554 research outputs found

### How to adapt broad-band gravitational-wave searches for r-modes

Up to now there has been no search for gravitational waves from the r-modes
of neutron stars in spite of the theoretical interest in the subject. Several
oddities of r-modes must be addressed to obtain an observational result: The
gravitational radiation field is dominated by the mass current
(gravitomagnetic) quadrupole rather than the usual mass quadrupole, and the
consequent difference in polarization affects detection statistics and
parameter estimation. To astrophysically interpret a detection or upper limit
it is necessary to convert the wave amplitude to an r-mode amplitude. Also, it
is helpful to know indirect limits on gravitational-wave emission to gauge the
interest of various searches. Here I address these issues, thereby providing
the ingredients to adapt broad-band searches for continuous gravitational waves
to obtain r-mode results. I also show that searches of existing data can
already have interesting sensitivities to r-modes.Comment: 8 pages, no figure

### Conditions for the occurrence of mean-motion resonances in a low mass planetary system

The dynamical interactions that occur in newly formed planetary systems may
reflect the conditions occurring in the protoplanetary disk out of which they
formed. With this in mind, we explore the attainment and maintenance of orbital
resonances by migrating planets in the terrestrial mass range. Migration time
scales varying between millions of years and thousands of years are considered.
In the former case, for which the migration time is comparable to the lifetime
of the protoplanetary gas disk, a 2:1 resonance may be formed. In the latter,
relatively rapid migration regime commensurabilities of high degree such as 8:7
or 11:10 may be formed. However, in any one large-scale migration several
different commensurabilities may be formed sequentially, each being associated
with significant orbital evolution. We also use a simple analytic theory to
develop conditions for first order commensurabilities to be formed. These
depend on the degree of the commensurability, the imposed migration and
circularization rates, and the planet mass ratios. These conditions are found
to be consistent with the results of our simulations.Comment: 11 pages with 4 figures, pdflatex, to appear in the proceedings of
the conference "Extra-solar Planets in Multi-body Systems: Theory and
Observations"; eds. K. Gozdziewski, A. Niedzielski and J. Schneider, EAS
Publication Serie

### Dust settling in local simulations of turbulent protoplanetary disks

In this paper, we study the effect of MHD turbulence on the dynamics of dust
particles in protoplanetary disks. We vary the size of the particles and relate
the dust evolution to the turbulent velocity fluctuations. We performed
numerical simulations using two Eulerian MHD codes, both based on finite
difference techniques: ZEUS--3D and NIRVANA. These were local shearing box
simulations incorporating vertical stratification. Both ideal and non ideal MHD
simulations with midplane dead zones were carried out. The codes were extended
to incorporate different models for the dust as an additional fluid component.
Good agreement between results obtained using the different approaches was
obtained. The simulations show that a thin layer of very small dust particles
is diffusively spread over the full vertical extent of the disk. We show that a
simple description obtained using the diffusion equation with a diffusion
coefficient simply expressed in terms of the velocity correlations accurately
matches the results. Dust settling starts to become apparent for particle sizes
of the order of 1 to 10 centimeters for which the gas begins to decouple in a
standard solar nebula model at 5.2 AU. However, for particles which are 10
centimeters in size, complete settling toward a very thin midplane layer is
prevented by turbulent motions within the disk, even in the presence of a
midplane dead zone of significant size. These results indicate that, when
present, MHD turbulence affects dust dynamics in protoplanetary disks. We find
that the evolution and settling of the dust can be accurately modelled using an
advection diffusion equation that incorporates vertical settling. The value of
the diffusion coefficient can be calculated from the turbulent velocity field
when that is known for a time of several local orbits.Comment: 15 pages, 16 figures, accepted in Astronomy & Astrophysic

### Corotation Resonance and Diskoseismology Modes of Black Hole Accretion Disks

We demonstrate that the corotation resonance affects only some
non-axisymmetric g-mode oscillations of thin accretion disks, since it is
located within their capture zones. Using a more general (weaker radial WKB
approximation) formulation of the governing equations, such g-modes, treated as
perfect fluid perturbations, are shown to formally diverge at the position of
the corotation resonance. A small amount of viscosity adds a small imaginary
part to the eigenfrequency which has been shown to induce a secular instability
(mode growth) if it acts hydrodynamically. The g-mode corotation resonance
divergence disappears, but the mode magnitude can remain largest at the place
of the corotation resonance. For the known g-modes with moderate values of the
radial mode number and axial mode number (and any vertical mode number), the
corotation resonance lies well outside their trapping region (and inside the
innermost stable circular orbit), so the observationally relevant modes are
unaffected by the resonance. The axisymmetric g-mode has been seen by Reynolds
& Miller in a recent inviscid hydrodynamic accretion disk global numerical
simulation. We also point out that the g-mode eigenfrequencies are
approximately proportional to m for axial mode numbers |m|>0.Comment: 16 pages, no figures. Submitted to The Astrophysical Journa

### Global m=1 modes and migration of protoplanetary cores in eccentric protoplanetary discs

We calculate global $m=1$ modes with low pattern speed corresponding to
introducing a finite eccentricity into a protoplanetary disc. We consider disc
models which are either isolated or contain one or two protoplanets orbiting in
an inner cavity. Global modes that are strongly coupled to inner protoplanets
are found to have disc orbits which tend to have apsidal lines antialigned with
respect to those of the inner protoplanets. Other modes corresponding to free
disc modes may be global over a large range of length scales and accordingly be
long lived. We consider the motion of a protoplanet in the earth mass range
embedded in an eccentric disc and determine the equilibrium orbits which
maintain fixed apsidal alignment with respect to the disc gas orbits.
Equilibrium eccentricities are found to be comparable or possibly exceed the
disc eccentricity. We then approximately calculate the tidal interaction with
the disc in order to estimate the orbital migration rate. Results are found to
deviate from the case of axisymmetric disc with near circular protoplanet orbit
once eccentricities of protoplanet and disc orbits become comparable to the
disc aspect ratio in magnitude. Aligned protoplanet orbits with very similar
eccentricity to that of the gas disc are found to undergo litle eccentricity
change while undergoing inward migration in general. However, for significantly
larger orbital eccentricities, migration may be significantly reduced or even
reverse from inwards to outwards. Thus the existence of global non circular
motions in discs with radial excursions comparable to the semi-thickness may
have important consequences for the migration and survival of protoplanetary
cores in the earth mass range.Comment: Accepted for publication by A &

### 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

### Evolutionary outcomes for pairs of planets undergoing orbital migration and circularization: second order resonances and observed period ratios in Kepler's planetary systems

In order to study the origin of the architectures of low mass planetary
systems, we perform numerical surveys of the evolution of pairs of coplanar
planets in the mass range (1-4)\ \rmn{M}_{\oplus}. These evolve for up to
2\times10^7 \rmn{yr} under a range of orbital migration torques and
circularization rates assumed to arise through interaction with a
protoplanetary disc. Near the inner disc boundary, significant variations of
viscosity, interaction with density waves or with the stellar magnetic field
could occur and halt migration, but allow ircularization to continue. This was
modelled by modifying the migration and circularization rates. Runs terminated
without an extended period of circularization in the absence of migration
torques gave rise to either a collision, or a system close to a resonance.
These were mostly first order with a few $\%$ terminating in second order
resonances. Both planetary eccentricities were small $< 0.1$ and all resonant
angles liberated. This type of survey produced only a limited range of period
ratios and cannot reproduce Kepler observations. When circularization alone
operates in the final stages, divergent migration occurs causing period ratios
to increase. Depending on its strength the whole period ratio range between $1$
and $2$ can be obtained. A few systems close to second order commensurabilities
also occur. In contrast to when arising through convergent migration, resonant
trapping does not occur and resonant angles circulate. Thus the behaviour of
the resonant angles may indicate the form of migration that led to near
resonance.Comment: 15 pages, 12 figures, 2014, MNRAS, 449, 304

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