49 research outputs found
Diffusive Versus Free-Streaming Cosmic Ray Transport in Molecular Clouds
Understanding the cosmic ray (CR) ionization rate is crucial in order to
simulate the dynamics of, and interpret the chemical species observed in
molecular clouds. Calculating the CR ionization rate requires both accurate
knowledge of the spectrum of MeV to GeV protons at the edge of the cloud as
well as a model for the propagation of CRs into molecular clouds. Some models
for the propagation of CRs in molecular clouds assume the CRs to stream freely
along magnetic field lines, while in others they propagate diffusively due to
resonant scattering off of magnetic disturbances excited by MHD turbulence
present in the medium. We discuss the conditions under which CR diffusion can
operate in a molecular cloud, calculate the local CR spectrum and ionization
rate in both a free-streaming and diffusive propagation model, and highlight
the different results from the two models. We also apply these two models to
the propagation through the ISM to obtain the spectrum seen by Voyager 1, and
show that such a spectrum favors a diffusive propagation model.Comment: Submitted to Ap
Cosmic-ray ionisation in circumstellar discs
Galactic cosmic rays are a ubiquitous source of ionisation of the
interstellar gas, competing with UV and X-ray photons as well as natural
radioactivity in determining the fractional abundance of electrons, ions and
charged dust grains in molecular clouds and circumstellar discs. We model the
propagation of different components of Galactic cosmic rays versus the column
density of the gas. Our study is focussed on the propagation at high densities,
above a few g cm, especially relevant for the inner regions of
collapsing clouds and circumstellar discs. The propagation of primary and
secondary CR particles (protons and heavier nuclei, electrons, positrons, and
photons) is computed in the continuous slowing down approximation, diffusion
approximation, or catastrophic approximation, by adopting a matching procedure
for the different transport regimes. A choice of the proper regime depends on
the nature of the dominant loss process, modelled as continuous or
catastrophic. The CR ionisation rate is determined by CR protons and their
secondary electrons below g cm and by electron/positron
pairs created by photon decay above g cm. We show that a
proper description of the particle transport is essential to compute the
ionisation rate in the latter case, since the electron/positron differential
fluxes depend sensitively on the fluxes of both protons and photons. Our
results show that the CR ionisation rate in high-density environments, like,
e.g., the inner parts of collapsing molecular clouds or the mid-plane of
circumstellar discs, is larger than previously assumed. It does not decline
exponentially with increasing column density, but follows a more complex
behaviour due to the interplay of different processes governing the generation
and propagation of secondary particles.Comment: 19 pages, 11 figures, accepted by A&
Production of atomic hydrogen by cosmic rays in dark clouds
The presence of small amounts of atomic hydrogen, detected as absorption dips
in the 21 cm line spectrum, is a well-known characteristic of dark clouds. The
abundance of hydrogen atoms measured in the densest regions of molecular clouds
can be only explained by the dissociation of H due to cosmic rays. We want
to assess the role of Galactic cosmic rays in the formation of atomic hydrogen,
by using recent developments in the characterisation of the low-energy spectra
of cosmic rays and advances in the modelling of their propagation in molecular
clouds. We model the attenuation of the interstellar cosmic rays entering a
cloud and compute the dissociation rate of molecular hydrogen due to collisions
with cosmic-ray protons and electrons as well as fast hydrogen atoms. We
compare our results with the available observations. The cosmic-ray
dissociation rate is entirely determined by secondary electrons produced in
primary ionisation collisions. These secondary particles constitute the only
source of atomic hydrogen at column densities above cm. We
also find that the dissociation rate decreases with column density, while the
ratio between the dissociation and ionisation rates varies between about 0.6
and 0.7. From comparison with observations we conclude that a relatively flat
spectrum of interstellar cosmic-ray protons, as the one suggested by the most
recent Voyager 1 data, can only provide a lower bound for the observed atomic
hydrogen fraction. An enhanced spectrum of low-energy protons is needed to
explain most of the observations. Our findings show that a careful description
of molecular hydrogen dissociation by cosmic rays can explain the abundance of
atomic hydrogen in dark clouds. An accurate characterisation of this process at
high densities is crucial for understanding the chemical evolution of
star-forming regions.Comment: 7 pages, 7 figures, accepted by Astronomy and Astrophysic
Structural correlations in diffusiophoretic colloidal mixtures with nonreciprocal interactions
Nonreciprocal effective interaction forces can occur between mesoscopic particles in colloidal suspensions that are driven out of equilibrium. These forces violate Newton's third law actio  =  reactio on coarse-grained length and time scales. Here we explore the statistical mechanics of Brownian particles with nonreciprocal effective interactions. Our model system is a binary fluid mixture of spherically symmetric, diffusiophoretic mesoscopic particles, and we focus on the time-averaged particle pair- and triplet-correlation functions. Based on the many-body Smoluchowski equation we develop a microscopic statistical theory for the particle correlations and test it by computer simulations. For model systems in two and three spatial dimensions, we show that nonreciprocity induces distinct nonequilibrium pair correlations. Our predictions can be tested in experiments with chemotactic colloidal suspensions
Impact of magneto-rotational instability on grain growth in protoplanetary disks: I. Relevant turbulence properties
Turbulence in the protoplanetary disks induces collisions between dust
grains, and thus facilitates grain growth. We investigate the two fundamental
assumptions of the turbulence in obtaining grain collisional velocities -- the
kinetic energy spectrum and the turbulence autocorrelation time -- in the
context of the turbulence generated by the magneto-rotational instability
(MRI). We carry out numerical simulations of the MRI as well as driven
turbulence, for a range of physical and numerical parameters. We find that the
convergence of the turbulence -parameter does not necessarily imply the
convergence of the energy spectrum. The MRI turbulence is largely solenoidal,
for which we observe a persistent kinetic energy spectrum of . The
same is obtained for solenoidal driven turbulence with and without magnetic
field, over more than 1 dex near the dissipation scale. This power-law slope
appears to be converged in terms of numerical resolution, and to be due to the
bottleneck effect. The kinetic energy in the MRI turbulence peaks at the
fastest growing mode of the MRI. In contrast, the magnetic energy peaks at the
dissipation scale. The magnetic energy spectrum in the MRI turbulence does not
show a clear power-law range, and is almost constant over approximately 1 dex
near the dissipation scale. The turbulence autocorrelation time is nearly
constant at large scales, limited by the shearing timescale, and shows a
power-law drop close to at small scales, with a slope steeper than
that of the eddy crossing time. The deviation from the standard picture of the
Kolmogorov turbulence with the injection scale at the disk scale height can
potentially have a significant impact on the grain collisional velocities.Comment: Accepted by Ap
Magnetic Mirroring and Focusing of Cosmic Rays
We study the combined impact of magnetic mirroring and focusing on the
ionization by cosmic rays (CRs) in dense molecular clouds and circumstellar
disks. We show that for effective column densities of up to
cm (where ionization is the main mechanism of energy losses by CRs) the
two effects practically cancel each other out, provided the magnetic field
strength has a single peak along field lines. In this case the ionization rate
at a given location is controlled solely by attenuation of interstellar CRs due
to energy losses. The situation is very different in the presence of magnetic
pockets -- local minima of the field strength, where the CR density and thus
ionization can be reduced drastically. We obtain simple analytical expressions
allowing accurate calculation of the ionization rate in these regions.Comment: Accepted to Ap
Coagulation-Fragmentation Equilibrium for Charged Dust: Abundance of Submicron Grains Increases Dramatically in Protoplanetary Disks
Dust coagulation in protoplanetary disks is not straightforward and is
subject to several slow-down mechanisms, such as bouncing, fragmentation and
radial drift to the star. Furthermore, dust grains in UV-shielded disk regions
are negatively charged due to collisions with the surrounding electrons and
ions, which leads to their electrostatic repulsion. For typical disk
conditions, the relative velocities between micron-size grains are small and
their collisions are strongly affected by the repulsion. On the other hand,
collisions between pebble-size grains can be too energetic, leading to grain
fragmentation. The aim of the present paper is to study a combined effect of
the electrostatic and fragmentation barriers on dust evolution. We numerically
solve the Smoluchowski coagulation-fragmentation equation for grains whose
charging occurs under conditions typical for the inner disk regions, where
thermal ionization operates. We find that dust fragmentation efficiently
resupplies the population of small grains under the electrostatic barrier. As a
result, the equilibrium abundance of sub-micron grains is enhanced by several
orders of magnitude compared to the case of neutral dust. For some conditions
with fragmentation velocities m s, macroscopic grains are
completely destroyed.Comment: accepted for publication in Ap
Dust grains cannot grow to millimeter sizes in protostellar envelopes
A big question in the field of star and planet formation is the time at which
substantial dust grain growth occurs. The observed properties of dust emission
across different wavelength ranges have been used as an indication that
millimeter-sized grains are already present in the envelopes of young
protostars. However, this interpretation is in tension with results from
coagulation simulations, which are not able to produce such large grains in
these conditions. In this work, we show analytically that the production of
millimeter-sized grains in protostellar envelopes is impossible under the
standard assumptions about the coagulation process. We discuss several
possibilities that may serve to explain the observed dust emission in the
absence of in-situ grain growth to millimeter sizes.Comment: Accepted to Ap