49 research outputs found
Scaling relations of supersonic turbulence in star-forming molecular clouds
We present a direct numerical and analytical study of driven supersonic MHD
turbulence that is believed to govern the dynamics of star-forming molecular
clouds. We describe statistical properties of the turbulence by measuring the
velocity difference structure functions up to the fifth order. In particular,
the velocity power spectrum in the inertial range is found to be close to E(k)
\~ k^{-1.74}, and the velocity difference scales as ~ L^{0.42}. The
results agree well with the Kolmogorov--Burgers analytical model suggested for
supersonic turbulence in [astro-ph/0108300]. We then generalize the model to
more realistic, fractal structure of molecular clouds, and show that depending
on the fractal dimension of a given molecular cloud, the theoretical value for
the velocity spectrum spans the interval [-1.74 ... -1.89], while the
corresponding window for the velocity difference scaling exponent is [0.42 ...
0.78].Comment: 17 pages, 6 figures include
From the CMF to the IMF: Beyond the Core-Collapse Model
Observations have indicated that the prestellar core mass function (CMF) is
similar to the stellar initial mass function (IMF), except for an offset
towards larger masses. This has led to the idea that there is a one-to-one
relation between cores and stars, such that the whole stellar mass reservoir is
contained in a gravitationally-bound prestellar core, as postulated by the
core-collapse model, and assumed in recent theoretical models of the stellar
IMF. We test the validity of this assumption by comparing the final mass of
stars with the mass of their progenitor cores in a high-resolution
star-formation simulation that generates a realistic IMF under physical
conditions characteristic of observed molecular clouds. Using a definition of
bound cores similar to previous works we obtain a CMF that converges with
increasing numerical resolution. We find that the CMF and the IMF are closely
related in a statistical sense only; for any individual star there is only a
weak correlation between the progenitor core mass and the final stellar mass.
In particular, for high mass stars only a small fraction of the final stellar
mass comes from the progenitor core, and even for low mass stars the fraction
is highly variable, with a median fraction of only about 50%. We conclude that
the core-collapse scenario and related models for the origin of the IMF are
incomplete. We also show that competitive accretion is not a viable
alternative.Comment: 23 pages, 29 figures. Link to supplementary material and full Table
1: http://www.erda.dk/vgrid/core-mass-function/ . Submitted to MNRA
Structure Function Scaling in Compressible Super-Alfvenic MHD Turbulence
Supersonic turbulent flows of magnetized gas are believed to play an
important role in the dynamics of star-forming clouds in galaxies.
Understanding statistical properties of such flows is crucial for developing a
theory of star formation. In this letter we propose a unified approach for
obtaining the velocity scaling in compressible and super--Alfv\'{e}nic
turbulence, valid for arbitrary sonic Mach number, \ms. We demonstrate with
numerical simulations that the scaling can be described with the
She--L\'{e}v\^{e}que formalism, where only one parameter, interpreted as the
Hausdorff dimension of the most intense dissipative structures, needs to be
varied as a function of \ms. Our results thus provide a method for obtaining
the velocity scaling in interstellar clouds once their Mach numbers have been
inferred from observations.Comment: published in Physical Review Letter
The Star Formation Rate of Molecular Clouds
24 pages, 5 figures, Accepted for publication as a chapter in Protostars and Planets VI, University of Arizona Press (2014), eds. H. Beuther, R. S. Klessen, C. P. Dullemond, Th. HenningWe review recent advances in the analytical and numerical modeling of the star formation rate in molecular clouds and discuss the available observational constraints. We focus on molecular clouds as the fundamental star formation sites, rather than on the larger-scale processes that form the clouds and set their properties. Molecular clouds are shaped into a complex filamentary structure by supersonic turbulence, with only a small fraction of the cloud mass channeled into collapsing protostars over a free-fall time of the system. In recent years, the physics of supersonic turbulence has been widely explored with computer simulations, leading to statistical models of this fragmentation process, and to the prediction of the star formation rate as a function of fundamental physical parameters of molecular clouds, such as the virial parameter, the rms Mach number, the compressive fraction of the turbulence driver, and the ratio of gas to magnetic pressure. Infrared space telescopes, as well as ground-based observatories have provided unprecedented probes of the filamentary structure of molecular clouds and the location of forming stars within them.PP is supported by the FP7-PEOPLE-
2010-RG grant PIRG07-GA-2010- 261359. Simulations
by PP were carried out on the NASA/Ames Pleiades supercomputer,
and under the PRACE project pra50751 running
on SuperMUC at the LRZ (project ID pr86li). CF
thanks for support from the Australian Research Council
for a Discovery Projects Fellowship (Grant DP110102191).
NJE was supported by NSF Grant AST-1109116 to the
University of Texas at Austin. The research of CFM is
supported in part by NSF grant AST-1211729 and NASA
grant NNX13AB84G. DJ is supported by the National Research
Council of Canada and by a Natural Sciences and
Engineering Research Council of Canada (NSERC) Discovery
Grant. JKJ is supported by a Lundbeck Foundation
Junior Group Leader Fellowship. Research at Centre for
Star and Planet Formation was funded by the Danish National
Research Foundation and the University of Copenhagens
Programme of Excellence. Supercomputing time at
Leibniz Rechenzentrum (PRACE projects pr86li, pr89mu,
and project pr32lo), at Forschungszentrum J¨ulich (project
hhd20), and at DeIC/KU in Copenhagen are gratefully acknowledged
Simulating Supersonic Turbulence in Magnetized Molecular Clouds
We present results of large-scale three-dimensional simulations of weakly
magnetized supersonic turbulence at grid resolutions up to 1024^3 cells. Our
numerical experiments are carried out with the Piecewise Parabolic Method on a
Local Stencil and assume an isothermal equation of state. The turbulence is
driven by a large-scale isotropic solenoidal force in a periodic computational
domain and fully develops in a few flow crossing times. We then evolve the flow
for a number of flow crossing times and analyze various statistical properties
of the saturated turbulent state. We show that the energy transfer rate in the
inertial range of scales is surprisingly close to a constant, indicating that
Kolmogorov's phenomenology for incompressible turbulence can be extended to
magnetized supersonic flows. We also discuss numerical dissipation effects and
convergence of different turbulence diagnostics as grid resolution refines from
256^3 to 1024^3 cells.Comment: 10 pages, 3 figures, to appear in the proceedings of the DOE/SciDAC
2009 conferenc
Synthetic Molecular Clouds from Supersonic MHD and Non-LTE Radiative Transfer Calculations
The dynamics of molecular clouds is characterized by supersonic random
motions in the presence of a magnetic field. We study this situation using
numerical solutions of the three-dimensional compressible magneto-hydrodynamic
(MHD) equations in a regime of highly supersonic random motions. The non-LTE
radiative transfer calculations are performed through the complex density and
velocity fields obtained as solutions of the MHD equations, and more than
5x10^5 synthetic molecular spectra are obtained. We use a numerical flow
without gravity or external forcing. The flow is super-Alfvenic and corresponds
to model A of Padoan and Nordlund (1997). Synthetic data consist of sets of
90x90 synthetic spectra with 60 velocity channels, in five molecular
transitions: J=1-0 and J=2-1 for 12CO and 13CO, and J=1-0 for CS. Though we do
not consider the effects of stellar radiation, gravity, or mechanical energy
input from discrete sources, our models do contain the basic physics of
magneto-fluid dynamics and non-LTE radiation transfer and are therefore more
realistic than previous calculations. As a result, these synthetic maps and
spectra bear a remarkable resemblance to the corresponding observations of real
clouds.Comment: 33 pages, 12 figures included, 5 jpeg figures not included (fig1a,
fig1b, fig3, fig4 fig5), submitted to Ap
A Super-Alfvenic Model of Dark Clouds
Supersonic random motions are observed in dark clouds and are traditionally
interpreted as Alfven waves, but the possibility that these motions are
super-Alfvenic has not been ruled out. In this work we report the results of
numerical experiments in two opposite regimes; M_a ~ 1 and M_a >> 1, where M_a
is the initial Alfvenic Mach number --the ratio of the rms velocity to the
Alfven speed. Our results show that models with M_a >> 1 are consistent with
the observed properties of molecular clouds that we have tested --statistics of
extinction measurements, Zeeman splitting measurements of magnetic field
strength, line width versus integrated antenna temperature of molecular
emission line spectra, statistical B-n relation, and scatter in that relation--
while models with M_a ~ 1 have properties that are in conflict with the
observations. We find that both the density and the magnetic field in molecular
clouds may be very intermittent. The statistical distributions of magnetic
field and gas density are related by a power law, with an index that decreases
with time in experiments with decaying turbulence. After about one dynamical
time it stabilizes at B ~ n^{0.4}. Magnetically dominated cores form early in
the evolution, while later on the intermittency in the density field wins out,
and also cores with weak field can be generated, by mass accretion along
magnetic field lines.Comment: 10 figures, 2 tables include
Supersonic turbulence and structure of interstellar molecular clouds
The interstellar medium (ISM) provides a unique laboratory for highly
supersonic, driven hydrodynamics turbulence. We present a theory of such
turbulence, confirm it by numerical simulations, and use the results to explain
observational properties of interstellar molecular clouds, the regions where
stars are born.Comment: 5 pages, 3 figures include