732 research outputs found
Integration of Particle-Gas Systems with Stiff Mutual Drag Interaction
Numerical simulation of numerous mm/cm-sized particles embedded in a gaseous
disk has become an important tool in the study of planet formation and in
understanding the dust distribution in observed protoplanetary disks. However,
the mutual drag force between the gas and the particles can become so stiff,
particularly because of small particles and/or strong local solid
concentration, that an explicit integration of this system is computationally
formidable. In this work, we consider the integration of the mutual drag force
in a system of Eulerian gas and Lagrangian solid particles. Despite the
entanglement between the gas and the particles under the particle-mesh
construct, we are able to devise a numerical algorithm that effectively
decomposes the globally coupled system of equations for the mutual drag force
and makes it possible to integrate this system on a cell-by-cell basis, which
considerably reduces the computational task required. We use an analytical
solution for the temporal evolution of each cell to relieve the time-step
constraint posed by the mutual drag force as well as to achieve the highest
degree of accuracy. To validate our algorithm, we use an extensive suite of
benchmarks with known solutions in one, two, and three dimensions, including
the linear growth and the nonlinear saturation of the streaming instability. We
demonstrate numerical convergence and satisfactory consistency in all cases.
Our algorithm can for example be applied to model the evolution of the
streaming instability with mm/cm-sized pebbles at high mass loading, which has
important consequences for the formation scenarios of planetesimals.Comment: Accepted for publication in the Astrophysical Journal Supplement
Series. 21 pages, 15 figures. Fixed cross references for equation
On the Feeding Zone of Planetesimal Formation by the Streaming Instability
The streaming instability is a promising mechanism to overcome the barriers
in direct dust growth and lead to the formation of planetesimals. Most previous
studies of the streaming instability, however, were focused on a local region
of a protoplanetary disk with a limited simulation domain such that only one
filamentary concentration of solids has been observed. The characteristic
separation between filaments is therefore not known. To address this, we
conduct the largest-scale simulations of the streaming instability to date,
with computational domains up to 1.6 gas scale heights both horizontally and
vertically. The large dynamical range allows the effect of vertical gas
stratification to become prominent. We observe more frequent merging and
splitting of filaments in simulation boxes of high vertical extent. We find
multiple filamentary concentrations of solids with an average separation of
about 0.2 local gas scale heights, much higher than the most unstable
wavelength from linear stability analysis. This measures the characteristic
separation of planetesimal forming events driven by the streaming instability
and thus the initial feeding zone of planetesimals.Comment: AASTeX preprint, 21 pages, including 7 figures. Accepted by Ap
Initial mass function of planetesimals formed by the streaming instability
The streaming instability is a mechanism to concentrate solid particles into
overdense filaments that undergo gravitational collapse and form planetesimals.
However, it remains unclear how the initial mass function of these
planetesimals depends on the box dimensions of numerical simulations. To
resolve this, we perform simulations of planetesimal formation with the largest
box dimensions to date, allowing planetesimals to form simultaneously in
multiple filaments that can only emerge within such large simulation boxes. In
our simulations, planetesimals with sizes between 80 km and several hundred
kilometers form. We find that a power law with a rather shallow exponential
cutoff at the high-mass end represents the cumulative birth mass function
better than an integrated power law. The steepness of the exponential cutoff is
largely independent of box dimensions and resolution, while the exponent of the
power law is not constrained at the resolutions we employ. Moreover, we find
that the characteristic mass scale of the exponential cutoff correlates with
the mass budget in each filament. Together with previous studies of
high-resolution simulations with small box domains, our results therefore imply
that the cumulative birth mass function of planetesimals is consistent with an
exponentially tapered power law with a power-law exponent of approximately -1.6
and a steepness of the exponential cutoff in the range of 0.3-0.4.Comment: 11 pages, 5 figures, 3 tables; accepted for publication in Astronomy
& Astrophysics; language editing complete
Diffusion and Concentration of Solids in the Dead Zone of a Protoplanetary Disk
The streaming instability is a promising mechanism to drive the formation of planetesimals in protoplanetary disks. To trigger this process, it has been argued that sedimentation of solids onto the mid-plane needs to be efficient, and therefore that a quiescent gaseous environment is required. It is often suggested that dead-zone or disk-wind structure created by non-ideal magnetohydrodynamical (MHD) effects meets this requirement. However, simulations have shown that the mid-plane of a dead zone is not completely quiescent. In order to examine the concentration of solids in such an environment, we use the local-shearing-box approximation to simulate a particlegas system with an Ohmic dead zone including mutual drag force between the gas and the solids. We systematically compare the evolution of the system with ideal or non-ideal MHD, with or without backreaction drag force from particles on gas, and with varying solid abundances. Similar to previous investigations of deadzone dynamics, we find that particles of dimensionless stopping time ts = 0.1 do not sediment appreciably more than those in ideal magnetorotational turbulence, resulting in a vertical scale height an order of magnitude larger than in a laminar disk. Contrary to the expectation that this should curb the formation of planetesimals, we nevertheless find that strong clumping of solids still occurs in the dead zone when solid abundances are similar to the critical value for a laminar environment. This can be explained by the weak radial diffusion of particles near the mid-plane. The results imply that the sedimentation of particles to the mid-plane is not a necessary criterion for the formation of planetesimals by the streaming instability
Streaming Instability With Multiple Dust Species-II. Turbulence and Dust-Gas Dynamics at Non-linear Saturation
The streaming instability is a fundamental process that can drive dust-gas dynamics and ultimately planetesimal formation in protoplanetary discs. As a linear instability, it has been shown that its growth with a distribution of dust sizes can be classified into two distinct regimes, fast-and slow-growth, depending on the dust-size distribution and the total dust-To-gas density ratio . Using numerical simulations of an unstratified disc, we bring three cases in different regimes into non-linear saturation. We find that the saturation states of the two fast-growth cases are similar to its single-species counterparts. The one with maximum dimensionless stopping time Ď„s,max = 0.1 and = 2 drives turbulent vertical dust-gas vortices, while the other with Ď„s,max = 2 and = 0.2 leads to radial traffic jams and filamentary structures of dust particles. The dust density distribution for the former is flat in low densities, while the one for the latter has a low-end cut-off. By contrast, the one slow-growth case results in a virtually quiescent state. Moreover, we find that in the fast-growth regime, significant dust segregation by size occurs, with large particles moving towards dense regions while small particles remain in the diffuse regions, and the mean radial drift of each dust species is appreciably altered from the (initial) drag-force equilibrium. The former effect may skew the spectral index derived from multiwavelength observations and change the initial size distribution of a pebble cloud for planetesimal formation. The latter along with turbulent diffusion may influence the radial transport and mixing of solid materials in young protoplanetary discs
Streaming Instability With Multiple Dust Species-II. Turbulence and Dust-Gas Dynamics at Non-linear Saturation
The streaming instability is a fundamental process that can drive dust-gas dynamics and ultimately planetesimal formation in protoplanetary discs. As a linear instability, it has been shown that its growth with a distribution of dust sizes can be classified into two distinct regimes, fast-and slow-growth, depending on the dust-size distribution and the total dust-To-gas density ratio . Using numerical simulations of an unstratified disc, we bring three cases in different regimes into non-linear saturation. We find that the saturation states of the two fast-growth cases are similar to its single-species counterparts. The one with maximum dimensionless stopping time Ď„s,max = 0.1 and = 2 drives turbulent vertical dust-gas vortices, while the other with Ď„s,max = 2 and = 0.2 leads to radial traffic jams and filamentary structures of dust particles. The dust density distribution for the former is flat in low densities, while the one for the latter has a low-end cut-off. By contrast, the one slow-growth case results in a virtually quiescent state. Moreover, we find that in the fast-growth regime, significant dust segregation by size occurs, with large particles moving towards dense regions while small particles remain in the diffuse regions, and the mean radial drift of each dust species is appreciably altered from the (initial) drag-force equilibrium. The former effect may skew the spectral index derived from multiwavelength observations and change the initial size distribution of a pebble cloud for planetesimal formation. The latter along with turbulent diffusion may influence the radial transport and mixing of solid materials in young protoplanetary discs
Star Formation in the LMC: Gravitational Instability and Dynamical Triggering
Evidence for triggered star formation is difficult to establish because
energy feedback from massive stars tend to erase the interstellar conditions
that led to the star formation. Young stellar objects (YSOs) mark sites of {\it
current} star formation whose ambient conditions have not been significantly
altered. Spitzer observations of the Large Magellanic Cloud (LMC) effectively
reveal massive YSOs. The inventory of massive YSOs, in conjunction with surveys
of interstellar medium, allows us to examine the conditions for star formation:
spontaneous or triggered. We examine the relationship between star formation
and gravitational instability on a global scale, and we present evidence of
triggered star formation on local scales in the LMC.Comment: 6 pages, 6 figures, IAU Symposium 237, Triggered Star Formation in a
Turbulent Medium, eds. Elmegreen and Palou
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