arXiv subjects

Tatiana A. Michtchenko

Publications and source records attributed to Tatiana A. Michtchenko.

At least 19 recordsLinked to original sources

arXiv2026

Comparing dynamical effects of the central bar and the spiral arms in the solar neighborhood

The dynamical effects on the stellar motion produced by the Galactic central bar and the spiral arms perturbations are investigated separately and compared. The stars from the Gaia DR3 catalog are selected in the region of observable completeness, which we estimate as $\sim$1 kpc from the Sun. We apply the 2D model of the Galactic potential consisting of three axisymmetric components, the disk, the bulge, and the dark matter halo, and two non-axisymmetric components, the central bar and the spiral arms. The stellar dynamics is studied using analytical and numerical techniques, such as Hamiltonian topology analysis, the construction of dynamical maps on the representative planes, dynamic spectra, and Poincaré sections. We identify the main dynamical features in the solar neighborhood (SNd), the corotation (CR) and Lindblad resonances (LRs). By assuming that the main moving groups (MGs) in the SNd originate from the resonances, we compare their locations, structures, and intensities with the theoretical predictions and provide a description of the process involved in the formation of the MGs. In addition, we explore parametric planes by adjusting the values of the pattern rotation speed $Ω_{p}$ with the positions of the MGs, for both the spiral arms and bar models, and conclude that the spiral arms model shows better results when compared to those of the bar, under the hypothesis of the dynamical origin of MGs.

astro-ph.GA↗

arXiv2023

3D stellar motion in the axisymmetric Galactic potential and the e-z resonances

The full phase space information on the kinematics of a huge number of stars provided by the Gaia third Data Release raises the demand for a better understanding of the 3D stellar dynamics. In this paper, we investigate the possible regimes of motion of stars in the axisymmetric approximation of a Galactic potential model. The model consists of three components: the axisymmetric disk, the central spheroidal bulge and the spherical halo of dark matter. The axisymmetric disk is divided into stellar and gaseous disk subcomponents, each one modeled by three Miyamoto-Nagai profiles. The physical and structural parameters of the Galaxy components are adjusted by observational kinematic constraints. The phase space of the two-degrees-of-freedom model is studied by means of the Poincaré and dynamical mapping, the dynamical spectrum method and the direct numerical integrations of the Hamiltonian equations of motion. For the chosen physical parameters, the nearly-circular and low-altitude stellar behaviour is composed of two weakly coupled simple oscillations, radial and vertical motions. The amplitudes of the vertical oscillations of these orbits are gradually increasing with the growing Galactocentric distances, in concordance with the exponential mass decay assumed. However, for increasing planar eccentricities and the altitudes over the equatorial disk, new regimes of stellar motion emerge as a result of the beating between the radial and vertical oscillation frequencies, which we refer to as e-z resonances. The corresponding resonant motion produces characteristic sudden increase or decrease of the amplitude of the vertical oscillation, bifurcations in the dynamical spectra and the chains of islands of stable motion in the phase space. The results obtained can be useful in the understanding and interpretation of the features observed in the stellar 3D distribution around the Sun.

astro-ph.GA↗

arXiv2021

Past and present dynamics of the circumbinary moons in the Pluto-Charon system

The Pluto-Charon (PC) pair is usually thought of as a binary in the dual synchronous state, which is the endpoint of its tidal evolution. The discovery of the small circumbinary moons, Styx, Nix, Kerberos, and Hydra, placed close to the mean motions resonances (MMRs) 3/1, 4/1, 5/1, and 6/1 with Charon, respectively, reveals a complex dynamical architecture of the system. Several formation mechanisms for the PC system have been proposed. Our goal is to analyse the past and current orbital dynamics of the satellite system. We study the past and current dynamics of the PC system through a large set of numerical integrations of the exact equations of motion, accounting for the gravitational interactions of the PC binary with the small moons and the tidal evolution, modelled by the constant time lag approach. We construct the stability maps in a pseudo-Jacobian coordinate system. In addition, considering a more realistic model, which accounts for the zonal harmonic $J_2$ of the Pluto's oblateness and the accreting mass of Charon, we investigate the tidal evolution of the whole system. Our results show that, in the chosen reference frame, the current orbits of all satellites are nearly circular, nearly planar and nearly resonant with Charon that can be seen as an indicator of the convergent dissipative migration experimented by the system in the past. We verify that, under the assumption that Charon completes its formation during the tidal expansion, the moons can safely cross the main MMRs, without their motions being strongly excited and consequently ejected. In the more realistic scenario proposed here, the small moons survive the tidal expansion of the PC binary, without having to invoke the hypothesis of the resonant transport. Our results point out that the possibility to find additional small moons in the PC system cannot be ruled out.

astro-ph.EP↗

arXiv2021

Dynamics of the spiral-arm corotation and its observable footprints in the Solar Neighborhood

This article discusses the effects of the spiral-arm corotation on the stellar dynamics in the Solar Neighborhood (SN). All our results presented here rely on: 1) observational evidence that the Sun lies near the corotation circle, where stars rotate with the same angular velocity as the spiral-arm pattern; the corotation circle establishes domains of the corotation resonance (CR) in the Galactic disk; 2) dynamical constraints that put the spiral-arm potential as the dominant perturbation in the SN, comparing with the effects of the central bar in the SN; 3) a long-lived nature of the spiral structure, promoting a state of dynamical relaxing and phase-mixing of the stellar orbits in response to the spiral perturbation. With an analytical model for the Galactic potential, composed of an axisymmetric background deduced from the observed rotation curve, and perturbed by a four-armed spiral pattern, numerical simulations of stellar orbits are performed to delineate the domains of regular and chaotic motions shaped by the resonances. Such studies show that stars can be trapped inside the stable zones of the spiral CR, and this orbital trapping mechanism could explain the dynamical origin of the Local arm of the Milky Way (MW). The spiral CR and the near high-order epicyclic resonances influence the velocity distribution in the SN, creating the observable structures such as moving groups and their radially extended counterpart known as diagonal ridges. The Sun and most of the SN stars evolve inside a stable zone of the spiral CR, never crossing the main spiral-arm structure, but oscillating in the region between the Sagittarius-Carina and Perseus arms. This orbital behavior of the Sun brings insights to our understanding of questions concerning the solar system evolution, the Earth environment changes, and the preservation of life on Earth.

astro-ph.GA↗

arXiv2020

Eclipse timing variation of GK Vir: evidence of a possible Jupiter-like planet in a circumbinary orbit

Eclipse timing variation analysis has become a powerful method to discover planets around binary systems. We applied this technique to investigate the eclipse times of GK Vir. This system is a post-common envelope binary with an orbital period of 8.26 h. Here, we present 10 new eclipse times obtained between 2013 and 2020. We calculated the O-C diagram using a linear ephemeris and verified a clear orbital period variation (OPV) with a cyclic behavior. We investigated if this variation could be explained by the Applegate mechanism, the apsidal motion, or the light travel time (LTT) effect. We found that the Applegate mechanism would hardly explain the OPV with its current theoretical description. We obtained using different approaches that the apsidal motion is a less likely explanation than the LTT effect. We showed that the LTT effect with one circumbinary body is the most likely cause for the OPV, which was reinforced by the orbital stability of the third body. The LTT best solution provided an orbital period of ~24 yr for the outer body. Under the assumption of coplanarity between the external body and the inner binary, we obtained a Jupiter-like planet around the GK Vir. In this scenario, the planet has one of the longest orbital periods, with a full observational baseline, discovered so far. However, as the observational baseline of GK Vir is smaller than twice the period found in the O-C diagram, the LTT solution must be taken as preliminary.

astro-ph.SR↗

arXiv2019

Exploring the origin of moving groups and diagonal ridges by simulations of stellar orbits and birthplaces

The present paper is the culminating one of a series aimed to contribute to the understanding of the kinematic structures of the solar neighbourhood (SN), explaining the origin of the Local Arm and relating the moving groups with the spiral-arms resonances in the disk. With a model for the Galactic potential, with the Sun inside the spiral corotation resonance (CR), we integrate the 2D orbits of test particles distributed in birthplaces along the main spiral arms, the Local Arm, and in the axisymmetric disk. A comparison of the resulting U-V plane of the SN with that provided by Gaia DR2 confirms our previous conclusion that the moving groups of Coma Berenices, Pleiades, and Hyades are associated with the CR, and that the Hercules stream is formed by the bulk of high-order inner Lindblad resonances. The kinematic structures result from stellar orbits trapped by the spiral resonances in a timespan of ~ 1 Gyr, indicating the long-living nature of the spiral structure and challenging recent arguments in favor of short-lived structures originated from incomplete phase mixing in the Galactic disk. As a byproduct, our simulations give some insight into the birthplaces of the stars presently located in the SN; the majority of stars of the main moving groups and the Hercules stream were likely born in the Local Arm, while stars of the Sirius group possibly originated from the outer segment of the Sagittarius-Carina arm. We also propose the spiral resonances as the dynamical origin for the diagonal ridges in the Galactic distribution of rotation velocities.

astro-ph.GA↗

arXiv2019

The moving groups as the origin of the vertical phase space spiral

Using the Gaia data release 2 (DR2), we analyzed the distribution of stars in the close vicinity of the Sun in the full 3D position-velocity space. We have found no evidence of incomplete phase mixing in the vertical direction of the disk, which could be originated by some external events. We show that the vertical phase space spiral $Z$-$V_z$ is produced by the well-known moving groups (MGs), mainly by Coma-Berenices, Pleiades-Hyades and Sirius, when the statistical characteristics (mean, median, or mode) of the azimuthal velocity $V_φ$ are used to analyze the distribution in the vertical position-velocity plane. This result does not invoke external perturbations and is independent on the internal dynamical mechanisms that originate the MGs. Our conclusions counterbalance current arguments in favor of short-lived (between 300 and 900 Myr) structures in the solar neighborhood. Contrarily, they support the hypothesis of a longer formation time scale (around a few Gyr) for the MGs.

astro-ph.GA↗

arXiv2018

Relativistic chaos in the anisotropic harmonic oscillator

The harmonic oscillator is an essential tool, widely used in all branches of Physics in order to understand more realistic systems, from classical to quantum and relativistic regimes. We know that the harmonic oscillator is integrable in Newtonian mechanics, whether forced, damped or multidimensional. On the other hand, it is known that relativistic, one-dimensional driven oscillators present chaotic behavior. However, there is no analogous result in the literature concerning relativistic conservative, two-dimensional oscillators. We consider in this paper different separable potentials for two-dimensional oscillators in the context of special relativistic dynamics. We show, by means of different chaos indicators, that all these systems present chaotic behavior under specific initial conditions. In particular, the relativistic anisotropic, two-dimensional harmonic oscillator is chaotic. The non-integrability of the system is shown to come from the momentum coupling in the kinetic part of the Hamiltonian, even if there are no coupling terms in the potential. It follows that chaos must appear in most integrable classical systems once we introduce relativistic corrections to the dynamics. The chaotic nature of the relativistic, anisotropic harmonic oscillator may be detected in the laboratory using Bose condensates in a two-dimensional optical lattice, extending the recent experiments on the one-dimensional case.

nlin.CD↗

arXiv2018

On the stellar velocity distribution in the solar neighborhood in the light of Gaia DR2

The aim of this work is to contribute to the understanding of the stellar velocity distribution in the solar neighborhood (SN). We propose that the structures on the $U-V$ planes, known as the moving groups, can be mainly explained by the spiral arms perturbations. The applied model of the Galactic disk and spiral arms, with the parameters defined by observational data and with pattern speed $Ω_p=$28.0 km s$^{-1}$ kpc$^{-1}$, is the same that allowed us to explain the origin of the Local Arm and the Sun's orbit trapped inside the corotation resonance (CR). We show that the $U-V$ picture of the SN consists of the main component, associated with the CR, and the inner and outer structures, which we could associate with the Hercules and Sirius streams, respectively. The Coma-Berenices and Hyades-Pleiades groups and the Sun itself belong to the main part. The substructures of Hercules are formed mainly by the nearby 8/1, 12/1, and even 6/1 inner Lindblad resonances, while Sirius is shaped by the bulk of overlapping outer Lindblad resonances, -8/1, -12/1, -16/1, which are stuck to the CR. This richness in resonances only exists near corotation, which should be of the spiral arms, not of the Galactic bar, whose stable corotation zone is far away from the Sun. The model's predictions of the velocity distribution match qualitatively and quantitatively the distribution provided by Gaia DR2.

astro-ph.GA↗

arXiv2018

Combined dynamical effects of the bar and spiral arms in a Galaxy model. Application to the solar neighbourhood

Observational data indicate that the Milky Way is a barred spiral galaxy. Computation facilities and availability of data from Galactic surveys stimulate the appearance of models of the Galactic structure. More efforts to build dynamical models containing both spiral arms and the central bar/bulge are needed. We expand the study of the stellar dynamics in the Galaxy by adding the bar/bulge component to a model with spiral arms introduced in our previous paper. The model is tested by applying it to the solar neighborhood, where observational data are more precise. We model analytically the potential of the Galaxy to derive the force field in its equatorial plane. The model comprises an axisymmetric disc derived from the observable rotation curve, four arms with Gaussian-shaped groove profiles, and a classical elongated/oblate ellipsoidal bar/bulge structure. The parameters describing the bar/bulge are constrained by observations and the stellar dynamics, and their possible limits are determined. A basic model results in a bar of 2.9 kpc in length, with a mass of the order of a few 10$^9M_\odot$. The size and orientation of the bar are also restricted by the position of masers with VLBI distances. The bar's rotation speed is constrained to $Ω_{\rm bar}<50$ km s$^{-1}$ kpc$^{-1}$ taking into account the allowed mass range. We conclude that our basic model is compatible with observations and with the dynamical constraints. The model explains simultaneously the bulk of the main moving groups, associated here with the spiral corotation resonance, and the Hercules stream, associated with several inner high-order spiral resonances; in particular, with the 8/1 resonance. From the dynamical constraints on the bar's angular speed, it is unlikely that the bar's OLR lies near the solar circle; moreover, its proximity would compromise the stability of the Local Arm structure.

astro-ph.GA↗

arXiv2017

The dynamical origin of the Local arm and the Sun's trapped orbit

The Local arm of the Milky Way, a short spiral feature near the Sun whose existence is known for decades, was recently observed in detail with different tracers. Many efforts have been dedicated to elaborate plausible hypotheses concerning the origin of the main spiral arms of the Galaxy; however, up to now, no specific mechanism for the origin of the Local arm was proposed. Here we explain, for the first time, the Local arm as an outcome of the spiral corotation resonance, which traps arm tracers and the Sun inside it. We show that the majority of maser sources belonging to the Local arm, together with the Sun, evolve inside the corotation resonance, never crossing the main spiral arms but instead oscillating in the region between them. This peculiar behavior of the Sun could have numerous consequences to our understanding of the local kinematics of stars, the Galactic Habitable Zone, and the Solar System evolution.

astro-ph.GA↗

arXiv2016

Modelling resonances and orbital chaos in disk galaxies. Application to a Milky Way spiral model

Context: Resonances in the stellar orbital motion under perturbations from spiral arms structure play an important role in the evolution of the disks of spiral galaxies. The epicyclic approximation allows the determination of the corresponding resonant radii on the equatorial plane (for nearly circular orbits), but is not suitable in general. Aims: We expand the study of resonant orbits by analysing stellar motions perturbed by spiral arms with Gaussian-shaped profiles without any restriction on the stellar orbital configurations, and we expand the concept of Lindblad (epicyclic) resonances for orbits with large radial excursions. Methods: We define a representative plane of initial conditions, which covers the whole phase space of the system. Dynamical maps on representative planes are constructed numerically, in order to characterize the phase-space structure and identify the precise location of resonances. The study is complemented by the construction of dynamical power spectra, which provide the identification of fundamental oscillatory patterns in the stellar motion. Results: Our approach allows a precise description of the resonance chains in the whole phase space, giving a broader view of the dynamics of the system when compared to the classical epicyclic approach, even for objects in retrograde motion. The analysis of the solar neighbourhood shows that, depending on the current azimuthal phase of the Sun with respect to the spiral arms, a star with solar kinematic parameters may evolve either inside the stable co-rotation resonance or in a chaotic zone. Conclusions: Our approach contributes to quantifying the domains of resonant orbits and the degree of chaos in the whole Galactic phase-space structure. It may serve as a starting point to apply these techniques to the investigation of clumps in the distribution of stars in the Galaxy, such as kinematic moving groups.

astro-ph.GA↗

arXiv2014

Dynamical Stability of Terrestrial Planets in the Binary α Centauri System

In this paper, we investigate whether hypothetical Earth-like planets have high probability of remaining on stable orbits inside the habitable zones around the stars A and B of α Centauri, for lengths of time compatible with the evolution of life. We introduce a stability criterion based on the solution of the restricted three-body problem and apply it to the α Centauri system. In this way, we determine the regions of the short-term stability of the satellite-type (S-type) planetary orbits, in both planar and three-dimensional cases. We also study the long-term stability of hypothetical planets through the dynamical mapping of the habitable zones of the stars. The topology of the maps is analyzed using the semi-analytical secular Hamiltonian model and possible processes responsible for long-lasting instabilities are identified. We verify that the planetary motion inside the habitable zones is regular, regardless of high eccentricities, for inclinations smaller than 40°. We show that the variation of the orbital distance of the planet located in the habitable zones of the binary is comparable to that of Earth, if the planet is close to the Mode I stationary solution. This result brings positive expectations for finding habitable planets in binary stars.

astro-ph.EP↗

arXiv2013

Tidal evolution of close-in exoplanets in co-orbital configurations

In this paper, we study the behavior of a pair of co-orbital planets, both orbiting a central star on the same plane and undergoing tidal interactions. Our goal is to investigate final orbital configurations of the planets, initially involved in the 1/1 mean-motion resonance (MMR), after long-lasting tidal evolution. The study is done in the form of purely numerical simulations of the exact equations of motions accounting for gravitational and tidal forces. The results obtained show that, at least for equal mass planets, the combined effects of the resonant and tidal interactions provoke the orbital instability of the system, often resulting in collision between the planets. We first discuss the case of two hot-super-Earth planets, whose orbital dynamics can be easily understood in the frame of our semi-analytical model of the 1/1 MMR. Systems consisting of two hot-Saturn planets are also briefly discussed.

astro-ph.EP↗

arXiv2012

Angular momentum exchange during secular migration of two-planet systems

We investigate the secular dynamics of two-planet coplanar systems evolving under mutual gravitational interactions and dissipative forces. We consider two mechanisms responsible for the planetary migration: star-planet (or planet-satellite) tidal interactions and interactions of a planet with a gaseous disc. We show that each migration mechanism is characterized by a specific law of orbital angular momentum exchange. Calculating stationary solutions of the conservative secular problem and taking into account the orbital angular momentum leakage, we trace the evolutionary routes followed by the planet pairs during the migration process. This procedure allows us to recover the dynamical history of two-planet systems and constrain parameters of the involved physical processes.

astro-ph.EP↗

arXiv2012

Spin-orbit coupling for tidally evolving super-Earths

We investigate the spin behavior of close-in rocky planets and the implications for their orbital evolution. Considering that the planet rotation evolves under simultaneous actions of the torque due to the equatorial deformation and the tidal torque, both raised by the central star, we analyze the possibility of temporary captures in spin-orbit resonances. The results of the numerical simulations of the exact equations of motions indicate that, whenever the planet rotation is trapped in a resonant motion, the orbital decay and the eccentricity damping are faster than the ones in which the rotation follows the so-called pseudo-synchronization. Analytical results obtained through the averaged equations of the spin-orbit problem show a good agreement with the numerical simulations. We apply the analysis to the cases of the recently discovered hot super-Earths Kepler-10 b, GJ 3634 b and 55 Cnc e. The simulated dynamical history of these systems indicates the possibility of capture in several spin-orbit resonances; particularly, GJ 3634 b and 55 Cnc e can currently evolve under a non-synchronous resonant motion for suitable values of the parameters. Moreover, 55 Cnc e may avoid a chaotic rotation behavior by evolving towards synchronization through successive temporary resonant trappings.

astro-ph.EP↗

arXiv2011

The periodic and chaotic regimes of motion in the exoplanet 2/1 mean-motion resonance

We present the dynamical structure of the phase space of the planar planetary 2/1 mean-motion resonance (MMR). Inside the resonant domain, there exist two families of periodic orbits, one associated to the librational motion of the critical angle ($σ$-family) and the other related to the circulatory motion of the angle between the pericentres ($Δ\varpi$-family). The well-known apsidal corotation resonances (ACR) appear at the intersections of these families. A complex web of secondary resonances exists also for low eccentricities, whose strengths and positions are dependent on the individual masses and spatial scale of the system. Depending on initial conditions, a resonant system is found in one of the two topologically different states, referred to as \textit{internal} and \textit{external} resonances. The internal resonance is characterized by symmetric ACR and its resonant angle is $2\,λ_2-λ_1-\varpi_1$, where $λ_i$ and $\varpi_i$ stand for the planetary mean longitudes and longitudes of pericentre, respectively. In contrast, the external resonance is characterized by asymmetric ACR and the resonant angle is $2\,λ_2-λ_1-\varpi_2$. We show that systems with more massive outer planets always envolve inside internal resonances. The limit case is the well-known asteroidal resonances with Jupiter. At variance, systems with more massive inner planets may evolve in either internal or external resonances; the internal resonances are typical for low-to-moderate eccentricity configurations, whereas the external ones for high eccentricity configurations of the systems. In the limit case, analogous to Kuiper belt objects in resonances with Neptune, the systems are always in the external resonances characterized by asymmetric equilibria.

astro-ph.EP↗

arXiv2011

Mineralogical Characterization of Baptistina Asteroid Family: Implications for K/T Impactor Source

Bottke et al. (2007) linked the catastrophic formation of Baptistina Asteroid Family (BAF) to the K/T impact event. This linkage was based on dynamical and compositional evidence, which suggested the impactor had a composition similar to CM2 carbonaceous chondrites. However, our recent study (Reddy et al. 2009) suggests that the composition of (298) Baptistina is similar to LL-type ordinary chondrites rather than CM2 carbonaceous chondrites. This rules out any possibility of it being related to the source of the K/T impactor, if the impactor was of CM-type composition. Mineralogical study of asteroids in the vicinity of BAF has revealed a plethora of compositional types suggesting a complex formation and evolution environment. A detailed compositional analysis of 16 asteroids suggests several distinct surface assemblages including ordinary chondrites (Gaffey SIV subtype), primitive achondrites (Gaffey SIII subtype), basaltic achondrites (Gaffey SVII subtype and V-type), and a carbonaceous chondrite. Based on our mineralogical analysis we conclude that (298) Baptistina is similar to ordinary chondrites (LL-type) based on olivine and pyroxene mineralogy and moderate albedo. S-type and V-type in and around the vicinity of BAF we characterized show mineralogical affinity to (8) Flora and (4) Vesta and could be part of their families. Smaller BAF asteroids with lower SNR spectra showing only a 'single' band are compositionally similar to (298) Baptistina and L/LL chondrites. It is unclear at this point why the silicate absorption bands in spectra of asteroids with formal family definition seem suppressed relative to background population, despite having similar mineralogy.

astro-ph.EP↗