83 research outputs found
Growing dust grains in protoplanetary discs - II. The Radial drift barrier problem
We aim to study the migration of growing dust grains in protoplanetary discs,
where growth and migration are tightly coupled. This includes the crucial issue
of the radial-drift barrier for growing dust grains. We therefore extend the
study performed in Paper I, considering models for grain growth and grain
dynamics where both the migration and growth rate depend on the grain size and
the location in the disc. The parameter space of disc profiles and growth
models is exhaustively explored. In doing so, interpretations for the grain
motion found in numerical simulations are also provided.
We find that a large number of cases is required to characterise entirely the
grains radial motion, providing a large number of possible outcomes. Some of
them lead dust particles to be accreted onto the central star and some of them
don't.
We find then that q<1 is required for discs to retain their growing
particles, where q is the exponent of the radial temperature profile T(R)
proportional to R^-q. Additionally, the initial dust-to gas ratio has to exceed
a critical value for grains to pile up efficiently, thus avoiding being
accreted onto the central star. Discs are also found to retain efficiently
small dust grains regenerated by fragmentation. We show how those results are
sensitive to the turbulent model considered.
Even though some physical processes have been neglected, this study allows to
sketch a scenario in which grains can survive the radial-drift barrier in
protoplanetary discs as they grow.Comment: 18 pages, 10 figures. Accepted for publication in MNRAS. v2: typos
correcte
Linear growth of streaming instability in pressure bumps
Streaming instability is a powerful mechanism which concentrates dust grains
in pro- toplanetary discs, eventually up to the stage where they collapse
gravitationally and form planetesimals. Previous studies inferred that it
should be ineffective in viscous discs, too efficient in inviscid discs, and
may not operate in local pressure maxima where solids accumulate. From a linear
analysis of stability, we show that streaming instability behaves differently
inside local pressure maxima. Under the action of the strong differential
advection imposed by the bump, a novel unstable mode develops and grows even
when gas viscosity is large. Hence, pressure bumps are found to be the only
places where streaming instability occurs in viscous discs. This offers a
promising way to conciliate models of planet formation with recent observations
of young discs.Comment: 11 pages, 17 figures, accepted for publication in MNRA
Diversity in the outcome of dust radial drift in protoplanetary discs
The growth of dust particles into planet embryos needs to circumvent the
radial-drift barrier, i.e. the accretion of dust particles onto the central
star by radial migration. The outcome of the dust radial migration is governed
by simple criteria between the dust-to-gas ratio and the exponents p and q of
the surface density and temperature power laws. The transfer of radiation
provides an additional constraint between these quantities because the disc
thermal structure is fixed by the dust spatial distribution. To assess which
discs are primarily affected by the radial-drift barrier, we used the radiative
transfer code MCFOST to compute the temperature structure of a wide range of
disc models, stressing the particular effects of grain size distributions and
vertical settling.
We find that the outcome of the dust migration process is very sensitive to
the physical conditions within the disc. For high dust-to-gas ratios (> 0.01)
or flattened disc structures (H/R < 0.05), growing dust grains can efficiently
decouple from the gas, leading to a high concentration of grains at a critical
radius of a few AU. Decoupling of grains can occur at a large fraction (> 0.1)
of the initial radius, for a dust-to-gas ratio greater than ~ 0.05. The exact
value of the required dust-to-gas ratio for dust to stop its migration is
strongly dependent on the disc temperature structure. Non growing dust grains
are accreted for discs with flat surface density profiles (p<0.7) while they
always remain in the disc if the surface density is steep enough (p>1.2). Both
the presence of large grains and vertical settling tend to favour the accretion
of non growing dust grains onto the central object, but it slows down the
migration of growing dust grains. All the disc configurations are found to have
favourable temperature profiles over most of the disc to retain their
planetesimals.Comment: 9 pages, 8 figures, accepted for publications in A&A, corrected typo
An opening criterion for dust gaps in protoplanetary discs
We aim to understand under which conditions a low mass planet can open a gap
in viscous dusty protoplanetary discs. For this purpose, we extend the theory
of dust radial drift to include the contribution from the tides of an embedded
planet and from the gas viscous forces. From this formalism, we derive i) a
grain size-dependent criterion for dust gap opening in discs, ii) an estimate
of the location of the outer edge of the dust gap and iii) an estimate of the
minimum Stokes number above which low-mass planets are able to carve gaps which
appear only in the dust disc. These analytical estimates are particularly
helpful to appraise the minimum mass of an hypothetical planet carving gaps in
discs observed at long wavelengths and high resolution. We validate the theory
against 3D SPH simulations of planet-disc interaction in a broad range of dusty
protoplanetary discs. We find a remarkable agreement between the theoretical
model and the numerical experiments.Comment: 17 pages, 13 figures. Accepted for publication in MNRA
A solution to the overdamping problem when simulating dust-gas mixtures with smoothed particle hydrodynamics
We present a fix to the overdamping problem found by Laibe & Price (2012)
when simulating strongly coupled dust-gas mixtures using two different sets of
particles using smoothed particle hydrodynamics. Our solution is to compute the
drag at the barycentre between gas and dust particle pairs when computing the
drag force by reconstructing the velocity field, similar to the procedure in
Godunov-type solvers. This fixes the overdamping problem at negligible
computational cost, but with additional memory required to store velocity
derivatives. We employ slope limiters to avoid spurious oscillations at shocks,
finding the van Leer Monotonized Central limiter most effective.Comment: 6 pages, 5 figures, accepted to MNRA
Dusty gas with one fluid
In this paper, we show how the two-fluid equations describing the evolution
of a dust and gas mixture can be reformulated to describe a single fluid moving
with the barycentric velocity of the mixture. This leads to evolution equations
for the total density, momentum, the differential velocity between the dust and
the gas phases and either the dust-to-gas ratio or the dust fraction. The
equations are similar to the usual equations of gas dynamics, providing a
convenient way to extend existing codes to simulate two-fluid mixtures without
modifying the code architecture. Our approach avoids the inherent difficulties
related to the standard approach where the two phases are separate and coupled
via a drag term. In particular, the requirements of infinite spatial and
temporal resolution as the stopping time tends to zero are no longer necessary.
This means that both small and large grains can be straightforwardly treated
with the same method, with no need for complicated implicit schemes. Since
there is only one resolution scale the method also avoids the problem of
unphysical trapping of one fluid (e.g. dust) below the resolution of the other.
We also derive a simplified set of equations applicable to the case of strong
drag/small grains, consisting of the standard fluid equations with a modified
sound speed, plus an advection-diffusion equation for the dust-to-gas ratio.
This provides a simple and fast way to evolve the mixture when the stopping
time is smaller than the Courant timestep. We present a Smoothed Particle
Hydrodynamics implementation in a companion paper.Comment: Accepted for publication in MNRAS (very minor revisions included
A fast and explicit algorithm for simulating the dynamics of small dust grains with smoothed particle hydrodynamics
We describe a simple method for simulating the dynamics of small grains in a
dusty gas, relevant to micron-sized grains in the interstellar medium and
grains of centimetre size and smaller in protoplanetary discs. The method
involves solving one extra diffusion equation for the dust fraction in addition
to the usual equations of hydrodynamics. This "diffusion approximation for
dust" is valid when the dust stopping time is smaller than the computational
timestep. We present a numerical implementation using Smoothed Particle
Hydrodynamics (SPH) that is conservative, accurate and fast. It does not
require any implicit timestepping and can be straightforwardly ported into
existing 3D codes.Comment: 15 pages, 10 figures, accepted to MNRAS. Code implementation (ndspmhd
v2.1) and setup of test problems available at:
http://users.monash.edu.au/~dprice/ndspmhd/. v3: sign errors fixed as per
erratum to published pape
Dusty gas with one fluid in smoothed particle hydrodynamics
In a companion paper we have shown how the equations describing gas and dust
as two fluids coupled by a drag term can be reformulated to describe the system
as a single fluid mixture. Here we present a numerical implementation of the
one-fluid dusty gas algorithm using Smoothed Particle Hydrodynamics (SPH). The
algorithm preserves the conservation properties of the SPH formalism. In
particular, the total gas and dust mass, momentum, angular momentum and energy
are all exactly conserved. Shock viscosity and conductivity terms are
generalised to handle the two-phase mixture accordingly. The algorithm is
benchmarked against a comprehensive suit of problems: dustybox, dustywave,
dustyshock and dustyoscill, each of them addressing different properties of the
method. We compare the performance of the one-fluid algorithm to the standard
two-fluid approach. The one-fluid algorithm is found to solve both of the
fundamental limitations of the two- fluid algorithm: it is no longer possible
to concentrate dust below the resolution of the gas (they have the same
resolution by definition), and the spatial resolution criterion h < csts,
required in two-fluid codes to avoid over-damping of kinetic energy, is
unnecessary. Implicit time stepping is straightforward. As a result, the
algorithm is up to ten billion times more efficient for 3D simulations of small
grains. Additional benefits include the use of half as many particles, a single
kernel and fewer SPH interpolations. The only limitation is that it does not
capture multi-streaming of dust in the limit of zero coupling, suggesting that
in this case a hybrid approach may be required.Comment: Accepted for publication in MNRAS. Numerical code and input files for
dustybox, wave and shock tests available from
http://users.monash.edu.au/~dprice/ndspmhd
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