arXiv subjects

Cezary Migaszewski

Publications and source records attributed to Cezary Migaszewski.

At least 19 recordsLinked to original sources

arXiv2023

On the origin of extreme trans-Neptunian objects within Modified Newtonian Dynamics

In this work, we investigate the dynamical origin of extreme trans-Neptunian objects (ETNOs) under the action of the External Field Effect (EFE), which is a consequence of Modified Newtonian Dynamics (MOND) applied to gravity around the Sun embedded in the gravitational field of the Galaxy. We perform N-body integrations of known ETNOs treated as massless particles and perturbed by four giant planets and EFE. Backward integrations show that these objects originated in the giant planet region, from where they were scattered and then evolved to their current orbits. A striking example of such evolution is Sedna, which may have been temporarily in a horseshoe orbit with Jupiter and Saturn only $30$~Myr ago. Another interesting example is the newly discovered retrograde ETNOs, whose dynamical connection with prograde ETNOs and Centaurs is shown. The EFE is considered as an alternative to Planet Nine in explaining the anomalous distribution of ETNO orbits, namely the orbital plane clustering and apsidal confinement. We also analyse the effect of MOND on the obliquity of the solar spin with respect to the invariant plane of the solar system.

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arXiv2020

An exact, generalised Laplace resonance in the HR 8799 planetary system

A system of four super-Jupiter planets around HR 8799 is the first multi-planet configuration discovered via the direct imaging technique. Despite over decade of research, the system's architecture remains not fully resolved. The main difficulty comes from still narrow observing window of ~20 years that covers small arcs of orbits with periods from roughly 50 to 500 years. Soon after the discovery it became clear that unconstrained best-fitting astrometric configurations self-disrupt rapidly, due to strong mutual gravitational interactions between ~10-Jupiter-mass companions. Recently, we showed that the HR 8799 system may be long term stable when locked in a generalized Laplace 8:4:2:1 mean motion resonance (MMR) chain, and we constrained its orbits through the planetary migration. Here we qualitatively improve this approach by considering the MMR in terms of an exactly periodic configuration. This assumption enables us to construct for the first time the self-consistent $N$-body model of the long-term stable orbital architecture, using only available astrometric positions of the planets relative to the star. We independently determine planetary masses, which are consistent with thermodynamic evolution, and the parallax overlapping to $1σ$ with the most recent GAIA DR2 value. We also determine the global structure of the inner and outer debris discs in the [8, 600] au range, consistent with the updated orbital solution.

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arXiv2018

A periodic configuration of the Kepler-25 planetary system?

We study proximity of the Kepler-25 planetary system to a periodic configuration, which is known to be the final state of a system that undergoes smooth migration resulting from the planet-disc interaction. We show that the system is close to the periodic configuration of 2:1 mean motion resonance (MMR) what indicates that its past migration was neither disturbed significantly by turbulence in the disc nor the orbits were perturbed by planetesimals that left after the disc dispersal. We show that, because of the TTV model degeneracy, a periodic configuration is difficult to be found when the standard modelling of the transit timing variations (TTVs) is used. The TTV signal of a periodic configuration (with anti-aligned apsidal lines) may be misinterpreted as an aligned non-resonant system. We demonstrate that the standard MCMC modelling of the Kepler-25 TTVs is very sensitive to an a~priori information on the eccentricities (prior probability distributions). Wide priors (of the order of the ones typically used in the literature) result in favouring the aligned non-resonant configurations with small planets' masses and moderate eccentricities, while for the narrower priors the most likely are the anti-aligned resonant systems with larger masses and very low eccentricities.

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arXiv2018

The orbital architecture and debris disks of the HR 8799 planetary system

The HR8799 planetary system with four ~10 mJup planets in wide orbits up to 70 au, and periods up to 500 yr has been detected with the direct imaging. Its intriguing orbital architecture is not fully resolved due to time-limited astrometry covering ~20 years. Earlier, we constructed a heuristic model of the system based on rapid, convergent migration of the planets. We developed a better structured and CPU-efficient variant of this model. We re-analyzed the self-consistent, homogeneous astrometric dataset in Konopacky (2016). The best-fitting configuration agrees with our earlier findings. The planets are likely involved in dynamically robust Laplace resonance chain. Hypothetical planets with masses below the current detection limit of 0.1-3 Jupiter masses, within the observed inner, or beyond the outer orbit, respectively, do not influence the long term stability of the system. We predict positions of such non-detected objects. The long-term stable orbital model of the observed planets helps to simulate the dynamical structure of debris disks in the system. A CPU-efficient fast indicator technique makes it possible to reveal their complex, resonant shape in 10^6 particles scale. We examine the inner edge of the outer disk detected between 90-145 au. We also reconstruct the outer disk assuming that it has been influenced by convergent migration of the planets. A complex shape of the disk strongly depends on various dynamical factors, like orbits and masses of non-detected planets. It may be highly non-circular and its models are yet non-unique, regarding both observational constraints, as well as its origin.

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arXiv2018

The architecture and formation of the Kepler-30 planetary system

We study the orbital architecture, physical characteristics of planets, formation and long-term evolution of the Kepler-30 planetary system, detected and announced in 2012 by the KEPLER team. We show that the Kepler-30 system belongs to a particular class of very compact and quasi-resonant, yet long-term stable planetary systems. We re-analyse the light curves of the host star spanning Q1-Q17 quarters of the KEPLER mission. A huge variability of the Transit Timing Variations (TTV) exceeding 2 days is induced by a massive Jovian planet located between two Neptune-like companions. The innermost pair is near to the 2:1 mean motion resonance (MMR), and the outermost pair is close to higher order MMRs, such as 17:7 and 7:3. Our re-analysis of photometric data allows us to constrain, better than before, the orbital elements, planets' radii and masses, which are $9.2 \pm 0.1$, $536 \pm 5$, and $23.7 \pm 1.3$ Earth masses for Kepler-30b, Kepler-30c and Kepler-30d, respectively. The masses of the inner planets are determined within $\sim 1\%$ uncertainty. We infer the internal structures of the Kepler-30 planets and their bulk densities in a wide range from $ (0.19 \pm 0.01)$ g$\cdot$cm$^{-3}$ for Kepler-30d, $(0.96\pm0.15)$ g$\cdot$cm$^{-3}$ for Kepler-30b, to $(1.71 \pm 0.13)$ g$\cdot$cm$^{-3}$ for the Jovian planet Kepler-30c. We attempt to explain the origin of this unique planetary system and a deviation of the orbits from exact MMRs through the planetary migration scenario. We anticipate that the Jupiter-like planet plays an important role in determining the present dynamical state of this system.

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arXiv2017

On the migration-induced formation of the 9:7 mean motion resonance

We study formation of 9:7 mean motion resonance (MMR) as a result of convergent migration of two planets embedded in a disc. Depending on the migration parameters, initial orbits and planets' masses the system may pass through the resonance or enter it (permanently or temporarily). We illustrate that a stable equilibrium of the averaged system (a periodic orbit of the N-body model) is surrounded by the region of permanent resonance capture, whose size depends on the migration parameters and the planets mass ratio. A system located inside this region tends towards the equilibrium (the capture is permanent), while a system located outside the region evolves away from the equilibrium and leaves the resonance. We verify recent results of Delisle et al. and Xu & Lai where they show that for $m_1 \lesssim m_2$ ($m_1, m_2$ are the inner and outer planets' masses) the equilibrium is unstable when the migration is added, so the capture cannot be permanent. We show that for particular migration parameters the situation may be reversed (the equilibria are unstable for $m_1 \gtrsim m_2$). We illustrate that 9:7 MMR consists of two modes separated with a separatrix. The inner one is centred at the equilibrium and the outer one has no equilibrium in its centre. A system located outside the region of stable capture evolves from the inner into the outer mode. The evolution occurs along families of periodic orbits of the averaged system, that play a crucial role in the dynamics after the resonance capture.

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arXiv2016

A resonant chain of four transiting, sub-Neptune planets

Surveys have revealed many multi-planet systems containing super-Earths and Neptunes in orbits of a few days to a few months. There is debate whether in situ assembly or inward migration is the dominant mechanism of the formation of such planetary systems. Simulations suggest that migration creates tightly packed systems with planets whose orbital periods may be expressed as ratios of small integers (resonances), often in a many-planet series (chain). In the hundreds of multi-planet systems of sub-Neptunes, more planet pairs are observed near resonances than would generally be expected, but no individual system has hitherto been identified that must have been formed by migration. Proximity to resonance enables the detection of planets perturbing each other. Here we report transit timing variations of the four planets in the Kepler-223 system, model these variations as resonant-angle librations, and compute the long-term stability of the resonant chain. The architecture of Kepler-223 is too finely tuned to have been formed by scattering, and our numerical simulations demonstrate that its properties are natural outcomes of the migration hypothesis. Similar systems could be destabilized by any of several mechanisms, contributing to the observed orbital-period distribution, where many planets are not in resonances. Planetesimal interactions in particular are thought to be responsible for establishing the current orbits of the four giant planets in the Solar System by disrupting a theoretical initial resonant chain similar to that observed in Kepler-223.

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arXiv2016

The origin and 9:7 MMR dynamics of the Kepler-29 system

We analyse the Transit Timing Variation (TTV) measurements of a~system of two super-Earths detected as Kepler-29, in order to constrain the planets' masses and orbital parameters. A dynamical analysis of the best-fitting configurations constrains the masses to be $\sim 6$ and $\sim 5$ Earth masses for the inner and the outer planets, respectively. The analysis also reveals that the system is likely locked in the 9:7~mean motion resonance. However, a variety of orbital architectures regarding eccentricities and the relative orientation of orbits is permitted by the observations as well as by stability constraints. We attempt to find configurations preferred by the planet formation scenarios as an additional, physical constraint. We show that configurations with low eccentricities and anti-aligned apsidal lines of the orbits are a natural and most likely outcome of the convergent migration. However, we show that librations of the critical angles are not necessary for the Kepler-29 system to be dynamically resonant, and such configurations may be formed on the way of migration as well. We argue, on the other hand, that aligned configurations with $e \gtrsim 0.03$ may be not consistent with the migration scenario.

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arXiv2016

On the migration of three planets in a protoplanetary disc and the formation of chains of mean motion resonances

We study the migration of three-planet systems in an irradiated 1+1D $α$-disc with photoevaporation. We performed $2700$ simulations with various planets' masses and initial orbits. We found that most of the systems which ended up as compact configurations form chains of mean motion resonances (MMRs) of the first and higher orders. Most of the systems involved in chains of MMRs are periodic configurations. The period ratios of such system, though, are not necessarily close to exact commensurability. If a given system resides in a divergent migration zone in the disc, the period ratios increase and evolve along resonant divergent migration paths at ($P_2/P_1, P_3/P_2)$-diagram, where $P_1, P_2, P_3$ are the orbital periods of the first, second and third planet, respectively. The observed systems, though, do not lie on those paths. We show that an agreement between the synthetic and the observed systems distributions could be achieved if the orbital circularization was slower than it results from models of the planet-disc interactions. Therefore, we conclude that most of those systems unlikely formed as a result of divergent migration out of nominal chains of MMRs.

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arXiv2015

The Laplace resonance in the Kepler-60 system

We investigate the dynamical stability of the Kepler-60 planetary system with three super-Earths. We first determine their orbital elements and masses by Transit Timing Variation (TTV) data spanning quarters Q1-Q16 of the KEPLER mission. The system is dynamically active but the TTV data constrain masses to ~4 Earth masses and orbits in safely wide stable zones. The observations prefer two types of solutions. The true three-body Laplace MMR exhibits the critical angle librating around 45 degrees and aligned apsides of the inner and outer pair of planets. In the Laplace MMR formed through a chain of two-planet 5:4 and 4:3 MMRs, all critical angles librate with small amplitudes of ~30 degrees and apsidal lines in planet's pairs are anti-aligned. The system is simultaneously locked in a three-body MMR with librations amplitude of ~10 degrees. The true Laplace MMR can evolve towards a chain of two-body MMRs in the presence of planetary migration. Therefore the three-body MMR formed in this way seems to be more likely state of the system. However, the true three-body MMR cannot be disregarded a priori and it remains a puzzling configuration that may challenge the planet formation theory.

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arXiv2015

On the migration of two planets in a disc and the formation of mean motion resonances

We study the dynamics of a system of two super-Earths embedded in a protoplanetary disc. We build a simple model of an irradiated viscous disc and use analytical prescriptions for the planet-disc interactions which lead to migration. We show that depending on the disc parameters, planets' masses and their positions in the disc, the migration of each planet can be inward or outward and the migration of a two-planet system can be convergent (which may lead to formation of a first order mean motion resonance, MMR) or divergent (a system moves away from MMR). We performed $3500$ simulations of the migration of two-planet systems with various masses and initial orbits. Almost all of them end up as resonant configurations, although the period ratios may be very distant from the nominal values of a given MMR. We found that almost all the systems resulting from the migration are periodic configurations.

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arXiv2014

Multiple mean motion resonances in the HR 8799 planetary system

HR 8799 is a nearby star hosting at least four ~10 Jovian mass planets in wide orbits up to ~70au, detected through the direct, high-contrast infrared imaging. Large companions and debris disks reported interior to ~10au, and exterior to ~100au indicate massive protoplanetary disc in the past. The dynamical state of the HR 8799 system is not yet fully resolved, due to limited astrometric data covering tiny orbital arcs. We construct a new, orbital model of the HR 8799 system, assuming rapid migration of the planets after their formation in wider orbits. We found that the HR 8799 planets are likely involved in double Laplace resonance, 1e:2d:4c:8b MMR. Quasi-circular planetary orbits are coplanar with the stellar equator and inclined by ~25 degrees to the sky plane. This best-fit orbital configuration matches astrometry, debris disk models, and mass estimates from cooling models. The multiple MMR is stable for the age of the star ~160Myr, for at least 1 Gyr unless significant perturbations to the N-body dynamics are present. We predict four configurations with the fifth hypothetical innermost planet HR 8799f in ~9.7au, or ~7.5au orbit, extending the MMR chain to triple Laplace resonance 1f:2e:4d:8c:16b MMR or to the 1f:3e:6d:12c:24b MMR, respectively. Our findings may establish strong boundary conditions for the system formation and its early history.

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arXiv2014

Mechanic: the MPI/HDF code framework for dynamical astronomy

We introduce the Mechanic, a new open-source code framework. It is designed to reduce the development effort of scientific applications by providing unified API (Application Programming Interface) for configuration, data storage and task management. The communication layer is based on the well-established Message Passing Interface (MPI) standard, which is widely used on variety of parallel computers and CPU-clusters. The data storage is performed within the Hierarchical Data Format (HDF5). The design of the code follows em core-module approach which allows to reduce the user's codebase and makes it portable for single- and multi-CPU environments. The framework may be used in a local user's environment, without administrative access to the cluster, under the PBS or Slurm job schedulers. It may become a helper tool for a wide range of astronomical applications, particularly focused on processing large data sets, such as dynamical studies of long-term orbital evolution of planetary systems with Monte Carlo methods, dynamical maps or evolutionary algorithms. It has been already applied in numerical experiments conducted for Kepler-11 (Migaszewski et al., 2012), and nuOctantis planetary systems (Goździewski et al., 2013). In this paper we describe the basics of the framework, including code listings for the implementation of a sample user's module. The code is illustrated on a model Hamiltonian introduced by (Froeschle et al., 2000) presenting the Arnold diffusion. The Arnold Web is shown with the help of the MEGNO (Mean Exponential Growth of Nearby Orbits) fast indicator (Goździewski et al., 2008a) applied onto symplectic SABA integrators family (Laskar and Robutel, 2001).

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arXiv2013

A linear distribution of orbits in compact planetary systems?

We report a linear ordering of orbits in a sample of multiple extrasolar planetary systems with super-Earth planets. We selected 20 cases, mostly discovered by the Kepler mission, hosting at least four planets within \sim 0.5 au. The semi-major axis a_n of an n-th planet in each system of this sample obeys a(n) = a_1 + (n-1) Δa, where a_1 is the semi-major axis of the innermost orbit and Δa is a spacing between subsequent planets, which are specific for a particular system. For instance, the Kepler-33 system hosting five super-Earth planets exhibits the relative deviations between the observed and linearly predicted semi-major axes of only a few percent. At least half of systems in the sample fulfill the linear law with a similar accuracy. We explain the linear distribution of semi-major axes as a natural implication of multiple chains of mean motion resonances between subsequent planets, which emerge due to planet--disk interactions and convergent migration at early stages of their evolution.

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arXiv2012

Testing a hypothesis of the νOctantis planetary system

We investigate the orbital stability of a putative Jovian planet in a compact binary νOctantis 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.

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arXiv2012

A dynamical analysis of the Kepler-11 planetary system

The Kepler-11 star hosts at least six transiting super-Earth planets detected through the precise photometric observations of the Kepler mission (Lissauer et al.). In this paper, we re-analyze the available Kepler data, using the direct N-body approach rather than an indirect TTV method in the discovery paper. The orbital modeling in the realm of the direct approach relies on the whole data set, not only on the mid-transits times. Most of the results in the original paper are confirmed and extended. We constrained the mass of the outermost planet g to less than 30 Earth masses. The mutual inclinations between orbits b and c as well as between orbits d and e are determined with a good precision, in the range of [1,5] degrees. Having several solutions to four qualitative orbital models of the Kepler-11 system, we analyze its global dynamics with the help of dynamical maps. They reveal a sophisticated structure of the phase space, with narrow regions of regular motion. The dynamics are governed by a dense net of three- and four-body mean motion resonances, forming the Arnold web. Overlapping of these resonances is a main source of instability. We found that the Kepler-11 system may be long-term stable only in particular multiple resonant configurations with small relative inclinations. The mass-radius data derived for all companions reveal a clear anti-correlation between the mean density of the planets with their distance from the star. This may reflect the formation and early evolution history of the system.

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arXiv2012

The generalized non-conservative model of a 1-planet system - revisited

We study the long-term dynamics of a planetary system composed of a star and a planet. Both bodies are considered as extended, non-spherical, rotating objects. There are no assumptions made on the relative angles between the orbital angular momentum and the spin vectors of the bodies. Thus, we analyze full, spatial model of the planetary system. Both objects are assumed to be deformed due to their own rotations, as well as due to the mutual tidal interactions. The general relativity corrections are considered in terms of the post-Newtonian approximation. Besides the conservative contributions to the perturbing forces, there are also taken into account non-conservative effects, i.e., the dissipation of the mechanical energy. This dissipation is a result of the tidal perturbation on the velocity field in the internal zones with non-zero turbulent viscosity (convective zones). Our main goal is to derive the equations of the orbital motion as well as the equations governing time-evolution of the spin vectors (angular velocities). We derive the Lagrangian equations of the second kind for systems which do not conserve the mechanical energy. Next, the equations of motion are averaged out over all fast angles with respect to time-scales characteristic for conservative perturbations. The final equations of motion are then used to study the dynamics of the non-conservative model over time scales of the order of the age of the star. We analyze the final state of the system as a function of the initial conditions. Equilibria states of the averaged system are finally discussed.

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arXiv2012

Mechanic: a new numerical MPI framework for the dynamical astronomy

We develop the Mechanic package, which is a new numerical framework for dynamical astronomy. The aim of our software is to help in massive numerical simulations by efficient task management and unified data storage. The code is built on top of the Message Passing Interface (MPI) and Hierarchical Data Format (HDF5) standards and uses the Task Farm approach to manage numerical tasks. It relies on the core-module approach. The numerical problem implemented in the user-supplied module is separated from the host code (core). The core is designed to handle basic setup, data storage and communication between nodes in a computing pool. It has been tested on large CPU-clusters, as well as desktop computers. The Mechanic may be used in computing dynamical maps, data optimization or numerical integration. The code and sample modules are freely available at http://git.astri.umk.pl/projects/mechanic.

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