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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).
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Planets are observed to orbit the component star(s) of stellar binary systems on so-called circumprimary or circumsecondary orbits, as well as around the entire binary system on so-called circumbinary orbits. Depending on the orbital parameters of the binary system a planet will be dynamically stable if it orbits within some critical separation of the semimajor axis in the circumprimary case, or beyond some critical separation for the circumbinary case. We present N-body simulations of star-forming regions that contain populations of primordial binaries to determine the fraction of binary systems that can host stable planets at various semimajor axes, and how this fraction of stable systems evolves over time. Dynamical encounters in star-forming regions can alter the orbits of some binary systems, which can induce long-term dynamical instabilities in the planetary system and can even change the size of the habitable zone(s) of the component stars. However, the overall fraction of binaries that can host stable planetary systems is not greatly affected by either the assumed binary population, or the density of the star-forming region. Instead, the critical factor in determining how many stable planetary systems exist in the Galaxy is the stellar binary fraction - the more stars that are born as singles in stellar nurseries, the higher the fraction of stable planetary systems.
Context: The accretion history of the Milky Way is still unknown, despite the recent discovery of stellar systems that stand out in terms of their energy-angular momentum space, such as Gaia-Enceladus-Sausage. In particular, it is still unclear how these groups are linked and to what extent they are well-mixed. Aims: We investigate the similarities and differences in the properties between the prograde and retrograde (counter-rotating) stars and set those results in context by using the properties of Gaia-Enceladus-Sausage, Thamnos/Sequoia, and other suggested accreted populations. Methods: We used the stellar metallicities of the major large spectroscopic surveys (APOGEE, Gaia-ESO, GALAH, LAMOST, RAVE, SEGUE) in combination with astrometric and photometric data from Gaias second data-release. We investigated the presence of radial and vertical metallicity gradients as well as the possible correlations between the azimuthal velocity, $v_phi,$ and metallicity, [M/H], as qualitative indicators of the presence of mixed populations. Results: We find that a handful of super metal-rich stars exist on retrograde orbits at various distances from the Galactic center and the Galactic plane. We also find that the counter-rotating stars appear to be a well-mixed population, exhibiting radial and vertical metallicity gradients on the order of $sim$ -0.04 dex/kpc and -0.06 dex/kpc, respectively, with little (if any) variation when different regions of the Galaxy are probed. The prograde stars show a $v_phi$-[M/H] relation that flattens -- and, perhaps, even reverses as a function of distance from the plane. Retrograde samples selected to roughly probe Thamnos and Gaia-Enceladus-Sausage appear to be different populations yet they also appear to be quite linked, as they follow the same trend in terms of the eccentricity versus metallicity space.
We present observations of the Rossiter-McLaughlin effect for two exoplanetary systems, revealing the orientations of their orbits relative to the rotation axes of their parent stars. HAT-P-4b is prograde, with a sky-projected spin-orbit angle of lambda = -4.9 +/- 11.9 degrees. In contrast, HAT-P-14b is retrograde, with lambda = 189.1 +/- 5.1 degrees. These results conform with a previously noted pattern among the stellar hosts of close-in giant planets: hotter stars have a wide range of obliquities and cooler stars have low obliquities. This, in turn, suggests that three-body dynamics and tidal dissipation are responsible for the short-period orbits of many exoplanets. In addition, our data revealed a third body in the HAT-P-4 system, which could be a second planet or a companion star.
We study the capture of galactic dark matter particles (DMP) in two-body and few-body systems with a symplectic map description. This approach allows modeling the scattering of $10^{16}$ DMPs after following the time evolution of the captured particle on about $10^9$ orbital periods of the binary system. We obtain the DMP density distribution inside such systems and determine the enhancement factor of their density in a center vicinity compared to its galactic value as a function of the mass ratio of the bodies and the ratio of the body velocity to the velocity of the galactic DMP wind. We find that the enhancement factor can be on the order of tens of thousands.
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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