12 research outputs found
Convergence studies of mass transport in disks with gravitational instabilities. I. the constant cooling time case
We conduct a convergence study of a protostellar disk, subject to a constant global cooling time and susceptible to gravitational instabilities (GIs), at a time when heating and cooling are roughly balanced. Our goal is to determine the gravitational torques produced by GIs, the level to which transport can be represented by a simple α-disk formulation, and to examine fragmentation criteria. Four simulations are conducted, identical except for the number of azimuthal computational grid points used. A Fourier decomposition of non-axisymmetric density structures in cos (), sin () is performed to evaluate the amplitudes of these structures. The , gravitational torques, and the effective Shakura & Sunyaev α arising from gravitational stresses are determined for each resolution. We find nonzero for all -values and that summed over all is essentially independent of resolution. Because the number of measurable -values is limited to half the number of azimuthal grid points, higher-resolution simulations have a larger fraction of their total amplitude in higher-order structures. These structures act more locally than lower-order structures. Therefore, as the resolution increases the total gravitational stress decreases as well, leading higher-resolution simulations to experience weaker average gravitational torques than lower-resolution simulations. The effective also depends upon the magnitude of the stresses, thus also decreases with increasing resolution. Our converged is consistent with predictions from an analytic local theory for thin disks by Gammie, but only over many dynamic times when averaged over a substantial volume of the disk
The Formation of Fragments at Corotation in Isothermal Protoplanetary Disks
Numerical hydrodynamics simulations have established that disks which are
evolved under the condition of local isothermality will fragment into small
dense clumps due to gravitational instabilities when the Toomre stability
parameter is sufficiently low. Because fragmentation through disk
instability has been suggested as a gas giant planet formation mechanism, it is
important to understand the physics underlying this process as thoroughly as
possible. In this paper, we offer analytic arguments for why, at low ,
fragments are most likely to form first at the corotation radii of growing
spiral modes, and we support these arguments with results from 3D hydrodynamics
simulations.Comment: 21 pages, 1 figur
Magnetic fields in protoplanetary disks
Magnetic fields likely play a key role in the dynamics and evolution of
protoplanetary discs. They have the potential to efficiently transport angular
momentum by MHD turbulence or via the magnetocentrifugal acceleration of
outflows from the disk surface, and magnetically-driven mixing has implications
for disk chemistry and evolution of the grain population. However, the weak
ionisation of protoplanetary discs means that magnetic fields may not be able
to effectively couple to the matter. I present calculations of the ionisation
equilibrium and magnetic diffusivity as a function of height from the disk
midplane at radii of 1 and 5 AU. Dust grains tend to suppress magnetic coupling
by soaking up electrons and ions from the gas phase and reducing the
conductivity of the gas by many orders of magnitude. However, once grains have
grown to a few microns in size their effect starts to wane and magnetic fields
can begin to couple to the gas even at the disk midplane. Because ions are
generally decoupled from the magnetic field by neutral collisions while
electrons are not, the Hall effect tends to dominate the diffusion of the
magnetic field when it is able to partially couple to the gas.
For a standard population of 0.1 micron grains the active surface layers have
a combined column of about 2 g/cm^2 at 1 AU; by the time grains have aggregated
to 3 microns the active surface density is 80 g/cm^2. In the absence of grains,
x-rays maintain magnetic coupling to 10% of the disk material at 1 AU (150
g/cm^2). At 5 AU the entire disk thickness becomes active once grains have
aggregated to 1 micron in size.Comment: 11 pages, 11 figs, aastex.cls. Accepted for publication in
Astrophysics & Space Science. v3 corrects bibliograph
Formation of stars and planets: the role of magnetic fields
Star formation is thought to be triggered by gravitational collapse of the
dense cores of molecular clouds. Angular momentum conservation during the
collapse results in the progressive increase of the centrifugal force, which
eventually halts the inflow of material and leads to the development of a
central mass surrounded by a disc. In the presence of an angular momentum
transport mechanism, mass accretion onto the central object proceeds through
this disc, and it is believed that this is how stars typically gain most of
their mass. However, the mechanisms responsible for this transport of angular
momentum are not well understood. Although the gravitational field of a
companion star or even gravitational instabilities (particularly in massive
discs) may play a role, the most general mechanisms are turbulence viscosity
driven by the magnetorotational instability (MRI), and outflows accelerated
centrifugally from the surfaces of the disc. Both processes are powered by the
action of magnetic fields and are, in turn, likely to strongly affect the
structure, dynamics, evolutionary path and planet-forming capabilities of their
host discs. The weak ionisation of protostellar discs, however, may prevent the
magnetic field from effectively coupling to the gas and shear and driving these
processes. Here I examine the viability and properties of these
magnetically-driven processes in protostellar discs. The results indicate that,
despite the weak ionisation, the magnetic field is able to couple to the gas
and shear for fluid conditions thought to be satisfied over a wide range of
radii in these discs.Comment: Invited Review. 11 figures and 1 table. Accepted for publication in
Astrophysics & Space Scienc