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Register a new userStability of Planetary Motion in Binary Star Systems
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Added by
Roberto Capuzzo-Dolcetta
Publication date
2020
fields
Physics
and research's language is
English
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We considered the problem of stability for planets of finite mass in binary star systems. We selected a huge set of initial conditions for planetary orbits of the S-type, to perform high precision and very extended in time integrations. For our numerical integrations, we resorted to the use of a 15th order integration scheme (IAS15, available within the REBOUND framework), that provides an optimal solution for long-term time integrations. We estimated the probability of different types of instability: planet collisions with the primary or secondary star or planet ejected away from the binary star system. We confirm and generalize to massive planets the dependence of the critical semi-major axis on eccentricity and mass ratio of the binary already found by Holman and Wiegert (1999). We were also able to pick a significant number of orbits that are only `marginally stable, according to the classification introduced by Musielak et al. (2005). A, natural, extension of this work has been the study of the effect of perturbations induced to circumbinary planet motion by a passing-by star, like it often happens in a star cluster. One of the targets of this analysis is the investigation of the possibility that a planet, formerly on a stable S-type orbit around one of the two stars, could transit to a stable P-type orbit (or viceversa). We performed a series of more than 4500 scattering experiments with different initial conditions typical of encounters in small star clusters. We found some interesting behaviors of the systems after perturbation and showed how a transition from an inner (S-type) stable orbit to a circumbinary (P-type) (and vice-versa) has a very low (but non null) probability.
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Many exoplanets are discovered in binary star systems in internal or in circumbinary orbits. Whether the planet can be habitable or not depends on the possibility to maintain liquid water on its surface, and therefore on the luminosity of its host stars and on the dynamical properties of the planetary orbit. The trajectory of a planet in a double star system can be determined, approximating stars and planets with point masses, by solving numerically the equations of motion of the classical three-body system. In this study, we analyze a large data set of planetary orbits, made up with high precision long integration at varying: the mass of the planet, its distance from the primary star, the mass ratio for the two stars in the binary system, and the eccentricity of the star motion. To simulate the gravitational dynamics, we use a 15th order integration scheme (IAS15, available within the REBOUND framework), that provides an optimal solution for long-term integration. In our data analysis, we evaluate if an orbit is stable or not and also provide the statistics of different types of instability: collisions with the primary or secondary star and planets ejected away from the binary star system. Concerning the stability, we find a significant number of orbits that are only marginally stable, according to the classification introduced by Musielak et al. 2005. For planets of negligible mass, we estimate the critical semi-major axis $a_c$ as a function of the mass ratio and the eccentricity of the binary, in agreement with the results of Holman and Wiegert 1999. However, we find that for very massive planets (Super-Jupiters) the critical semi-major axis decrease in some cases by a few percent, compared to cases in which the mass of the planet is negligible.
Most stars form in dense stellar environments. It is speculated that some dense star clusters may host intermediate-mass black holes (IMBHs), which may have formed from runaway collisions between high-mass stars, or from the mergers of less massive black holes. Here, we numerically explore the evolution of populations of planets in star clusters with an IMBH. We study the dynamical evolution of single-planet systems and free-floating planets, over a period of 100~Myr, in star clusters without an IMBH, and in clusters with a central IMBH of mass $100~M_odot$ or $200~M_odot$. In the central region ($rlesssim 0.2$~pc), the IMBHs tidal influence on planetary systems is typically 10~times stronger than the average neighbour star. For a star cluster with a $200M_odot$ IMBH, the region in which the IMBHs influence is stronger within the virial radius ($sim 1$~pc). The IMBH quenches mass segregation, and the stars in the core tend to move towards intermediate regions. The ejection rate of both stars and planets is higher when an IMBH is present. The rate at which planets are expelled from their host star rate is higher for clusters with higher IMBH masses, for $t<0.5 t_{rh}$, while remains mostly constant while the star cluster fills its Roche lobe, similar to a star cluster without an IMBH. The disruption rate of planetary systems is higher in initially denser clusters, and for wider planetary orbits, but this rate is substantially enhanced by the presence of a central IMBH.
We investigate the stability of prograde versus retrograde planets in circular binary systems using numerical simulations. We show that retrograde planets are stable up to distances closer to the perturber than prograde planets. We develop an analytical model to compute the prograde and retrograde mean motion resonances locations and separatrices. We show that instability is due to single resonance forcing, or caused by nearby resonances overlap. We validate our results regarding the role of single resonances and resonances overlap on orbit stability, by computing surfaces of section of the CR3BP. We conclude that the observed enhanced stability of retrograde planets with respect to prograde planets is due to essential differences between the phase-space topology of retrograde versus prograde resonances (at p/q mean motion ratio, prograde resonance is of order p - q while retrograde resonance is of order p + q).
We present preliminary though statistically significant evidence that shows that multiplanetary systems that exhibit a 2/1 period commensurability are in general younger than multiplanetary systems without commensurabilities, or even systems with other commensurabilities. An immediate possible conclusion is that the 2/1 mean-motion resonance in planetary systems, tends to be disrupted after typically a few Gyrs.
Discs in binaries have a complex behavior because of the perturbations of the companion star. Planet formation in binary-star systems both depend on the companion star parameters and on the properties of the circumstellar disc. An eccentric disc may increase the impact velocity of planetesimals and therefore jeopardize the accumulation process. We model the evolution of discs in close binaries including the effects of self-gravity and adopting different prescriptions to model the discs radiative properties. We focus on the dynamical properties and evolutionary tracks of the discs. We use the hydrodynamical code FARGO and we include in the energy equation heating and cooling effects. Radiative discs have a lower disc eccentricity compared to locally isothermal discs with same temperature profile. As a consequence, we do not observe the formation of an internal elliptical low density region as in locally isothermal disc models. However, the disc eccentricity depends on the disc mass through the opacities. Akin to locally isothermal disc models, self-gravity forces the discs longitude of pericenter to librate about a fixed orientation with respect to the binary apsidal line ($pi$). The discs radiative properties play an important role in the evolution of discs in binaries. A radiative disc has an overall shape and internal structure that are significantly different compared to a locally isothermal disc with same temperature profile. This is an important finding both for describing the evolutionary track of the disc during its progressive mass loss, and for planet formation since the internal structure of the disc is relevant for planetesimals growth in binary systems. The non-symmetrical distribution of mass in these discs causes large eccentricities for planetesimals that may affect their growth.
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