86 research outputs found
Three-dimensional waves generated at Lindblad resonances in thermally stratified disks
We analyze the linear, 3D response to tidal forcing of a disk that is thin
and thermally stratified in the direction normal to the disk plane. We model
the vertical disk structure locally as a polytrope which represents a disk of
high optical depth. We solve the 3D gas-dynamic equations semi-analytically in
the neighborhood of a Lindblad resonance. These solutions match asymptotically
on to those valid away from resonances and provide solutions valid at all
radii. We obtain the following results. 1) A variety of waves are launched at
resonance. However, the f mode carries more than 95% of the torque exerted at
the resonance. 2) These 3D waves collectively transport exactly the amount of
angular momentum predicted by the 2D torque formula. 3) Near resonance, the f
mode occupies the full vertical extent of the disk. Away from resonance, the f
mode becomes confined near the surface of the disk, and, in the absence of
other dissipation mechanisms, damps via shocks. The radial length scale for
this process is roughly r_L/m (for resonant radius r_L and azimuthal wavenumber
m), independent of the disk thickness H. This wave channeling process is due to
the variations of physical quantities in r and is not due to wave refraction.
4) However, the inwardly propagating f mode launched from an m=2 inner Lindblad
resonance experiences relatively minor channeling.
We conclude that for binary stars, tidally generated waves in highly
optically thick circumbinary disks are subject to strong nonlinear damping by
the channeling mechanism, while those in circumstellar accretion disks are
subject to weaker nonlinear effects. We also apply our results to waves excited
by young planets for which m is approximately r/H and conclude that the waves
are damped on the scale of a few H.Comment: 15 pages, 3 figures, 2 colour plates, to be published in the
Astrophysical Journa
Tidal dissipation in rotating fluid bodies: a simplified model
We study the tidal forcing, propagation and dissipation of linear inertial
waves in a rotating fluid body. The intentionally simplified model involves a
perfectly rigid core surrounded by a deep ocean consisting of a homogeneous
incompressible fluid. Centrifugal effects are neglected, but the Coriolis force
is considered in full, and dissipation occurs through viscous or frictional
forces. The dissipation rate exhibits a complicated dependence on the tidal
frequency and generally increases with the size of the core. In certain
intervals of frequency, efficient dissipation is found to occur even for very
small values of the coefficient of viscosity or friction. We discuss the
results with reference to wave attractors, critical latitudes and other
features of the propagation of inertial waves within the fluid, and comment on
their relevance for tidal dissipation in planets and stars.Comment: 14 pages, 13 figures, to be published in MNRA
On internal wave breaking and tidal dissipation near the centre of a solar-type star
We study the fate of internal gravity waves, which are excited by tidal
forcing by a short-period planet at the interface of convection and radiation
zones, approaching the centre of a solar-type star. We study at what amplitude
these wave are subject to instabilities. These instabilities lead to wave
breaking whenever the amplitude exceeds a critical value. Below this value, the
wave reflects perfectly from the centre of the star. Wave breaking results in
spinning up the central regions of the star, and the formation of a critical
layer, which acts as an absorbing barrier for ingoing waves. As these waves are
absorbed, the star is spun up from the inside out. This results in an important
amplitude dependence of the tidal quality factor Q'. If the tidal forcing
amplitude exceeds the value required for wave breaking, efficient dissipation
results over a continuous range of tidal frequencies, leading to Q' \approx
10^5 (P/1day)^(8/3), for the current Sun. This varies by less than a factor of
5 throughout the range of G and K type main sequence stars, for a given orbit.
We predict fewer giant planets with orbital periods of less than about 2 days
around such stars, if they cause breaking at the centre, due to the efficiency
of this process. This mechanism would, however, be ineffective in stars with a
convective core, such as WASP-18, WASP-12 and OGLE-TR-56, perhaps partly
explaining the survival of their close planetary companions.Comment: 22 pages, 10 figures, accepted in MNRAS, abstract shortened (!
Holographic entropy and brane FRW-dynamics from AdS black hole in d5 higher derivative gravity
Higher derivative bulk gravity (without Riemann tensor square term) admits
AdS-Schwarzschild black hole as exact solution. It is shown that induced brane
geometry on such background is open, flat or closed FRW radiation dominated
Universe. Higher derivative terms contributions appear in the Hawking
temperature, entropy and Hubble parameter via the redefinition of 5-dimensional
gravitational constant and AdS scale parameter. These higher derivative terms
do not destroy the AdS-dual description of radiation represented by
strongly-coupled CFT. Cardy-Verlinde formula which expresses cosmological
entropy as square root from other parameters and entropies is derived in
gravity. The corresponding cosmological entropy bounds are briefly discussed.Comment: LaTeX file, 19 page
Tidal dissipation in rotating giant planets
[Abridged] Tides may play an important role in determining the observed
distributions of mass, orbital period, and eccentricity of the extrasolar
planets. In addition, tidal interactions between giant planets in the solar
system and their moons are thought to be responsible for the orbital migration
of the satellites, leading to their capture into resonant configurations. We
treat the underlying fluid dynamical problem with the aim of determining the
efficiency of tidal dissipation in gaseous giant planets. In cases of interest,
the tidal forcing frequencies are comparable to the spin frequency of the
planet but small compared to its dynamical frequency. We therefore study the
linearized response of a slowly and possibly differentially rotating planet to
low-frequency tidal forcing. Convective regions of the planet support inertial
waves, while any radiative regions support generalized Hough waves. We present
illustrative numerical calculations of the tidal dissipation rate and argue
that inertial waves provide a natural avenue for efficient tidal dissipation in
most cases of interest. The resulting value of Q depends in a highly erratic
way on the forcing frequency, but we provide evidence that the relevant
frequency-averaged dissipation rate may be asymptotically independent of the
viscosity in the limit of small Ekman number. In short-period extrasolar
planets, if the stellar irradiation of the planet leads to the formation of a
radiative outer layer that supports generalized Hough modes, the tidal
dissipation rate can be enhanced through the excitation and damping of these
waves. These dissipative mechanisms offer a promising explanation of the
historical evolution and current state of the Galilean satellites as well as
the observed circularization of the orbits of short-period extrasolar planets.Comment: 74 pages, 12 figures, submitted to The Astrophysical Journa
Towards the entropy of gravity time-dependent models via the Cardy-Verlinde formula
For models with several time-dependent components generalized entropies can
be defined. This is shown for the Bianchi type IX model. We first derive the
Cardy-Verlinde formula under the assumption that the first law of
thermodynamics is valid. This leads to an explicit expression of the total
entropy associated with this type of universes. Assuming the validity of the
Cardy entropy formula, we obtain expressions for the corresponding Bekenstein,
Bekenstein-Hawking and Hubble entropies. We discuss the validity of the
Cardy-Verlinde formula and possible extensions of the outlined procedure to
other time-dependent models.Comment: 13 page
Tidally distorted accretion discs in binary stars
The non-axisymmetric features observed in the discs of dwarf novae in
outburst are usually considered to be spiral shocks, which are the non-linear
relatives of tidally excited waves. This interpretation suffers from a number
of problems. For example, the natural site of wave excitation lies outside the
Roche lobe, the disc must be especially hot, and most treatments of wave
propagation do not take into account the vertical structure of the disc.
In this paper I construct a detailed semi-analytical model of the non-linear
tidal distortion of a thin, three-dimensional accretion disc by a binary
companion on a circular orbit. The analysis presented here allows for vertical
motion and radiative energy transport, and introduces a simple model for the
turbulent magnetic stress. The m=2 inner vertical resonance has an important
influence on the amplitude and phase of the tidal distortion. I show that the
observed patterns find a natural explanation if the emission is associated with
the tidally thickened sectors of the outer disc, which may be irradiated from
the centre. According to this hypothesis, it may be possible to constrain the
physical parameters of the disc through future observations.Comment: 13 pages, 3 figures, to be published in MNRA
High resolution simulations of unstable modes in a collisionless disc
We present N-body simulations of unstable spiral modes in a dynamically cool
collisionless disc. We show that spiral modes grow in a thin collisionless disk
in accordance with the analytical perturbation theory. We use the particle-mesh
code SUPERBOX with nested grids to follow the evolution of unstable spirals
that emerge from an unstable equilibrium state. We use a large number of
particles (up to 40 million particles) and high-resolution spatial grids in our
simulations (128^3 cells). These allow us to trace the dynamics of the unstable
spiral modes until their wave amplitudes are saturated due to nonlinear
effects. In general, the results of our simulations are in agreement with the
analytical predictions. The growth rate and the pattern speed of the most
unstable bar-mode measured in N-body simulations agree with the linear
analysis. However the parameters of secondary unstable modes are in lesser
agreement because of the still limited resolution of our simulations.Comment: 11 pages, 8 figures in 22 files, A&A in print: Oct. 1st 200
On the tidal evolution of Hot Jupiters on inclined orbits
Tidal friction is thought to be important in determining the long-term
spin-orbit evolution of short-period extrasolar planetary systems. Using a
simple model of the orbit-averaged effects of tidal friction, we study the
evolution of close-in planets on inclined orbits, due to tides. We analyse the
effects of the inclusion of stellar magnetic braking by performing a
phase-plane analysis of a simplified system of equations, including the braking
torque. The inclusion of magnetic braking is found to be important, and its
neglect can result in a very different system history. We then present the
results of numerical integrations of the tidal evolution equations, where we
find that it is essential to consider coupled evolution of the orbital and
rotational elements, including dissipation in both the star and planet, to
accurately model the evolution. The main result of our integrations is that for
typical Hot Jupiters, tidal friction aligns the stellar spin with the orbit on
a similar time as it causes the orbit to decay. This means that if a planet is
observed to be aligned, then it probably formed coplanar. This reinforces the
importance of Rossiter-McLaughlin effect observations in determining the degree
of spin-orbit alignment in transiting systems. We apply these results to the
XO-3 system, and constrain the tidal quality factors Q' in both the star and
planet in this system. Using a model in which inertial waves are excited by
tidal forcing in the outer convective envelope and dissipated by turbulent
viscosity, we calculate Q' for a range of F-star models, and find it to vary
considerably within this class of stars. This means that assuming a single Q'
applies to all stars is probably incorrect. We propose an explanation for the
survival of WASP-12 b & OGLE-TR-56 b, in terms of weak dissipation in the star.Comment: 19 pages, 8 figures, accepted in MNRA
On the origin of episodic accretion in Dwarf Novae
We show that dwarf nova disks in quiescence have rather low magnetic Reynolds
number, of order 10^3. Numerical simulations of magnetized accretion disks
suggest that under these conditions magnetohydrodynamic turbulence and the
associated angular momentum transport is sharply reduced. This could be the
physical origin of episodic accretion in dwarf nova disks. If so, the standard
disk instability model needs to be revised.Comment: 4 pages, 2 postscript figures, Latex, uses emulateapj.sty. To be
published in Ap. J. Letter
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