401 research outputs found

### 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

### Precession of collimated outflows from young stellar objects

We consider several protostellar systems where either a precessing jet or at
least two misaligned jets have been observed. We assume that the precession of
jets is caused by tidal interactions in noncoplanar binary systems. For Cep E,
V1331 Cyg and RNO 15-FIR the inferred orbital separations and disk radii are in
the range 4-160 AU and 1-80 AU, respectively, consistent with those expected
for pre-main sequence stars. Furthermore, we assume or use the fact that the
source of misaligned outflows is a binary, and evaluate the lengthscale over
which the jets should precess as a result of tidal interactions. For T Tau, HH1
VLA 1/2 and HH 24 SVS63, it may be possible to detect a bending of the jets
rather than 'wiggling'. In HH 111 IRS and L1551 IRS5, 'wiggling' may be
detected on the current observed scale. Our results are consistent with the
existence of noncoplanar binary systems in which tidal interactions induce jets
to precess.Comment: 5 pages (including 1 figure), LaTeX, uses emulateapj.sty, to be
published in ApJ Letters, also available at
http://www.ucolick.org/~ct/home.html and
http://www.tls-tautenburg.de/research/research.htm

### Orbital circularisation of white dwarfs and the formation of gravitational radiation sources in star clusters containing an intermediate mass black hole

(abbreviated) We consider how tight binaries consisting of a super-massive
black hole of mass $M=10^{3}-10^{4}M_{\odot}$ and a white dwarf can be formed
in a globular cluster. We point out that a major fraction of white dwarfs
tidally captured by the black hole may be destroyed by tidal inflation during
ongoing circularisation, and the formation of tight binaries is inhibited.
However, some stars may survive being spun up to high rotation rates. Then the
energy loss through gravitational wave emission induced by tidally excited
pulsation modes and dissipation through non linear effects may compete with the
increase of pulsation energy due to dynamic tides. The semi-major axes of these
stars can be decreased below a 'critical' value where dynamic tides are not
effective because pulsation modes retain phase coherence between successive
pericentre passages. The rate of formation of such circularising stars is
estimated assuming that they can be modelled as $n=1.5$ polytropes and that
results of the tidal theory for slow rotators can be extrapolated to fast
rotators. We estimate the total capture rate as $\sim \dot N\sim 2.5\cdot
10^{-8}M_{4}^{1.3}r_{0.1}^{-2.1}yr^{-1}$, where $M_{4}=M/10^4M_{\odot}$ and
$r_{0.1}$ is the radius of influence of the black hole in units $0.1pc$. We
find that the formation rate of tight pairs is approximately 10 times smaller
than the total capture rate. It is used to estimate the probability of
detection of gravitational waves coming from such tight binaries by LISA. We
conclude that LISA may detect such binaries provided that the fraction of
globular clusters with black holes in the mass range of interest is substantial
and that the dispersion velocity of the cluster stars near the radius of
influence of the black hole exceeds $\sim 20km/s$.Comment: accepted for publication in Astronomy and Astrophysics, minor
corrections in proof

### 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

### Resonantly-forced Eccentric Ringlets: Relationships between Surface Density, Resonance location, Eccentricity and Eccentricity-gradient

We use a simple model of the dynamics of a narrow-eccentric ring, to put some
constraints on some of the observable properties of the real systems.In this
work we concentrate on the case of the `Titan ringlet of Saturn'.Our approach
is fluid-like, since our description is based on normal modes of oscillation
rather than in individual particle orbits. Thus, the rigid precession of the
ring is described as a global $m=1$ mode, which originates from a standing wave
superposed on an axisymmetric background. An integral balance condition for the
maintenance of the $m=1$ standing-wave can be set up, in which the differential
precession induced by the oblateness of the central planet must cancel the
contributions of self-gravity, the resonant satellite forcing and collisional
effects. We expect that in nearly-circular narrow rings dominated by
self-gravity, the eccentricity varies linearly across the ring. Thus, we take a
first order expansion and we derive two integral relationships from the
rigid-precession condition. These relate the surface density of the ring with
the eccentricity at the center, the eccentricity gradient and the location of
the secular resonance. These relationships are applied to the Titan ringlet of
Saturn, which has a secular resonance with the satellite Titan in which the
ring precession period is close to Titan's orbital period. In this case, we
estimate the mean surface density and the location of the secular resonance.Comment: Accepted for publication in Celestial Mechanics and Dynamical
Astronom

### 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

### 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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