73 research outputs found
Reanalysis of radial velocity data from the resonant planetary system HD128311
The multi-planetary system HD128311 hosts at least two planets. Its dynamical
formation history has been studied extensively in the literature. We reanalyse
the latest radial velocity data for this system with the affine-invariant
Markov chain Monte Carlo sampler EMCEE. Using the high order integrator IAS15,
we perform a fully dynamical fit, allowing the planets to interact during the
sampling process. A stability analysis using the MEGNO indicator reveals that
the system is located in a stable island of the parameter space. In contrast to
a previous study, we find that the system is locked in a 2:1 mean motion
resonance. The resonant angle is librating with a libration
amplitude of approximately 37{\deg}. The existence of mean motion resonances
has important implication for planet formation theories. Our results confirm
predictions of models involving planet migration and stochastic forces.Comment: 4 pages, 2 figures, accepted by MNRAS Letter
A proposal for community driven and decentralized astronomical databases and the Open Exoplanet Catalogue
I present a new kind of astronomical database based on small text files and a
distributed version control system. This encourages the community to work
collaboratively. It creates a decentralized, completely open and democratic way
of managing small to medium sized heterogeneous astronomical databases and
catalogues. The use of the XML file format allows an easy to parse and read,
yet dynamic and extendable database structure.
The Open Exoplanet Catalogue is based on these principles and presented as an
example. It is a catalogue of all discovered extra-solar planets. It is the
only catalogue that can correctly represent the orbital structure of planets in
arbitrary binary, triple and quadruple star systems, as well as orphan planets.Comment: 6 pages, 3 listings, 1 table, updated thanks to feedback from various
people, more comments welcom
WHFast: A fast and unbiased implementation of a symplectic Wisdom-Holman integrator for long term gravitational simulations
We present WHFast, a fast and accurate implementation of a Wisdom-Holman
symplectic integrator for long-term orbit integrations of planetary systems.
WHFast is significantly faster and conserves energy better than all other
Wisdom-Holman integrators tested. We achieve this by significantly improving
the Kepler-solver and ensuring numerical stability of coordinate
transformations to and from Jacobi coordinates. These refinements allow us to
remove the linear secular trend in the energy error that is present in other
implementations. For small enough timesteps we achieve Brouwer's law, i.e. the
energy error is dominated by an unbiased random walk due to floating-point
round-off errors. We implement symplectic correctors up to order eleven that
significantly reduce the energy error. We also implement a symplectic tangent
map for the variational equations. This allows us to efficiently calculate two
widely used chaos indicators the Lyapunov characteristic number (LCN) and the
Mean Exponential Growth factor of Nearby Orbits (MEGNO). WHFast is freely
available as a flexible C package, as a shared library, and as an easy-to-use
python module.Comment: Accepted by MNRAS, 13 pages, 4 figures, source code and tutorials
available at http://github.com/hannorein/reboun
Large-scale N-body simulations of the viscous overstability in Saturn's rings
We present results from large-scale particle simulations of the viscous
overstability in Saturn's rings. The overstability generates a variety of
structure on scales covering a few hundred metres to several kilometres,
including axisymmetric wavetrains and larger-scale modulations. Such patterns
have been observed in Saturn's rings by the Cassini spacecraft. Our simulations
model the collisional evolution of particles in a co-rotating patch of the
disk. These are the largest N-body simulations of the viscous overstability yet
performed. The radial box size is five orders of magnitude larger than a
typical particle radius, and so describes a 20-50 km radial portion of the
rings. Its evolution is tracked for more than 10,000 orbits. In agreement with
hydrodynamics, our N-body simulations reveal that the viscous overstability
exhibits a rich set of dynamics characterised by nonlinear travelling waves
with wavelengths of a few hundred meters. In addition, wave defects, such as
sources and shocks, punctuate this bed of waves and break them up into
large-scale divisions of radial width ~5 km. We find that the wavelength of the
travelling waves is positively correlated with the mean optical depth. In order
to assess the role of the numerical boundary conditions and also background
ring structure, we include simulations of broad spreading rings and simulations
with a gradient in the background surface density. Overall, our numerical
results and approach provide a tool with which to interpret Cassini occultation
observations of microstructure in Saturn's rings. We present an example of such
a synthetic occultation observation and discuss what features to expect. We
also make the entire source code freely available.Comment: 15 pages, 12 figures, accepted for publication by MNRA
Resonant structure, formation and stability of the planetary system HD155358
Two Jovian-sized planets are orbiting the star HD155358 near exact mean
motion resonance (MMR) commensurability. In this work we re-analyze the radial
velocity (RV) data previously collected by Robertson et al. (2012). Using a
Bayesian framework we construct two models - one that includes and one that
excludes gravitational planet-planet interactions (PPI). We find that the
orbital parameters from our PPI and noPPI models differ by up to ,
with our noPPI model being statistically consistent with previous results. In
addition, our new PPI model strongly favours the planets being in MMR while our
noPPI model strongly disfavours MMR. We conduct a stability analysis by drawing
samples from our PPI model's posterior distribution and simulating them for
years, finding that our best-fit values land firmly in a stable region
of parameter space.
We explore a series of formation models that migrate the planets into their
observed MMR. We then use these models to directly fit to the observed RV data,
where each model is uniquely parameterized by only three constants describing
its migration history. Using a Bayesian framework we find that a number of
migration models fit the RV data surprisingly well, with some migration
parameters being ruled out.
Our analysis shows that planet-planet interactions are important to take into
account when modelling observations of multi-planetary systems. The additional
information that one can gain from interacting models can help constrain planet
migration parameters.Comment: Accepted for publication in MNRAS, 8 Pages, 4 Figure
Tides Alone Cannot Explain Kepler Planets Close to 2:1 MMR
A number of Kepler planet pairs lie just wide of first-order mean motion
resonances (MMRs). Tides have been frequently proposed to explain these
pileups, but it is still an ongoing discussion. We contribute to this
discussion by calculating an optimistic theoretical estimate on the minimum
initial eccentricity required by Kepler planets to explain the current observed
spacing, and compliment these calculations with N-body simulations. In
particular, we investigate 27 Kepler systems having planets within 6% of the
2:1 MMR, and find that the initial eccentricities required to explain the
observed spacings are unreasonable from simple dynamical arguments.
Furthermore, our numerical simulations reveal resonant tugging, an effect which
conspires against the migration of resonant planets away from the 2:1 MMR,
requiring even higher initial eccentricities in order to explain the current
Kepler distribution. Overall, we find that tides alone cannot explain planets
close to 2:1 MMR, and additional mechanisms are required to explain these
systems.Comment: Accepted for publication in MNRAS, 9 pages, 5 figures, 1 tabl
Second-order variational equations for N-body simulations
First-order variational equations are widely used in N-body simulations to
study how nearby trajectories diverge from one another. These allow for
efficient and reliable determinations of chaos indicators such as the Maximal
Lyapunov characteristic Exponent (MLE) and the Mean Exponential Growth factor
of Nearby Orbits (MEGNO).
In this paper we lay out the theoretical framework to extend the idea of
variational equations to higher order. We explicitly derive the differential
equations that govern the evolution of second-order variations in the N-body
problem. Going to second order opens the door to new applications, including
optimization algorithms that require the first and second derivatives of the
solution, like the classical Newton's method. Typically, these methods have
faster convergence rates than derivative-free methods. Derivatives are also
required for Riemann manifold Langevin and Hamiltonian Monte Carlo methods
which provide significantly shorter correlation times than standard methods.
Such improved optimization methods can be applied to anything from
radial-velocity/transit-timing-variation fitting to spacecraft trajectory
optimization to asteroid deflection.
We provide an implementation of first and second-order variational equations
for the publicly available REBOUND integrator package. Our implementation
allows the simultaneous integration of any number of first and second-order
variational equations with the high-accuracy IAS15 integrator. We also provide
routines to generate consistent and accurate initial conditions without the
need for finite differencing.Comment: 11 pages, accepted for publication in MNRAS, code available at
https://github.com/hannorein/rebound, figures can be reproduced interactively
with binder at http://mybinder.org/repo/hannorein/variation
High Order Harmonics in Light Curves of Kepler Planets
The Kepler mission was launched in 2009 and has discovered thousands of
planet candidates. In a recent paper, Esteves et al. (2013) found a periodic
signal in the light curves of KOI-13 and HAT-P-7, with a frequency triple the
orbital frequency of a transiting planet. We found similar harmonics in many
systems with a high occurrence rate. At this time, the origins of the signal
are not entirely certain.
We look carefully at the possibility of errors being introduced through our
data processing routines but conclude that the signal is real. The harmonics on
multiples of the orbital frequency are a result of non-sinusoidal periodic
signals. We speculate on their origin and generally caution that these
harmonics could lead to wrong estimates of planet albedos, beaming mass
estimates, and ellipsoidal variations.Comment: Accepted for publication in MNRAS Letters, 6 pages, 2 figure
JANUS: A bit-wise reversible integrator for N-body dynamics
Hamiltonian systems such as the gravitational N-body problem have
time-reversal symmetry. However, all numerical N-body integration schemes,
including symplectic ones, respect this property only approximately. In this
paper, we present the new N-body integrator JANUS, for which we achieve exact
time-reversal symmetry by combining integer and floating point arithmetic.
JANUS is explicit, formally symplectic and satisfies Liouville's theorem
exactly. Its order is even and can be adjusted between two and ten. We discuss
the implementation ofJANUS and present tests of its accuracy and speed by
performing and analyzing long-term integrations of the Solar System. We show
that JANUS is fast and accurate enough to tackle a broad class of dynamical
problems. We also discuss the practical and philosophical implications of
running exactly time-reversible simulations.Comment: Accepted for publication by MNRAS, 7 pages, 4 figures, source code
available at https://github.com/hannorein/rebound , iPython notebooks to
reproduce figures available at https://github.com/hannorein/JanusPape
IAS15: A fast, adaptive, high-order integrator for gravitational dynamics, accurate to machine precision over a billion orbits
We present IAS15, a 15th-order integrator to simulate gravitational dynamics.
The integrator is based on a Gau\ss-Radau quadrature and can handle
conservative as well as non-conservative forces. We develop a step-size control
that can automatically choose an optimal timestep. The algorithm can handle
close encounters and high-eccentricity orbits. The systematic errors are kept
well below machine precision and long-term orbit integrations over
orbits show that IAS15 is optimal in the sense that it follows Brouwer's law,
i.e. the energy error behaves like a random walk. Our tests show that IAS15 is
superior to a mixed-variable symplectic integrator (MVS) and other popular
integrators, including high-order ones, in both speed and accuracy. In fact,
IAS15 preserves the symplecticity of Hamiltonian systems better than the
commonly-used nominally symplectic integrators to which we compared it.
We provide an open-source implementation of IAS15. The package comes with
several easy-to-extend examples involving resonant planetary systems,
Kozai-Lidov cycles, close encounters, radiation pressure, quadrupole moment,
and generic damping functions that can, among other things, be used to simulate
planet-disc interactions. Other non-conservative forces can be added easily.Comment: Accepted for publication in MNRAS, 14 pages, 7 figures, source code
in c and python bindings available at http://github.com/hannorein/reboun
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