414 research outputs found
Accurate numerical potential and field in razor-thin axisymmetric discs
We demonstrate the high accuracy of the density splitting method to compute
the gravitational potential and field in the plane of razor-thin, axially
symmetric discs, as preliminarily outlined in Pierens & Hure (2004).
Because residual kernels in Poisson integrals are not C^infinity-class
functions, we use a dynamical space mapping in order to increase the efficiency
of advanced quadrature schemes. In terms of accuracy, results are better by
orders of magnitude than for the classical FFT-methods.Comment: 11 pages, 5 color figures, 2 table
Three-dimensional evolution of radiative circumbinary discs: the size and shape of the inner cavity
The evolution of circumbinary discs and planets is often studied using
two-dimensional (2D) numerical simulations, although recent work suggests that
3D effects may significantly alter the structure of the inner cavity created by
the binary. In this study, we present the results of 3D hydrodynamical
simulations of circumbinary discs that orbit around analogues of the Kepler-16
and Kepler-34 systems, including the effect of stellar heating and radiative
cooling on the thermal disc structure. We find that compared to their 2D
counterparts, the structures of the cavities in 3D circumbinary disc models
appear to reach a quasi-stationary state more rapidly, and in a subset of our
runs the evidence for this is unambiguous. Furthermore, the sizes and
eccentricities of the inner cavity are smaller in 3D compared to 2D. We
attribute this difference to enhanced spiral wave dissipation in disc regions
above the midplane, where the cooling time is of the order of the dynamical
timescale, resulting in smaller inner cavity sizes in 3D disc models. Our
results suggest that migrating planets should park closer to the central binary
in 3D models of circumbinary discs, and point to the importance of including
the 3D structure when simulating circumbinary discs and planets.Comment: Accepted in A&
On the formation and migration of giant planets in circumbinary discs
We present the results of hydrodynamic simulations of the formation and
subsequent orbital evolution of giant planets embedded in a circumbinary disc.
We assume that a 20 earth masses core has migrated to the edge of the inner
cavity formed by the binary where it remains trapped by corotation torques.
This core is then allowed to accrete gas from the disc, and we study its
orbital evolution as it grows in mass. For each of the two accretion time
scales we considered, we performed three simulations. In two of the three
simulations, we stop the accretion onto the planet once its mass becomes
characteristic of that of Saturn or Jupiter. In the remaining case, the planet
can accrete disc material freely in such a way that its mass becomes higher
than Jupiter's. The simulations show different outcomes depending on the final
mass m_p of the giant. For m_p=1 M_S (where M_S is Saturn's mass), we find that
the planet migrates inward through its interaction with the disc until its
eccentricity becomes high enough to induce a torque reversal. The planet then
migrates outward, and the system remains stable on long time scales. For m_p >
1 M_J (where M_J is Jupiter's mass) we observed two different outcomes. In each
case the planet enters the 4:1 resonance with the binary, and resonant
interaction drives up the eccentricity of the planet until it undergoes a close
encounter with the secondary star. The result can either be ejection from the
system or scattering out into the disc followed by a prolonged period of
outward migration. These results suggest that circumbinary planets are more
likely to be quite common in the Saturn-mass range. Jupiter-mass circumbinary
planets are likely to be less common because of their less stable evolution.Comment: 12 pages, 12 figures. Accepted for publication in A&
Thermal structure of circumbinary discs: Circumbinary planets should be icy not rocky
The process of forming a circumbinary planet is thought to be intimately
related to the structure of the nascent circumbinary disc. It has been shown
that the structure of a circumbinary disc depends strongly on 3-dimensional
effects and on the detailed modelling of the thermodynamics. Here, we employ
3-dimensional hydrodynamical simulations, combined with a proper treatment of
the thermal physics using the RADMC-3D radiation transport code, to examine the
location of the snow line in circumbinary discs. The models have application to
the circumbinary planets that have been discovered in recent years by the
Kepler and TESS transit surveys. We find that the snow line is located in a
narrow region of the circumbinary disc, close to the inner cavity that is
carved out by the central binary, at typical orbital distances of
AU for the system parameters considered. In this region, previous work has
shown that both grain growth and pebble accretion are likely to be inefficient
because of the presence of hydrodynamical turbulence. Hence, in situ planet
formation interior to the snow line is unlikely to occur and circumbinary
planets should preferentially be icy, not rocky.Comment: Accepted in A&
Hydrodynamical turbulence in eccentric circumbinary discs and its impact on the in situ formation of circumbinary planets
Eccentric gaseous discs are unstable to a parametric instability involving
the resonant interaction between inertial-gravity waves and the eccentric mode
in the disc. We present 3D global hydrodynamical simulations of inviscid
circumbinary discs that form an inner cavity and become eccentric through
interaction with the central binary. The parametric instability grows and
generates turbulence that transports angular momentum with stress parameter
at distances , where
is the binary semi-major axis. Vertical turbulent diffusion occurs at
a rate corresponding to . We examine the
impact of turbulent diffusion on the vertical settling of pebbles, and on the
rate of pebble accretion by embedded planets. In steady state, dust particles
with Stokes numbers form a layer of finite thickness
, where is the gas scale height. Pebble accretion
efficiency is then reduced by a factor , where is the
accretion radius, compared to the rate in a laminar disc. For accreting core
masses with , pebble accretion for particles with
is also reduced because of velocity kicks induced by the
turbulence. These effects combine to make the time needed by a Ceres-mass
object to grow to the pebble isolation mass, when significant gas accretion can
occur, longer than typical disc lifetimes. Hence, the origins of circumbinary
planets orbiting close to their central binary systems, as discovered by the
Kepler mission, are difficult to explain using an in situ model that invokes a
combination of the streaming instability and pebble accretion.Comment: Accepted in MNRA
Do we expect to find the Super-Earths close to the gas giants?
We have investigated the evolution of a pair of interacting planets embedded
in a gaseous disc, considering the possibility of the resonant capture of a
Super-Earth by a Jupiter mass gas giant. First, we have examined the situation
where the Super-Earth is on the internal orbit and the gas giant on the
external one. It has been found that the terrestrial planet is scattered from
the disc or the gas giant captures the Super-Earth into an interior 3:2 or 4:3
mean-motion resonance. The stability of the latter configurations depends on
the initial planet positions and on eccentricity evolution. The behaviour of
the system is different if the Super-Earth is the external planet. We have
found that instead of being captured in the mean-motion resonance, the
terrestrial planet is trapped at the outer edge of the gap opened by the gas
giant. This effect prevents the occurrence of the first order mean-motion
commensurability. These results are particularly interesting in light of recent
exoplanet discoveries and provide predictions of what will become
observationally testable in the near future.Comment: 7 pages, 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
Planet Formation in Binary Stars: The case of Gamma Cephei
Over 30 planetary systems have been discovered to reside in binary stars. For
small separations gravitational perturbation of the secondary star has a strong
influence on the planet formation process. It truncates the protoplanetary
disk, may shortens its lifetime, and stirs up the embedded planetesimals. Due
to its small semi-major axis (18.5 AU) and large eccentricity (e=0.35) the
binary Cephei represents a particularly challenging example. In the
present study we model the orbital evolution and growth of embedded
protoplanetary cores of about 30 earth masses in the putative protoplanetary
disk surrounding the primary star in the Cep system. We assume
coplanarity of the disk, binary and planet and perform two-dimensional
hydrodynamic simulations of embedded cores in a protoplanetary disk. The
presence of the eccentric secondary star perturbs the disk periodically and
generates strong spiral arms at periapse which propagate toward the disk
centre. The disk also becomes slightly eccentric (with e_d = 0.1-0.15), and
displays a slow retrograde precession in the inertial frame. For all initial
separations (2.5 to 3.5 AU) we find inward migration of the cores. For initial
semi-major axes (a_p \gsim 2.7), we find a strong increase in the planetary
eccentricity despite the presence of inward migration. Only cores which are
initially far from the disk outer edge have a bounded orbital eccentricity
which converges, roughly to the value of the planet observed in the
Cep system. We have shown that under the condition protoplanetary cores can
form at around 2.5 AU, it is possible to evolve and grow such a core to form a
planet with final outcome similar to that observed.Comment: 12 pages, 17 figures, accepted by Astronomy & Astrophysic
How does disk gravity really influence type-I migration ?
We report an analytical expression for the locations of Lindblad resonances
induced by a perturbing protoplanet, including the effect of disk gravity.
Inner, outer and differential torques are found to be enhanced compared to
situations where a keplerian velocity field for the dynamics of both the disk
and the planet is assumed. Inward migration is strongly accelerated when the
disk gravity is only accounted for in the planet orbital motion. The addition
of disk self-gravity slows down the planet drift but not enough to stop it.Comment: 4 pages, accepted for publication in A&A Letter
Self-gravity at the scale of the polar cell
We present the exact calculus of the gravitational potential and acceleration
along the symmetry axis of a plane, homogeneous, polar cell as a function of
mean radius a, radial extension e, and opening angle f. Accurate approximations
are derived in the limit of high numerical resolution at the geometrical mean
of the inner and outer radii (a key-position in current FFT-based Poisson
solvers). Our results are the full extension of the approximate formula given
in the textbook of Binney & Tremaine to all resolutions. We also clarify
definitely the question about the existence (or not) of self-forces in polar
cells. We find that there is always a self-force at radius except if the
shape factor a.f/e reaches ~ 3.531, asymptotically. Such cells are therefore
well suited to build a polar mesh for high resolution simulations of
self-gravitating media in two dimensions. A by-product of this study is a newly
discovered indefinite integral involving complete elliptic integral of the
first kind over modulus.Comment: 4 pages, 4 figures, A&A accepte
Generation of potential/surface density pairs in flat disks Power law distributions
We report a simple method to generate potential/surface density pairs in flat
axially symmetric finite size disks. Potential/surface density pairs consist of
a ``homogeneous'' pair (a closed form expression) corresponding to a uniform
disk, and a ``residual'' pair. This residual component is converted into an
infinite series of integrals over the radial extent of the disk. For a certain
class of surface density distributions (like power laws of the radius), this
series is fully analytical. The extraction of the homogeneous pair is
equivalent to a convergence acceleration technique, in a matematical sense. In
the case of power law distributions, the convergence rate of the residual
series is shown to be cubic inside the source. As a consequence, very accurate
potential values are obtained by low order truncation of the series. At zero
order, relative errors on potential values do not exceed a few percent
typically, and scale with the order N of truncation as 1/N**3. This method is
superior to the classical multipole expansion whose very slow convergence is
often critical for most practical applications.Comment: Accepted for publication in Astronomy & Astrophysics 7 pages, 8
figures, F90-code available at
http://www.obs.u-bordeaux1.fr/radio/JMHure/intro2applawd.htm
- âŠ