190 research outputs found

### On the orbital evolution and growth of protoplanets embedded in a gaseous disc

We present a new computation of the linear tidal interaction of a
protoplanetary core with a thin gaseous disc in which it is fully embedded. For
the first time a discussion of the orbital evolution of cores with eccentricity
(e) significantly larger than the gas-disc scale height to radius ratio (H/r)
is given. We find that the direction of orbital migration reverses for
e>1.1H/r. This occurs as a result of the orbital crossing of resonances in the
disc that do not overlap the orbit when the eccentricity is very small. Simple
expressions giving approximate fits to the eccentricity damping rate and the
orbital migration rate are presented. We go on to calculate the rate of
increase of the mean eccentricity for a system of protoplanetary cores due to
dynamical relaxation. By equating the eccentricity damping time-scale with the
dynamical relaxation time-scale we deduce that an equilibrium between
eccentricity damping and excitation through scattering is attained on a 10^3 to
10^4 yr time-scale, at 1au. The equilibrium thickness of the protoplanet
distribution is such that it is generally well confined within the gas disc. By
use of a three dimensional N-body code we simulate the evolution of a system of
protoplanetary cores, incorporating our eccentricity damping and migration
rates. Assuming that collisions lead to agglomeration, we find that the
vertical confinement of the protoplanet distribution permits cores to build up
from 0.1 to 1 earth mass in only ~10^4 yr, within 1au. The time-scale required
to achieve this is comparable to the migration time-scale. We deduce that it is
not possible to build up a massive enough core to form a gas giant planet
before orbital migration ultimately results in the preferential delivery of all
such bodies to the neighbourhood of the central star. [Abridged]Comment: Latex in MNRAS style, 13 pages with 6 figures, also available from
http://www.maths.qmw.ac.uk/~jdl

### Rings in the Planetesimal Disk of Beta Pic

The nearby main sequence star Beta Pictoris is surrounded by an edge-on disk
of dust produced by the collisional erosion of larger planetesimals. Here we
report the discovery of substructure within the northeast extension of the disk
midplane that may represent an asymmetric ring system around Beta Pic. We
present a dynamical model showing that a close stellar flyby with a quiescient
disk of planetesimals can create such rings, along with previously unexplained
disk asymmetries. Thus we infer that Beta Pic's planetesimal disk was highly
disrupted by a stellar encounter in the last hundred thousand years.Comment: Accepted by ApJ Letters. LaTeX, 13 pages, 4 figures, full PostScript
file available from http://www.maths.qmw.ac.uk/~jdl

### Gas Giant Protoplanets Formed by Disk Instability in Binary Star Systems

We present a suite of three dimensional radiative gravitational hydrodynamics
models suggesting that binary stars may be quite capable of forming planetary
systems similar to our own. The new models with binary companions do not employ
any explicit artificial viscosity, and also include the third (vertical)
dimension in the hydrodynamic calculations, allowing for transient phases of
convective cooling. The calculations of the evolution of initially marginally
gravitationally stable disks show that the presence of a binary star companion
may actually help to trigger the formation of dense clumps that could become
giant planets. We also show that in models without binary companions, which
begin their evolution as gravitationally stable disks, the disks evolve to form
dense rings, which then break-up into self-gravitating clumps. These latter
models suggest that the evolution of any self-gravitating disk with sufficient
mass to form gas giant planets is likely to lead to a period of disk
instability, even in the absence of a trigger such as a binary star companion.Comment: 52 pages, 28 figure

### Close stellar encounters with planetesimal discs: The dynamics of asymmetry in the Beta Pictoris system

We numerically investigate the dynamics of how a close stellar fly-by
encounter of a symmetrical circumstellar planetesimal disc can give rise to the
many kinds of asymmetries and substructures attributed to the edge-on dusty
disc of Beta Pic. In addition we present new optical coronagraphic observations
of the outer parts of Beta Pic's disc, and report that the radial extent is
significantly greater than was found in previous measurements. The
northeasterly extension of the disc's midplane is now measured out to 1835au
from the star; the southwesterly component is measured out to 1450au. Hence we
use the length asymmetry induced in a distribution of simulation test particles
as the principal diagnostic feature when modelling the disc response, in order
to constrain fly-by parameters. In particular we favour a low inclination
prograde and near-parabolic orbit perturber of mass approximately 0.5 Solar
masses. These initial conditions suggest that the perturber could have been
physically associated with Beta Pic prior to the encounter. Thus we also
consider the possibility that the perturber could be bound to Beta Pic: a
consideration also of general interest where dust discs are known to exist in
binary star systems. In some of our models, we can relate groupings of
perturbed particles to the large-scale structure of the Beta Pic disc. The
groupings correspond to: high eccentricity and inclination particles that reach
apocentre and maximum height in the southwest, moderately eccentric and low
inclination particles that reach apocentre in the northeast, and relatively
unperturbed particles inside approximately 200au radius.Comment: Accepted by MNRAS. 15 pages, 19 figures (mainly low resolution). High
quality PostScript from http://www.maths.qmw.ac.uk/~jdl

### Collisional Cascades in Planetesimal Disks II. Embedded Planets

We use a multiannulus planetesimal accretion code to investigate the growth
of icy planets in the outer regions of a planetesimal disk. In a quiescent
minimum mass solar nebula, icy planets grow to sizes of 1000--3000 km on a
timescale t = 15-20 Myr (a/30 AU)^3 where a is the distance from the central
star. Planets form faster in more massive nebulae. Newly-formed planets stir up
leftover planetesimals along their orbits and produce a collisional cascade
where icy planetesimals are slowly ground to dust.
The dusty debris of planet formation has physical characteristics similar to
those observed in beta Pic, HR 4796A, and other debris disks. We derive dust
masses for small particles, 1 mm and smaller, and large particles, 1 mm and
larger, as a function of the initial conditions in the planetesimal disk. The
dust luminosities derived from these masses are similar to those observed in
Vega, HR 4796A, and other debris disks. The calculations produce bright rings
and dark gaps. Bright rings occur where 1000 km and larger planets have
recently formed. Dark gaps are regions where planets have cleared out dust or
shadows where planets have yet to form.Comment: to be published in the Astronomical Journal, January 2004; 7 pages of
text; 17 figures at
http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-figures.pdf; 2 animations at
http://cfa-www.harvard.edu/~kenyon/pf/emb-planet-movies.htm

### Angular Momentum Transfer in Star-Discs Encounters: The Case of Low-Mass Discs

A prerequisite for the formation of stars and planetary systems is that
angular momentum is transported in some way from the inner regions of the
accretion disc. Tidal effects may play an important part in this angular
momentum transport. Here the angular momentum transfer in an star-disc
encounter is investigated numerically for a variety of encounter parameters in
the case of low mass discs. Although good agreement is found with analytical
results for the entire disc, the loss {\it inside} the disc can be up to an
order of magnitude higher than previously assumed. The differences in angular
momentum transport by secondaries on a hyperbolic, parabolic and elliptical
path are shown, and it is found that a succession of distant encounters might
be equally, if not more, successful in removing angular momentum than single
close encounter.Comment: 11pages, 8 figures, 1 tabl

### Precessing warped discs in close binary systems

We describe some recent nonlinear three dimensional hydrodynamic simulations of accretion discs in binary systems where the orbit is circular and not necessarily coplanar with the disc midplane. The calculations are relevant to a number of observed astrophysical phenomena, including the precession of jets associated with young stars, the high spectral index of some T Tauri stars, and the light curves of X-ray binaries such as Hercules X-1 which suggest the presence of precessing accretion discs

### Hydrodynamic Simulations of Propagating Warps and Bending Waves In Accretion Discs

We present the results of a study of propagating warp or bending waves in
accretion discs. Three dimensional hydrodynamic simulations were performed
using SPH, and the results of these are compared with calculations based on the
linear theory of warped discs. We consider primarily the physical regime in
which the dimensionless viscosity parameter `alpha' < H/r, the disc aspect
ratio, so that bending waves are expected to propagate. We also present
calculations in which `alpha' > H/r, where the warps are expected to behave
diffusively. Small amplitude perturbations are studied in both Keplerian and
slightly non Keplerian discs, and we find that the SPH results can be
reasonably well fitted by those of the linear theory. The main results of these
calculations are: (1) the warp in Keplerian discs when `alpha' < H/r propagates
with little dispersion and damps at a rate expected from estimates of the code
viscosity, (2) warps evolve diffusively when `alpha' > H/r, (3) the non
Keplerian discs exhibit a substantially more dispersive behaviour of the warps.
Initially imposed higher amplitude nonlinear warping disturbances were studied
in Keplerian discs. The results indicate that nonlinear warps can lead to the
formation of shocks, and that the evolution of the warp becomes less wave-like
and more diffusive in character. This work is relevant to the study of the
warped accretion discs that may occur around Kerr black holes or in misaligned
binary systems. The results indicate that SPH can accurately model the
hydrodynamics of warped discs, even when using rather modest numbers of
particles.Comment: 14 pages, 9 figures, to appear in MNRA

### The tidally induced warping, precession and truncation of accretion discs in binary systems: three-dimensional simulations

We present the results of non linear, hydrodynamic simulations, in three
dimensions, of the tidal perturbation of accretion discs in binary systems
where the orbit is circular and not necessarily coplanar with the disc
mid-plane. The accretion discs are assumed to be geometrically thin, and of low
mass relative to the stellar mass so that they are governed by thermal pressure
and viscosity, but not self-gravity. The parameters that we consider in our
models are the ratio of the orbital distance to the disc radius, D/R, the
binary mass ratio, the initial inclination angle between the orbit and disc
planes and the Mach number in the outer parts of the unperturbed disc. For
binary mass ratios of around unity and D/R in the range 3 to 4, we find that
the global evolution of the discs is governed primarily by the value of the
Mach number. For relatively low Mach numbers (i.e. 10 to 20) we find that the
discs develop a mildly warped structure, are tidally truncated, and undergo a
near rigid body precession at a rate which is in close agreement with
analytical arguments. For higher Mach numbers (approx. 30), the evolution is
towards a considerably more warped structure, but the disc none the less
maintains itself as a long-lived, coherent entity. Additionally, it is found
that the inclination angle between the disc and orbital angular momentum
vectors evolves on a longer timescale which is probably the viscous evolution
timescale of the disc. The calculations are relevant to a number of observed
astrophysical phenomena, including the precession of jets associated with young
stars, the high spectral index of some T-Tauri stars, and the light curves of
X-ray binaries such as Hercules X-1 which suggest the presence of precessing
accretion discs.Comment: Accepted by MNRAS, received in original form 23 January 1996. LaTeX,
22 pages. 15 figures available from [email protected], or by anonymous
ftp (see http://www.maths.qmw.ac.uk/~jdl/preprint.html for instructions

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