44 research outputs found
The tidal excitation of r modes in a solar type star orbited by a giant planet companion and the effect on orbital evolution II: The effect of tides in the misaligned case
We extend the study of Papaloizou Savonije of the tidal interactions of close orbiting giant planets with a central solar type star to the situation where the spin axis of the central star and the orbital angular momentum are misaligned. We determine the tidal response taking into account the possibility of the excitation of r modes and the effect of tidal forcing due to potential perturbations which have zero frequency in a non rotating frame. Although there is near resonance with r modes with degree l′ = 1 and orders m = ±1, half widths turn out to be sufficiently narrow so that in practice dissipation rates are found to be similar to those produced by non resonant potential perturbations. We use our results to determine the evolution of the misalignment for the full range of initial inclination angles taking account of the spin down of the central star due to magnetic braking. Overall we find the rate of tidal evolution to be unimportant for a one Jupiter mass planet with orbital period ∼3.7d over a main sequence lifetime. However, it becomes significant for higher mass planets and shorter orbital periods, approximately scaling as the square of the planet mass and the inverse fourth power of the orbital period
Close encounters of a rotating star with planets in parabolic orbits of varying inclination and the formation of Hot Jupiters
(abbreviated) We extend the theory of close encounters of a planet on a
parabolic orbit with a star to include the effects of tides induced on the
central rotating star. Orbits with arbitrary inclination to the stellar
rotation axis are considered. We obtain results both from an analytic treatment
and numerical one that are in satisfactory agreement. These results are applied
to the initial phase of the tidal circularisation problem. We find that both
tides induced in the star and planet can lead to a significant decrease of the
orbital semi-major axis for orbits having periastron distances smaller than 5-6
stellar radii (corresponding to periods days after the
circularisation has been completed) with tides in the star being much stronger
for retrograde orbits compared to prograde orbits. We use the simple Skumanich
law for the stellar rotation with its rotational period equal to one month at
the age of 5Gyr. The strength of tidal interactions is characterised by
circularisation time scale, defined as a time scale of evolution of
the planet's semi-major axis due to tides considered as a function of orbital
period after the process of tidal circularisation has been completed.
We find that the ratio of the initial circularisation time scales corresponding
to prograde and retrograde orbits is of order 1.5-2 for a planet of one Jupiter
mass and four days. It grows with the mass of the planet, being
of order five for a five Jupiter mass planet with the same . Thus, the
effect of stellar rotation may provide a bias in the formation of planetary
systems having planets on close orbits around their host stars, as a
consequence of planet-planet scattering, favouring systems with retrograde
orbits. The results may also be applied to the problem of tidal capture of
stars in young stellar clusters.Comment: to be published in Celestial Mechanics and Dynamical Astronom
Apse-alignment in narrow-eccentric ringlets and its implications for the ϵ-ring of Uranus and the ring system of (10199) Chariklo
The discovery of ring systems around objects of the outer Solar System provides a strong motivation to apply theoretical models in order to better estimate their physical and orbital parameters, which can constrain scenarios for their origin. We review the criterion for maintaining apse-alignment across a ring and the balance between the energy input rate provided by a close by satellite and the internal dissipation rate occurring through ring particle collisions that is required to maintain ring eccentricity, as derived from the equations of motion governing the Lagrangian-displacements of the ring-particle orbits. We use the case of the ϵ -ring of Uranus, to calibrate our theoretical discussion and illustrate the basic dynamics governing these types of ring. In the case of the ring system of (10199) Chariklo, where the evidence that the rings are eccentric is not conclusive, we apply the theory of apse-alignment to derive information about the most plausible combination of values of the surface density and eccentricity-gradient, as well as the masses and locations of their postulated but -presently undetected- shepherd-satellites. When the balance conditions that we predict are applied to the ring system of (10199) Chariklo, we are able to estimate the minimum mass of a shepherd satellite required to prevent eccentricity decay, as a function of its orbital location, for two different models of dissipation. We conclude that the satellite mass required to maintain the m = 1 eccentric mode in the ring, would be similar or smaller than that needed to confine the rings radially. Our estimation of the most plausible combinations of eccentricity gradient and surface density consistent with apse-alignment are based on a standard model for the radial form of the surface density distribution, which approximately agrees with the optical depth profile derived by the stellar occultations. We find a diverse range of solutions, with combinations of eccentricity gradient and surface mass density that tend to minimize required enhanced collisional effects, having adopted estimated values of the form factor of the second degree harmonic of the gravitational potential.Facultad de Ciencias Astronómicas y Geofísica
Causal Viscosity in Accretion Disc Boundary Layers
The structure of the boundary layer region between the disc and a
comparatively slowly rotating star is studied using a causal prescription for
viscosity. The vertically integrated viscous stress relaxes towards its
equilibrium value on a relaxation timescale , which naturally yields a
finite speed of propagation for viscous information. For a standard alpha
prescription with alpha in the range 0.1-0.01, and ratio of viscous speed to
sound speed in the range 0.02-0.5, details in the boundary layer are strongly
affected by the causality constraint. We study both steady state polytropic
models and time dependent models, taking into account energy dissipation and
transport. Steady state solutions are always subviscous with a variety of
profiles which may exhibit near discontinuities. For alpha =0.01 and
small viscous speeds, the boundary layer adjusted to a near steady state. A
long wavelength oscillation generated by viscous overstability could be seen at
times near the outer boundary. Being confined there, the boundary layer
remained almost stationary. However, for alpha =0.1 and large viscous speeds,
short wavelength disturbances were seen throughout which could significantly
affect the power output in the boundary layer. This could be potentially
important in producing time dependent behaviour in accreting systems such as
CVs and protostars.Comment: 10 LateX pages, requires lamuphys.sty and psfig.sty, 3 figures
included, to appear in the Proceedings of the EARA Workshop on Accretion
Disks (Garching, Oct. 96), Lecture Notes in Physic
Structuring eccentric-narrow planetary rings
(Abridged) A simple and general description of the dynamics of a narrow
eccentric ring is presented.We view an eccentric ring which precesses uniformly
at a slow rate as exhibiting a global mode originating from a standing
wave superposed on an axisymmetric background.We adopt a continuum description
using the language of fluid dynamics which gives equivalent results for the
secular dynamics of thin rings as the the well known description using discrete
elliptical streamlines formulated by Goldreich and Tremaine (1979). We use this
to discuss the non linear mode interactions that appear through the excitation
of higher modes due to the coupling of the mode with an external
satellite potential, showing that they can lead to the excitation of the
mode through a feedback process.Two conditions for the maintainance of a steady
mode are obtained. One,being the condition for the normal mode pattern to
precess uniformly requires a balance between the differential precession
induced by the oblateness of the central planet,self-gravity and collisional
effects and is the continuum form of that obtained from the streamline
model of Goldreich and Tremaine (1979).The other condition is for the steady
maintenance of the non-zero radial action of the ring on account of the normal
mode.This requires a balance between input due to eccentric resonances due to
external satellites and additional collisional damping associated with the
presence of the mode We estimate that such a balance can occur in the
ring of Uranus,given its currently observed physical and orbital
parameters.Comment: Revised version accepted for publication in Icaru
Warp propagation in astrophysical discs
Astrophysical discs are often warped, that is, their orbital planes change
with radius. This occurs whenever there is a non-axisymmetric force acting on
the disc, for example the Lense-Thirring precession induced by a misaligned
spinning black hole, or the gravitational pull of a misaligned companion. Such
misalignments appear to be generic in astrophysics. The wide range of systems
that can harbour warped discs - protostars, X-ray binaries, tidal disruption
events, quasars and others - allows for a rich variety in the disc's response.
Here we review the basic physics of warped discs and its implications.Comment: To be published in Astrophysical Black Holes by Haardt et al.,
Lecture Notes in Physics, Springer 2015. 19 pages, 2 figure
The 1:1 resonance in Extrasolar Systems: Migration from planetary to satellite orbits
We present families of symmetric and asymmetric periodic orbits at the 1/1
resonance, for a planetary system consisting of a star and two small bodies, in
comparison to the star, moving in the same plane under their mutual
gravitational attraction. The stable 1/1 resonant periodic orbits belong to a
family which has a planetary branch, with the two planets moving in nearly
Keplerian orbits with non zero eccentricities and a satellite branch, where the
gravitational interaction between the two planets dominates the attraction from
the star and the two planets form a close binary which revolves around the
star. The stability regions around periodic orbits along the family are
studied. Next, we study the dynamical evolution in time of a planetary system
with two planets which is initially trapped in a stable 1/1 resonant periodic
motion, when a drag force is included in the system. We prove that if we start
with a 1/1 resonant planetary system with large eccentricities, the system
migrates, due to the drag force, {\it along the family of periodic orbits} and
is finally trapped in a satellite orbit. This, in principle, provides a
mechanism for the generation of a satellite system: we start with a planetary
system and the final stage is a system where the two small bodies form a close
binary whose center of mass revolves around the star.Comment: to appear in Cel.Mech.Dyn.Ast
A new analysis of the GJ581 extrasolar planetary system
We have done a new analysis of the available observations for the GJ581
exoplanetary system. Today this system is controversial due to choices that can
be done in the orbital determination. The main ones are the ocurrence of
aliases and the additional bodies - the planets f and g - announced in Vogt et
al. 2010. Any dynamical study of exoplanets requires the good knowledge of the
orbital elements and the investigations involving the planet g are particularly
interesting, since this body would lie in the Habitable Zone (HZ) of the star
GJ581. This region,for this system, is very attractive of the dynamical point
of view due to several resonances of two and three bodies present there. In
this work, we investigate the conditions under which the planet g may exist. We
stress the fact that the planet g is intimately related with the orbital
elements of the planet d; more precisely, we conclude that it is not possible
to disconnect its existence from the determination of the eccentricity of the
planet d. Concerning the planet f, we have found one solution with period
days, but we are judicious about any affirmation concernig this
body because its signal is in the threshold of detection and the high period is
in a spectral region where the ocorruence of aliases is very common. Besides,
we outline some dynamical features of the habitable zone with the dynamical map
and point out the role played by some resonances laying there.Comment: 12 pages, 9 figure
On the dynamics of Extrasolar Planetary Systems under dissipation. Migration of planets
We study the dynamics of planetary systems with two planets moving in the
same plane, when frictional forces act on the two planets, in addition to the
gravitational forces. The model of the general three-body problem is used.
Different laws of friction are considered. The topology of the phase space is
essential in understanding the evolution of the system. The topology is
determined by the families of stable and unstable periodic orbits, both
symmetric and non symmetric. It is along the stable families, or close to them,
that the planets migrate when dissipative forces act. At the critical points
where the stability along the family changes, there is a bifurcation of a new
family of stable periodic orbits and the migration process changes route and
follows the new stable family up to large eccentricities or to a chaotic
region. We consider both resonant and non resonant planetary systems. The 2/1,
3/1 and 3/2 resonances are studied. The migration to larger or smaller
eccentricities depends on the particular law of friction. Also, in some cases
the semimajor axes increase and in other cases they are stabilized. For
particular laws of friction and for special values of the parameters of the
frictional forces, it is possible to have partially stationary solutions, where
the eccentricities and the semimajor axes are fixed.Comment: Accepted in Celestial Mechanics and Dynamical Astronom