Numerical and semi-analytic core mass distributions in supersonic isothermal turbulence

¹ Institut für Astrophysik, Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany e-mail: schmidt@astro.physik.uni-goettingen.de
² Lehrstuhl für Astronomie, Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
³ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany e-mail: kern@mpia-hd.mpg.de
⁴ Zentrum für Astronomie, Institut für Theoretische Astrophysik, Universität Heidelberg, Albert-Ueberle-Str. 2, 69120 Heidelberg, Germany e-mail: chfeder@ita.uni-heidelberg.de

Received: 18 December 2009
Accepted: 19 February 2010

Abstract

Context. Supersonic turbulence in the interstellar medium plays an important role in the formation of stars. The origin of this observed turbulence and its impact on the stellar initial mass function (IMF) still remain open questions.

Aims. We investigate the influence of the turbulence forcing on the mass distributions of gravitationally unstable cores in simulations of isothermal supersonic turbulence.

Methods. Data from two sets of non-selfgravitating hydrodynamic FLASH3 simulations with external stochastic forcing are analysed, each with static grid resolutions of 256³, 512³ and 1024³ grid points. The first set applies solenoidal (divergence-free) forcing, while the second set uses purely compressive (curl-free) forcing to excite turbulent motions. From the resulting density field, we compute the mass distribution of gravitationally unstable cores by means of a clump-finding algorithm. Using the time-averaged probability density functions of the mass density, semi-analytic mass distributions are calculated from analytical theories. We apply stability criteria that are based on the Bonnor-Ebert mass resulting from the thermal pressure and from the sum of thermal and turbulent pressure.

Results. Although there are uncertainties in applying of the clump-finding algorithm, we find systematic differences in the mass distributions obtained from solenoidal and compressive forcing. Compressive forcing produces a shallower slope in the high-mass power-law regime compared to solenoidal forcing. The mass distributions also depend on the Jeans length resulting from the choice of the mass in the computational box, which is freely scalable for non-selfgravitating isothermal turbulence. If the Jeans length corresponding to the density peaks is less than the grid cell size, the distributions obtained by clump-finding show a strong resolution dependence. Provided that all cores are numerically resolved and most cores are small compared to the length scale of the forcing, the normalised core mass distributions are close to the semi-analytic models.

Conclusions. The driving mechanism of turbulence has a potential impact on the shape of the core mass function. Especially for the high-mass tails, the Hennebelle-Chabrier theory implies that the additional support due to turbulent pressure is important.