31 research outputs found
The orbital architecture and stability of the Arae planetary system
We re-analyze the global orbital architecture and dynamical stability of the
Arae planetary system. We have updated the best-fit elements and minimal
masses of the planets based on literature radial velocity (RV) measurements,
now spanning 15 years. This is twice the RVs interval used for the first
characterization of the system in 2006. It consists of a Saturn- and two
Jupiter-mass planets in low-eccentric orbits resembling the Earth-Mars-Jupiter
configuration in the Solar system, as well as the close-in warm Neptune with a
mass of ~14 Earth masses. Here, we constrain this early solution with the
outermost period to be accurate to one month. The best-fit Newtonian model is
characterized by moderate eccentricities of the most massive planets below 0.1
with small uncertainties ~0.02. It is close but meaningfully separated from the
2e:1b mean motion resonance of the Saturn-Jupiter-like pair, but may be close
to weak three-body MMRs. The system appears rigorously stable over a wide
region of parameter space covering uncertainties of several . The
system stability is robust to a five-fold increase in the minimal masses,
consistent with a wide range of inclinations, from 20 to 90 deg. This means
that all planetary masses are safely below the brown dwarf mass limit. We found
a weak statistical indication of the likely system inclination I~20-30 deg.
Given the well constrained orbital solution, we also investigate the structure
of hypothetical debris disks, which are analogs of the Main Belt and Kuiper
Belt, and may naturally occur in this system.Comment: Several errors in the text have been removed and references corrected
and expanded. This manuscript has 23 pages (20 pages+3 pages of supplementary
on-line material), 2 tables and 14+2 multi-panel figures. Accepted to Monthly
Notices of the RAS. Your comments are welcome
Relative equilibria in the unrestricted problem of a sphere and symmetric rigid body
We consider the unrestricted problem of two mutually attracting rigid bodies,
an uniform sphere (or a point mass) and an axially symmetric body. We present a
global, geometric approach for finding all relative equilibria (stationary
solutions) in this model, which was already studied by Kinoshita (1970). We
extend and generalize his results, showing that the equilibria solutions may be
found by solving at most two non-linear, algebraic equations, assuming that the
potential function of the symmetric rigid body is known explicitly. We
demonstrate that there are three classes of the relative equilibria, which we
call "cylindrical", "inclined co-planar", and "conic" precessions,
respectively. Moreover, we also show that in the case of conic precession,
although the relative orbit is circular, the point-mass and the mass center of
the body move in different parallel planes. This solution has been yet not
known in the literature.Comment: The manuscript with 10 pages, 5 figures; accepted to the Monthly
Notices of the Royal Astronomical Societ
Equilibria in the secular, non-coplanar two-planet problem
We investigate the secular dynamics of a planetary system composed of the
parent star and two massive planets in mutually inclined orbits. The dynamics
are investigated in wide ranges of semi-major axes ratios (0.1-0.667), and
planetary masses ratios (0.25-2) as well as in the whole permitted ranges of
the energy and total angular momentum. The secular model is constructed by
semi-analytic averaging of the three-body system. We focus on equilibria of the
secular Hamiltonian (periodic solutions of the full system), and we analyze
their stability. We attempt to classify families of these solutions in terms of
the angular momentum integral. We identified new equilibria, yet unknown in the
literature. Our results are general and may be applied to a wide class of
three-body systems, including configurations with a star and brown dwarfs and
sub-stellar objects. We also describe some technical aspects of the
semi-numerical averaging. The HD 12661 planetary system is investigated as an
example configuration.Comment: 18 pages, 17 figures, accepted to Monthly Notices of the Royal
Astronomical Societ
The long-term stability of extrasolar system HD 37124. Numerical study of resonance effects
We describe numerical tools for the stability analysis of extrasolar
planetary systems. In particular, we consider the relative Poincare variables
and symplectic integration of the equations of motion. We apply the tangent map
to derive a numerically efficient algorithm of the fast indicator MEGNO (a
measure of the maximal Lyapunov exponent) that helps to distinguish chaotic and
regular configurations. The results concerning the three-planet extrasolar
system HD 37124 are presented and discussed. The best fit solutions found in
earlier works are studied more closely. The system involves Jovian planets with
similar masses. The orbits have moderate eccentricities, nevertheless the best
fit solutions are found in dynamically active region of the phase space. The
long term stability of the system is determined by a net of low-order two-body
and three-body mean motion resonances. In particular, the three-body resonances
may induce strong chaos that leads to self-destruction of the system after Myrs
of apparently stable and bounded evolution. In such a case, numerically
efficient dynamical maps are useful to resolve the fine structure of the phase
space and to identify the sources of unstable behavior.Comment: 11 pages (total), 8 figures. Accepted for publication in MNRAS. The
definitive version will be/is available at
http://www.blackwellpublishing.com. The astro-ph version is prepared with low
resolution figures. To obtain the manuscript with full-resolution figures,
please visit http://www.astri.uni.torun.pl/~chris/mnrasIII.ps.g
Testing a hypothesis of the \nu Octantis planetary system
We investigate the orbital stability of a putative Jovian planet in a compact
binary \nu Octantis reported by Ramm et al. We re-analyzed published radial
velocity data in terms of self-consistent Newtonian model and we found stable
best-fit solutions that obey observational constraints. They correspond to
retrograde orbits, in accord with an earlier hypothesis of Eberle & Cuntz, with
apsidal lines anti-aligned with the apses of the binary. The best-fit solutions
are confined to tiny stable regions of the phase space. These regions have a
structure of the Arnold web formed by overlapping low-order mean motion
resonances and their sub-resonances. The presence of a real planet is still
questionable, because its formation would be hindered by strong dynamical
perturbations. Our numerical study makes use of a new computational Message
Passing Interface (MPI) framework MECHANIC developed to run massive numerical
experiments on CPU clusters.Comment: 12 pages, 12 figures, accepted to Monthly Notices of the RA
A secular theory of coplanar, non-resonant planetary system
We present the secular theory of coplanar -planet system, in the absence
of mean motion resonances between the planets. This theory relies on the
averaging of a perturbation to the two-body problem over the mean longitudes.
We expand the perturbing Hamiltonian in Taylor series with respect to the
ratios of semi-major axes which are considered as small parameters, without
direct restrictions on the eccentricities. Next, we average out the resulting
series term by term. This is possible thanks to a particular but in fact quite
elementary choice of the integration variables. It makes it possible to avoid
Fourier expansions of the perturbing Hamiltonian. We derive high order
expansions of the averaged secular Hamiltonian (here, up to the order of 24)
with respect to the semi-major axes ratio. The resulting secular theory is a
generalization of the octupole theory. The analytical results are compared with
the results of numerical (i.e., practically exact) averaging. We estimate the
convergence radius of the derived expansions, and we propose a further
improvement of the algorithm. As a particular application of the method, we
consider the secular dynamics of three-planet coplanar system. We focus on
stationary solutions in the HD 37124 planetary system.Comment: 14 pages, 4 figures, MATHEMATICA file expansion.m, accepted to
Monthly Notices of the Royal Astronomical Society. (minor corrections of
symbols