222 research outputs found
On the tilting of protostellar disks by resonant tidal effects
We consider the dynamics of a protostellar disk surrounding a star in a
circular-orbit binary system. Our aim is to determine whether, if the disk is
initially tilted with respect to the plane of the binary orbit, the inclination
of the system will increase or decrease with time. The problem is formulated in
the binary frame in which the tidal potential of the companion star is static.
We consider a steady, flat disk that is aligned with the binary plane and
investigate its linear stability with respect to tilting or warping
perturbations. The dynamics is controlled by the competing effects of the m=0
and m=2 azimuthal Fourier components of the tidal potential. In the presence of
dissipation, the m=0 component causes alignment of the system, while the m=2
component has the opposite tendency. We find that disks that are sufficiently
large, in particular those that extend to their tidal truncation radii, are
generally stable and will therefore tend to alignment with the binary plane on
a time-scale comparable to that found in previous studies. However, the effect
of the m=2 component is enhanced in the vicinity of resonances where the outer
radius of the disk is such that the natural frequency of a global bending mode
of the disk is equal to twice the binary orbital frequency. Under such
circumstances, the disk can be unstable to tilting and acquire a warped shape,
even in the absence of dissipation. The outer radius corresponding to the
primary resonance is always smaller than the tidal truncation radius. For disks
smaller than the primary resonance, the m=2 component may be able to cause a
very slow growth of inclination through the effect of a near resonance that
occurs close to the disk center. We discuss these results in the light of
recent observations of protostellar disks in binary systems.Comment: 21 pages, 7 figures, to be published in the Astrophysical Journa
Ring Formation in Magnetically Subcritical Clouds and Multiple Star Formation
We study numerically the ambipolar diffusion-driven evolution of
non-rotating, magnetically subcritical, disk-like molecular clouds, assuming
axisymmetry. Previous similar studies have concentrated on the formation of
single magnetically supercritical cores at the cloud center, which collapse to
form isolated stars. We show that, for a cloud with many Jeans masses and a
relatively flat mass distribution near the center, a magnetically supercritical
ring is produced instead. The supercritical ring contains a mass well above the
Jeans limit. It is expected to break up, through both gravitational and
possibly magnetic interchange instabilities, into a number of supercritical
dense cores, whose dynamic collapse may give rise to a burst of star formation.
Non-axisymmetric calculations are needed to follow in detail the expected ring
fragmentation into multiple cores and the subsequent core evolution.
Implications of our results on multiple star formation in general and the
northwestern cluster of protostars in the Serpens molecular cloud core in
particular are discussed.Comment: 25 pages, 4 figures, to appear in Ap
On disc driven inward migration of resonantly coupled planets with application to the system around GJ876
We consider two protoplanets gravitationally interacting with each other and
a protoplanetary disc. The two planets orbit interior to a tidally maintained
disc cavity while the disc interaction indices inward migration. When the
migration is slow enough, the more rapidly migrating outer protoplanet
approaches and becomes locked in a 2:1 commensurability with the inner one.
This is maintained in subsequent evolution. We study this evolution using a
simple anaytic model, full hydrodynamic 2D simulations of the disc planet
system and longer time N body integrations incorporating simple prescriptions
for the effect of the disc on the planet orbits. The eccentricity of the
protoplanets are found to be determined by the migration rate induced in the
outer planet orbit by the external disc. We apply our results to the recently
discovered resonant planets around GJ876. Simulation shows that a disc with
parameters expected for protoplanetary discs causes trapping in the 2:1
commensurability when the planets orbit in an inner cavity and that
eccentricities in the observed range may be obtained.Comment: 8 pages, 5 figures, submitted to A&A on 30/03/200
3D-MHD simulations of an accretion disk with star-disk boundary layer
We present global 3D MHD simulations of geometrically thin but unstratified
accretion disks in which a near Keplerian disk rotates between two bounding
regions with initial rotation profiles that are stable to the MRI. The inner
region models the boundary layer between the disk and an assumed more slowly
rotating central, non magnetic star. We investigate the dynamical evolution of
this system in response to initial vertical and toroidal fields imposed in a
variety of domains contained within the near Keplerian disk. Cases with both
non zero and zero net magnetic flux are considered and sustained dynamo
activity found in runs for up to fifty orbital periods at the outer boundary of
the near Keplerian disk. Simulations starting from fields with small radial
scale and with zero net flux lead to the lowest levels of turbulence and
smoothest variation of disk mean state variables. For our computational set up,
average values of the Shakura & Sunyaev (1973) parameter in the
Keplerian disk are typically Magnetic field eventually always
diffuses into the boundary layer resulting in the build up of toroidal field
inward angular momentum transport and the accretion of disk material. The mean
radial velocity, while exhibiting large temporal fluctuations is always
subsonic. Simulations starting with net toroidal flux may yield an average
While being characterized by one order of magnitude larger
average , simulations starting from vertical fields with large radial
scale and net flux may lead to the formation of persistent non-homogeneous,
non-axisymmetric magnetically dominated regions of very low density.Comment: Accepted for publication in Ap
Forced oscillations in a hydrodynamical accretion disk and QPOs
This is the second of a series of papers aimed to look for an explanation on
the generation of high frequency quasi-periodic oscillations (QPOs) in
accretion disks around neutron star, black hole, and white dwarf binaries. The
model is inspired by the general idea of a resonance mechanism in the accretion
disk oscillations as was already pointed out by Abramowicz & Klu{\'z}niak
(\cite{Abramowicz2001}). In a first paper (P\'etri \cite{Petri2005a}, paper I),
we showed that a rotating misaligned magnetic field of a neutron star gives
rise to some resonances close to the inner edge of the accretion disk. In this
second paper, we suggest that this process does also exist for an asymmetry in
the gravitational potential of the compact object. We prove that the same
physics applies, at least in the linear stage of the response to the
disturbance in the system. This kind of asymmetry is well suited for neutron
stars or white dwarfs possessing an inhomogeneous interior allowing for a
deviation from a perfectly spherically symmetric gravitational field. We show
by a linear analysis that the disk initially in a cylindrically symmetric
stationary state is subject to three kinds of resonances: a corotation
resonance, a Lindblad resonance due to a driven force and a parametric sonance.
The highest kHz QPOs are then interpreted as the orbital frequency of the disk
at locations where the response to the resonances are maximal. It is also found
that strong gravity is not required to excite the resonances.Comment: Accepte
The interaction of a giant planet with a disc with MHD turbulence I: The initial turbulent disc models
This is the first of a series of papers aimed at developing and interpreting
simulations of protoplanets interacting with turbulent accretion discs. Here we
study the disc models prior to the introduction of a protoplanet.We study
models in which a Keplerian domain is unstable to the magnetorotational
instability (MRI). Various models with B-fields having zero net flux are
considered.We relate the properties of the models to classical viscous disc
theory.All models attain a turbulent state with volume averaged stress
parameter alpha ~ 0.005. At any particular time the vertically and azimuthally
averaged value exhibited large fluctuations in radius. Time averaging over
periods exceeding 3 orbital periods at the outer boundary of the disc resulted
in a smoother quantity with radial variations within a factor of two or so. The
vertically and azimuthally averaged radial velocity showed much larger spatial
and temporal fluctuations, requiring additional time averaging for 7-8 orbital
periods at the outer boundary to limit them. Comparison with the value derived
from the averaged stress using viscous disc theory yielded schematic agreement
for feasible averaging times but with some indication that the effects of
residual fluctuations remained. The behaviour described above must be borne in
mind when considering laminar disc simulations with anomalous Navier--Stokes
viscosity. This is because the operation of a viscosity as in classical viscous
disc theory with anomalous viscosity coefficient cannot apply to a turbulent
disc undergoing rapid changes due to external perturbation. The classical
theory can only be used to describe the time averaged behaviour of the parts of
the disc that are in a statistically steady condition for long enough for
appropriate averaging to be carried out.Comment: 10 pages, 23 figures, accepted for publication in MNRAS. A gzipped
postscript version including high resolution figures is available at
http://www.maths.qmul.ac.uk/~rp
Observational Implications of Precessing Protostellar Discs and Jets
We consider the dynamics of a protostellar disc in a binary system where the
disc is misaligned with the orbital plane of the binary, with the aim of
determining the observational consequences for such systems. The disc wobbles
with a period approximately equal to half the binary's orbital period and
precesses on a longer timescale. We determine the characteristic timescale for
realignment of the disc with the orbital plane due to dissipation. If the
dissipation is determined by a simple isotropic viscosity then we find, in line
with previous studies, that the alignment timescale is of order the viscous
evolution timescale. However, for typical protostellar disc parameters, if the
disc tilt exceeds the opening angle of the disc, then tidally induced shearing
within the disc is transonic. In general, hydrodynamic instabilities associated
with the internally driven shear result in extra dissipation which is expected
to drastically reduce the alignment timescale. For large disc tilts the
alignment timescale is then comparable to the precession timescale, while for
smaller tilt angles , the alignment timescale varies as . We discuss the consequences of the wobbling, precession and
rapid realignment for observations of protostellar jets and the implications
for binary star formation mechanisms.Comment: MNRAS, in press. 10 pages. Also available at
http://www.ast.cam.ac.uk/~mbat
Disk Planet Interactions and Early Evolution in Young Planetary Systems
We study and review disk protoplanet interactions using local shearing box
simulations. These suffer the disadvantage of having potential artefacts
arising from periodic boundary conditions but the advantage, when compared to
global simulations, of being able to capture much of the dynamics close to the
protoplanet at high resolution for low computational cost. Cases with and
without self sustained MHD turbulence are considered. The conditions for gap
formation and the transition from type I migration are investigated and found
to depend on whether the single parameter M_p R^3/(M_* H^3), with M_p, M_*, R
and H being the protoplanet mass, the central mass, the orbital radius and the
disk semi-thickness respectively exceeds a number of order unity. We also
investigate the coorbital torques experienced by a moving protoplanet in an
inviscid disk. This is done by demonstrating the equivalence of the problem for
a moving protoplanet to one where the protoplanet is in a fixed orbit which the
disk material flows through radially as a result of the action of an
appropriate external torque. For sustainable coorbital torques to be realized a
quasi steady state must be realized in which the planet migrates through the
disk without accreting significant mass. In that case although there is
sensitivity to computational parameters, in agreement with earlier work by
Masset & Papaloizou (2003) based on global simulations, the coorbital torques
are proportional to the migration speed and result in a positive feedback on
the migration, enhancing it and potentially leading to a runaway. This could
lead to a fast migration for protoplanets in the Saturn mass range in massive
disks and may be relevant to the mass period correlation for extrasolar planets
which gives a preponderance of sub Jovian masses at short orbital period.Comment: To appear in Celestial Mechanics and Dynamical Astronomy (with higher
resolution figures
Rayleigh-Taylor stability of a strong vertical magnetic field at the Galactic center confined by a disk threaded with horizontal magnetic field
Observations of narrow radio-emitting filaments near the Galactic center have
been interpreted in previous studies as evidence of a pervasive vertical (i.e.
perpendicular to the Galactic plane) milliGauss magnetic field in the central
150 pc of the Galaxy. A simple cylindrically symmetric model for the
equilibrium in this central region is proposed in which horizontal (i.e.
parallel to the Galactic plane) magnetic fields embedded in an annular band of
partially ionized molecular material of radius 150 pc are wrapped around
vertical magnetic fields threading low-density hot plasma. The central vertical
magnetic field, which has a pressure that significantly exceeds the thermal
pressure of the medium, is confined by the weight of the molecular material.
The stability of this equilibrium is studied indirectly by analyzing a
uniformly rotating cylinder of infinite extent along the z axis in cylindrical
coordinates (r,theta,z), with low-density plasma and an axial magnetic field at
r 150 pc, and a
gravitational acceleration g* proportional to r directed in the negative-r-hat
direction. The density profile and gravity tend to destabilize the plasma, but
the plasma tends to be stabilized by rotation and magnetic tension--since the
interface between the high and low-density plasmas can not be perturbed without
bending either the horizontal or vertical field. It is shown analytically that
when beta= 8(pi)p/B^2 is small and the dense plasma is supported against
gravity primarily by rotation, the necessary and sufficient condition for
stability to k_z=0 modes is |g| < (2|Omega| a), where g = g* - Omega^2 r is the
effective gravity, Omega is the uniform angular velocity, and "a" is the sound
speed in the dense plasma.Comment: 18 pages, 8 figures. Completely changed from first version:
incorporates uniform rotation as well as orthogonal magnetic fields in the
equilibrium dense and low-density plasm
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