8,477 research outputs found
Power-law tails in probability density functions of molecular cloud column density
Power-law tails are often seen in probability density functions (PDFs) of
molecular cloud column densities, and have been attributed to the effect of
gravity. We show that extinction PDFs of a sample of five molecular clouds
obtained at a few tenths of a parsec resolution, probing extinctions up to
A 10 magnitudes, are very well described by lognormal
functions provided that the field selection is tightly constrained to the cold,
molecular zone and that noise and foreground contamination are appropriately
accounted for. In general, field selections that incorporate warm, diffuse
material in addition to the cold, molecular material will display apparent
core+tail PDFs. The apparent tail, however, is best understood as the high
extinction part of a lognormal PDF arising from the cold, molecular part of the
cloud. We also describe the effects of noise and foreground/background
contamination on the PDF structure, and show that these can, if not
appropriately accounted for, induce spurious tails or amplify any that are
truly present.Comment: Accepted for publication in MNRA
A method for reconstructing the PDF of a 3D turbulent density field from 2D observations
We introduce a method for calculating the probability density function (PDF)
of a turbulent density field in three dimensions using only information
contained in the projected two-dimensional column density field. We test the
method by applying it to numerical simulations of hydrodynamic and
magnetohydrodynamic turbulence in molecular clouds. To a good approximation,
the PDF of log(normalised column density) is a compressed, shifted version of
the PDF of log(normalised density). The degree of compression can be determined
observationally from the column density power spectrum, under the assumption of
statistical isotropy of the turbulence.Comment: 5 pages, 2 figures, accepted for publication in MNRAS Letter
Infinitely divisible nonnegative matrices, -matrices, and the embedding problem for finite state stationary Markov Chains
This paper explicitly details the relation between -matrices, nonnegative
roots of nonnegative matrices, and the embedding problem for finite-state
stationary Markov chains. The set of nonsingular nonnegative matrices with
arbitrary nonnegative roots is shown to be the closure of the set of matrices
with matrix roots in . The methods presented here employ nothing
beyond basic matrix analysis, however it answers a question regarding
-matrices posed over 30 years ago and as an application, a new
characterization of the set of all embeddable stochastic matrices is obtained
as a corollary
An Observational Method to Measure the Relative Fractions of Solenoidal and Compressible Modes in Interstellar Clouds
We introduce a new method for observationally estimating the fraction of
momentum density () power contained in solenoidal modes
(for which ) in molecular clouds. The
method is successfully tested with numerical simulations of supersonic
turbulence that produce the full range of possible solenoidal/compressible
fractions. At present the method assumes statistical isotropy, and does not
account for anisotropies caused by (e.g.) magnetic fields. We also introduce a
framework for statistically describing density--velocity correlations in
turbulent clouds.Comment: 20 pages, 13 figures, accepted for publication in MNRA
Explicit Solution and Fine Asymptotics for a Critical Growth-Fragmentation Equation
We give here an explicit formula for the following critical case of the
growth-fragmentation equation for some constants , and - the case being the emblematic binary fission case. We discuss
the links between this formula and the asymptotic ones previously obtained in
(Doumic, Escobedo, Kin. Rel. Mod., 2016), and use them to clarify how
periodicity may appear asymptotically
The Density Variance Mach Number Relation in the Taurus Molecular Cloud
Supersonic turbulence in molecular clouds is a key agent in generating
density enhancements that may subsequently go on to form stars. The stronger
the turbulence - the higher the Mach number - the more extreme the density
fluctuations are expected to be. Numerical models predict an increase in
density variance with rms Mach number of the form: sigma^{2}_{rho/rho_{0}} =
b^{2}M^{2}, where b is a numerically-estimated parameter, and this prediction
forms the basis of a large number of analytic models of star formation. We
provide an estimate of the parameter b from 13CO J=1-0 spectral line imaging
observations and extinction mapping of the Taurus molecular cloud, using a
recently developed technique that needs information contained solely in the
projected column density field to calculate sigma^{2}_{rho/rho_{0}}. We find b
~ 0.48, which is consistent with typical numerical estimates, and is
characteristic of turbulent driving that includes a mixture of solenoidal and
compressive modes. More conservatively, we constrain b to lie in the range
0.3-0.8, depending on the influence of sub-resolution structure and the role of
diffuse atomic material in the column density budget. We also report a break in
the Taurus column density power spectrum at a scale of ~1pc, and find that the
break is associated with anisotropy in the power spectrum. The break is
observed in both 13CO and dust extinction power spectra, which, remarkably, are
effectively identical despite detailed spatial differences between the 13CO and
dust extinction maps. [ abridged ]Comment: 8 pages, 9 figures. Accepted for publication in A&
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