regions
• Simulations of the IMF in Clusters