arXiv subjects

Ákos Bazsó

Publications and source records attributed to Ákos Bazsó.

8 recordsLinked to original sources

arXiv2020

Fear the Shadows of the Giants: On Secular Perturbations in Circumstellar Habitable Zones of Double Stars

After the detection of extrasolar planets in binary and multiple star systems questions arose about their dynamics and habitability. In this study we investigate a five-dimensional parameter space for wide binary stars with a massive planet beyond the habitable zone (HZ). Our aim is to reveal those orbital and physical parameter combinations that expose bodies in the primary star's HZ to secular perturbations. Building upon an established semi-analytical model, we combine two separate analytical models into a new one to treat the restricted four-body problem. We apply this new Combined Analytical Model (CAM) to different synthetic systems and systematically map the occurrence of secular resonances (SR). These maps are then visualized as two-dimensional sections of the parameter space. The CAM model has a median error below 3% relative to numerical reference simulations. We also derive a simplified CAM that performs well for hierarchical systems with moderate to large separations between the bodies. Our results show that SR appear in the HZ even for large secondary star distances (up to >1000 au) if either (i) the planet's distance is larger than Jupiter's, or (ii) its mass is about Saturn's or lower. Changes in the secondary star's eccentricity by stellar flybys or galactic tides can push a formerly dynamically quiet HZ to a high-eccentricity state. Based on these results we provide the easy-to-use online tool "SHaDoS" that evaluates the CAM for a given user input and traces the locations of SR in the HZ in two-dimensional parameter space plots.

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arXiv2019

Analytical estimates of secular frequencies for binary star systems

Binary and multiple star systems are extreme environments for the formation and long-term presence of extrasolar planets. Circumstellar planets are subject to gravitational perturbations from the distant companion star, and this interaction leads to a long-period precession of their orbits. We investigate analytical models that allow to quantify these perturbations and calculate the secular precession frequency in the dynamical model of the restricted three-body problem. These models are applied to test cases and we discuss some of their shortcomings. In addition, we introduce a modified Laplace-Lagrange model which allows to obtain better frequency estimates than the traditional model for large eccentricities of the perturber. We then generalize this model to any number of perturbers, and present an application to the four-body problem.

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arXiv2017

Stability of librational motion in the spatial circular restricted three-body problem for high inclinations and mass ratios

In the spatial circular restricted three-body problem librational motion around the Lagrangian points $L_4$ and $L_5$ exists up to high inclinations of the massless object. We report the results of numerical investigations on the stability of this librational motion for systematic variations in the inclination of the Trojan and the mass-ratio $μ$ of the two massive bodies. We show that stable motion prevails for inclinations below 60 degrees and mass-ratios $μ< 0.04$ for typical integration times up to $10^6$ revolution periods. At even higher mass-ratios -- beyond the critical mass-ratio for the planar case -- stable orbits were found to exist for up to $10^7$ periods at moderate inclinations. We extracted the librational frequencies on a grid in the parameter space from the Fourier spectra and traced their variation. Several resonances between the short and long period librational frequency as well as the vertical frequency lie inside the investigated region. The application of the Lyapunov characteristic indicator and spectral number methods also reveals the chaotic regions. This simple model is equally applicable in the Solar system for low mass ratios for Trojans of the planets, as well as to Trojan-type exoplanets in binary star systems at high mass-ratios.

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arXiv2016

Dynamics and habitability in circumstellar planetary systems of known binary stars

We present a survey on exoplanetary systems of binary stars with stellar separations less than 100 au. For a sample of 11 binaries that harbour detected circumstellar giant planets we investigate the frequency of systems with secular resonances (SR) affecting the habitable zone (HZ). Secular resonances are connected to dynamically unstable or chaotic regions by enforcing highly eccentric motion. We apply a semi-analytical method to determine the locations of linear SR, which is based on finding the apsidal precession frequencies of the massive bodies. For configurations where the giant planet is located exterior to the HZ we find that there is always a SR interior to its orbit, the exact location of the SR strongly depends on the system's architecture. In systems with the giant planet interior to the HZ no SR can occur in the Newtonian framework. Taking into account the general relativistic precession of the perihelion, which increases the precession frequencies, planets with $a < 0.1$ au can cause SR in the HZ. We find two cases where the SR is located inside the HZ, and some more where it is close to the HZ. Generally, giant planets interior to the HZ are more favourable than exterior planets to avoid SR in the HZ. Around the location of the SR weaker mean-motion resonances are excited, and resonance overlap is possible. Existing analytical models are not as accurate as the semi-analytical method in locating the SR and deviate by $\sim 0.1$ au or more.

astro-ph.EP↗

arXiv2016

On the possibility of habitable Trojan planets in binary star systems

Approximately 60 percent of all stars in the solar neighbourhood (up to 80 percent in our Milky Way) are members of binary or multiple star systems. This fact led to the speculations that many more planets may exist in binary systems than are currently known. To estimate the habitability of exoplanetary systems, we have to define the so-called habitable zone (HZ). The HZ is defined as a region around a star where a planet would receive enough radiation to maintain liquid water on its surface and to be able to build a stable atmosphere. We search for new dynamical configurations - where planets may stay in stable orbits - to increase the probability to find a planet like the Earth. Therefore we investigated five candidates and found that two systems (HD 41004 and HD 196885) which have small stable regions.

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arXiv2013

Fugitives from the Hungaria region: close encounters and impacts with terrestrial planets

Hungaria asteroids, whose orbits occupy the region in element space between $1.78< a< 2.03$ AU, $e<0.19$, $12^\circ<i<31^\circ$, are a possible source of Near-Earth Asteroids (NEAs). Named after (434) Hungaria these asteroids are relatively small, since the largest member of the group has a diameter of just about 11 km. They are mainly perturbed by Jupiter and Mars, possibly becoming Mars-crossers and, later, they may even cross the orbits of Earth and Venus. In this paper we analyze the close encounters and possible impacts of escaped Hungarias with the terrestrial planets. Out of about 8000 known Hungarias we selected 200 objects which are on the edge of the group. We integrated their orbits over 100 million years in a simplified model of the planetary system (Mars to Saturn) subject only to gravitational forces. We picked out a sample of 11 objects (each with 50 clones) with large variations in semi-major axis and restarted the numerical integration in a gravitational model including the planets from Venus to Saturn. Due to close encounters, some of them achieve high inclinations and eccentricities which, in turn, lead to relatively high velocity impacts on Venus, Earth, and Mars. We statistically analyze all close encounters and impacts with the terrestrial planets and determine the encounter and impact velocities of these fictitious Hungarias.

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arXiv2010

Where are the Uranus Trojans?

The area of stable motion for fictitious Trojan asteroids around Uranus' equilateral equilibrium points is investigated with respect to the inclination of the asteroid's orbit to determine the size of the regions and their shape. For this task we used the results of extensive numerical integrations of orbits for a grid of initial conditions around the points L4 and L5, and analyzed the stability of the individual orbits. Our basic dynamical model was the Outer Solar System (Jupiter, Saturn, Uranus and Neptune). We integrated the equations of motion of fictitious Trojans in the vicinity of the stable equilibrium points for selected orbits up to the age of the Solar system of 5 billion years. One experiment has been undertaken for cuts through the Lagrange points for fixed values of the inclinations, while the semimajor axes were varied. The extension of the stable region with respect to the initial semimajor axis lies between 19.05 < a < 19.3 AU but depends on the initial inclination. In another run the inclination of the asteroids' orbit was varied in the range 0 < i < 60 and the semimajor axes were fixed. It turned out that only four 'windows' of stable orbits survive: these are the orbits for the initial inclinations 0 < i < 7, 9 < i < 13, 31 < i < 36 and 38 < i < 50. We postulate the existence of at least some Trojans around the Uranus Lagrange points for the stability window at small and also high inclinations.

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arXiv2009

An Overview of the 13:8 Mean Motion Resonance between Venus and Earth

It is known since the seminal study of Laskar (1989) that the inner planetary system is chaotic with respect to its orbits and even escapes are not impossible, although in time scales of billions of years. The aim of this investigation is to locate the orbits of Venus and Earth in phase space, respectively to see how close their orbits are to chaotic motion which would lead to unstable orbits for the inner planets on much shorter time scales. Therefore we did numerical experiments in different dynamical models with different initial conditions -- on one hand the couple Venus-Earth was set close to different mean motion resonances (MMR), and on the other hand Venus' orbital eccentricity (or inclination) was set to values as large as e = 0.36 (i = 40deg). The couple Venus-Earth is almost exactly in the 13:8 mean motion resonance. The stronger acting 8:5 MMR inside, and the 5:3 MMR outside the 13:8 resonance are within a small shift in the Earth's semimajor axis (only 1.5 percent). Especially Mercury is strongly affected by relatively small changes in eccentricity and/or inclination of Venus in these resonances. Even escapes for the innermost planet are possible which may happen quite rapidly.

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