3,360 research outputs found
Super-Earths in the TW Hya disc
We test the hypothesis that the sub-millimetre thermal emission and scattered
light gaps seen in recent observations of TW Hya are caused by planet-disc
interactions. We perform global three-dimensional dusty smoothed particle
hydrodynamics simulations, comparing synthetic observations of our models with
dust thermal emission, CO emission and scattered light observations. We find
that the dust gaps observed at 24 au and 41 au can be explained by two
super-Earths (). A planet of approximately
Saturn-mass can explain the CO emission and the depth and width of the gap seen
in scattered light at 94 au. Our model produces a prominent spiral arm while
there are only hints of this in the data. To avoid runaway growth and migration
of the planets we require a disc mass of
in agreement with CO observations but 10100 times lower than the estimate
from HD line emission.Comment: 6 pages, 5 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 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
Dust and gas mixtures with multiple grain species - a one-fluid approach
GL acknowledges funding from the European Research Council for the FP7 ERC advanced grant project ECOGAL. DJP is very grateful for funding via an ARC Future Fellowship, FT130100034, and Discovery Project grant DP130102078.We derive the single-fluid evolution equations describing a mixture made of a gas phase and an arbitrary number of dust phases, generalizing the approach developed by Laibe & Price. A generalization for continuous dust distributions as well as analytic approximations for strong drag regimes is also provided. This formalism lays the foundation for numerical simulations of dust populations in a wide range of astrophysical systems while avoiding limitations associated with a multiple-fluid treatment. The usefulness of the formalism is illustrated on a series of analytical problems, namely the DUSTYBOX, DUSTYSHOCK and DUSTYWAVE problems as well as the radial drift of grains and the streaming instability in protoplanetary discs. We find physical effects specific to the presence of several dust phases and multiple drag time-scales, including non-monotonic evolution of the differential velocity between phases and increased efficiency of the linear growth of the streaming instability. Interestingly, it is found that under certain conditions, large grains can migrate outwards in protoplanetary discs. This may explain the presence of small pebbles at several hundreds of astronomical units from their central star.Publisher PDFPeer reviewe
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
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