575 research outputs found
The Star Formation Rate of Turbulent Magnetized Clouds: Comparing Theory, Simulations, and Observations
We derive and compare six theoretical models for the star formation rate
(SFR) - the Krumholz & McKee (KM), Padoan & Nordlund (PN), and Hennebelle &
Chabrier (HC) models, and three multi-freefall versions of these, suggested by
HC - all based on integrals over the log-normal distribution of turbulent gas.
We extend all theories to include magnetic fields, and show that the SFR
depends on four basic parameters: (1) virial parameter alpha_vir; (2) sonic
Mach number M; (3) turbulent forcing parameter b, which is a measure for the
fraction of energy driven in compressive modes; and (4) plasma beta=2(M_A/M)^2
with the Alfven Mach number M_A. We compare all six theories with MHD
simulations, covering cloud masses of 300 to 4x10^6 solar masses and Mach
numbers M = 3 to 50 and M_A = 1 to infinity, with solenoidal (b=1/3), mixed
(b=0.4) and compressive turbulent (b=1) forcings. We find that the SFR
increases by a factor of four between M=5 and 50 for compressive forcing and
alpha_vir~1. Comparing forcing parameters, we see that the SFR is more than 10x
higher with compressive than solenoidal forcing for Mach 10 simulations. The
SFR and fragmentation are both reduced by a factor of two in strongly
magnetized, trans-Alfvenic turbulence compared to hydrodynamic turbulence. All
simulations are fit simultaneously by the multi-freefall KM and multi-freefall
PN theories within a factor of two over two orders of magnitude in SFR. The
simulated SFRs cover the range and correlation of SFR column density with gas
column density observed in Galactic clouds, and agree well for star formation
efficiencies SFE = 1% to 10% and local efficiencies epsilon = 0.3 to 0.7 due to
feedback. We conclude that the SFR is primarily controlled by interstellar
turbulence, with a secondary effect coming from magnetic fields.Comment: 34 pages, 12 figures, ApJ in press, movies at
http://www.ita.uni-heidelberg.de/~chfeder/pubs/sfr/sfr.shtm
On the Star Formation Efficiency of Turbulent Magnetized Clouds
We study the star formation efficiency (SFE) in simulations and observations
of turbulent, magnetized, molecular clouds. We find that the probability
density functions (PDFs) of the density and the column density in our
simulations with solenoidal, mixed, and compressive forcing of the turbulence,
sonic Mach numbers of 3-50, and magnetic fields in the super- to the
trans-Alfvenic regime, all develop power-law tails of flattening slope with
increasing SFE. The high-density tails of the PDFs are consistent with
equivalent radial density profiles, rho ~ r^(-kappa) with kappa ~ 1.5-2.5, in
agreement with observations. Studying velocity-size scalings, we find that all
the simulations are consistent with the observed v ~ l^(1/2) scaling of
supersonic turbulence, and seem to approach Kolmogorov turbulence with v ~
l^(1/3) below the sonic scale. The velocity-size scaling is, however, largely
independent of the SFE. In contrast, the density-size and column density-size
scalings are highly sensitive to star formation. We find that the power-law
slope alpha of the density power spectrum, P(rho,k) ~ k^alpha, or equivalently
the Delta-variance spectrum of column density, DV(Sigma,l) ~ l^(-alpha),
switches sign from alpha 0 when star formation
proceeds (SFE > 0). We provide a relation to compute the SFE from a measurement
of alpha. Studying the literature, we find values ranging from alpha = -1.6 to
+1.6 in observations covering scales from the large-scale atomic medium, over
cold molecular clouds, down to dense star-forming cores. From those alpha
values, we infer SFEs and find good agreement with independent measurements
based on young stellar object (YSO) counts, where available. Our SFE-alpha
relation provides an independent estimate of the SFE based on the column
density map of a cloud alone, without requiring a priori knowledge of
star-formation activity or YSO counts.Comment: 23 pages, 14 figures, ApJ in press, more info at
http://www.ita.uni-heidelberg.de/~chfeder/pubs/sfe/sfe.shtml?lang=e
The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing
The probability density function (PDF) of the gas density in turbulent
supersonic flows is investigated with high-resolution numerical simulations. In
a systematic study, we compare the density statistics of compressible
turbulence driven by the usually adopted solenoidal forcing (divergence-free)
and by compressive forcing (curl-free). Our results are in agreement with
studies using solenoidal forcing. However, compressive forcing yields a
significantly broader density distribution with standard deviation ~3 times
larger at the same rms Mach number. The standard deviation-Mach number relation
used in analytical models of star formation is reviewed and a modification of
the existing expression is proposed, which takes into account the ratio of
solenoidal and compressive modes of the turbulence forcing.Comment: 5 pages, 3 figures, accepted to ApJL, simulation movies available at
http://www.ita.uni-heidelberg.de/~chfeder/videos.shtml?lang=e
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