From star-disc encounters to numerical solutions for a subset of the restricted three-body problem

Breslau, Andreas; Vincke, Kirsten; Pfalzner, Susanne

doi:10.1051/0004-6361/201526068

Cited by 14 publications

(29 citation statements)

References 30 publications

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“…(2) 4 To improve readability, we correct here a small inconsistency in Breslau et al (2017a): in the method, all lengths in that paper were scaled with rp,peri. Later on, for example rvpp/rp,peri was used even though rvpp would have been sufficient.…”

Section: Methodsmentioning

confidence: 99%

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Creating retrogradely orbiting planets by prograde stellar fly-bys

Breslau

Pfalzner

2019

A&A

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Several planets have been found that orbit their host star on retrograde orbits (spin-orbit angle ϕ > 90 • ). Currently, the largest measured projected angle between the orbital angular momentum axis of a planet and the rotation axis of its host star has been found for HAT-P-14b to be ≈ 171 • . One possible mechanism for the formation of such misalignments is through long-term interactions between the planet and other planetary or stellar companions. However, with this process, it has been found to be difficult to achieve retrogradely orbiting planets, especially planets that almost exactly counter-orbit their host star (ϕ ≈ 180 • ) such as HAT-P-14b. By contrast, orbital misalignment can be produced efficiently by perturbations of planetary systems that are passed by stars. Here we demonstrate that not only retrograde fly-bys, but surprisingly, even prograde fly-bys can induce retrograde orbits. Our simulations show that depending on the mass ratio of the involved stars, there are significant ranges of planetary pre-encounter parameters for which counter-orbiting planets are the natural consequence. We find that the highest probability to produce counter-orbiting planets (≈ 20%) is achieved with close prograde, coplanar fly-bys of an equal-mass perturber with a pericentre distance of one-third of the initial orbital radius of the planet. For fly-bys where the pericentre distance equals the initial orbital radius of the planet, we still find a probability to produce retrograde planets of ≈ 10 % for high-mass perturbers on inclined (60 • < i < 120 • ) orbits. As usually more distant fly-bys are more common in star clusters, this means that inclined fly-bys probably lead to more retrograde planets than those with inclinations < 60 • . Such close fly-bys are in general relatively rare in most types of stellar clusters, and only in very dense clusters will this mechanism play a significant role. The total production rate of retrograde planets depends then on the cluster environment. Finally, we briefly discuss the application of our results to the retrograde minor bodies in the solar system and to the formation of retrograde moons during the planet-planet scattering phase.

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Section: Methodsmentioning

confidence: 99%

“…An orbit was defined as stable when the orbital elements did not change more than 1% for δt = (t peri − t init )/50. A more detailed description can be found in Breslau et al (2017a).…”

Section: Methodsmentioning

confidence: 99%

Creating retrogradely orbiting planets by prograde stellar fly-bys

Breslau

Pfalzner

2019

A&A

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“…This is illustrated by Fig. 2, which shows the eccentricity of matter after the fly-by as a function of projected position at periastron distance (for additional information on this type of representation see Breslau et al 2017).…”

Section: Resultsmentioning

confidence: 99%

“…Then the effect on the disc size is less and it would have needed to be even closer to result in r d < 6 AU. Bhandare et al(2016) and Vincke & Pfalzner (2017) give two different approximation for an inclination angleaveraged disc size after a fly-by. Here we use the formula given by Vincke & Pfalzner (2017), which leads to the following for- Fig.…”

Section: Resultsmentioning

confidence: 99%

Did a stellar fly-by shape the planetary system around Pr 0211 in the cluster M44?

Pfalzner¹,

Bhandare²,

Vincke³

2018

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Aims. Out of the ∼ 3000 exoplanets detected so far, only fourteen planets are members of open clusters: among them an exoplanet system around Pr 0211 in the cluster M44 which consists of at least two planets with the outer planet moving on a highly eccentric orbit at 5.5 AU. One hypothesis is that a close fly-by of a neighbouring star was responsible for the eccentric orbit. We test this hypothesis. Methods. First we determine the type of fly-by that would lead to the observed parameters and then use this result to determine the history of such fly-bys in simulations of the early dynamics in an M44-like environment. Results. We find that although very close fly-bys are required to obtain the observed properties of Pr 0211c, such fly-bys are relatively common due to the high stellar density and longevity of the cluster. About 10% of stars actually experience a fly-by that would lead to such a small system-size as observed for Pr0211 or even smaller. Such close fly-bys are most frequent during the first 1-2 Myr after cluster formation, corresponding to a cluster age ≤ 3 Myr. It is unclear whether planets generally form on such short timescales. However, afterwards the close fly-by rate is still 0.2-0.5 Myr −1 , which means extrapolating this to the age of M44 12%-20% of stars would experience such close fly-bys over this timespan. Conclusions. Our simulations show that the fly-by scenario is a realistic option for the formation of eccentricity orbits of the planets in M44. The occurance of such events is relatively high leading to the expectation that similar systems are likely common in open clusters in general.

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After publication of Breslau et al (2017) we noticed a mistake in the plot script used to produce Figs. 2d, 3d, and 5d.

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confidence: 99%

From star-disc encounters to numerical solutions for a subset of the restricted three-body problem (Corrigendum)

Breslau

Vincke

Pfalzner

2017

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After publication of Breslau et al. (2017) we noticed a mistake in the plot script used to produce Figs. 2d, 3d, and 5d. These images should have shown the final semi-major axes of the bound particles relative to the radii of their initial orbits depending on their virtual pericentre positions (VPPs). Due to an incorrect multiplication with (1 − e), the images instead showed the final periapsides of the bound particles relative to their initial orbital radii. In this erratum we present the corrected images (see Fig. 1).Because the original images were not correct, the text in the paper also described the final periapsides and not the final semimajor axes. The correct descriptions for the final semi-major axes are presented below.In Fig. 1a the final semi-major axes are shown for a mass ratio of m 12 = 0.1. The final semi-major axes have large values ( > ∼ 2) along the regions where the particles become unbound. With increasing distance from these regions, the values of the final semi-major axes decrease. This decrease with distance is steeper in the regions where the particles move ahead of the perturber (e.g. around (1, -3) and (1, 2)) and is shallower where the particles move behind the perturber (e.g. around (-1, 4) and (3, 1)). Along the negative x-axis the values of the final semimajor axes are close to the radii of the initial orbits (green region). Above the negative x-axis there is a larger, elliptical region where the final semi-major axes are also larger even though the region is far away from the region where the particles become unbound. Ahead of the departing branch of the perturber's interaction orbit there is a wider band where the final semi-major axes are much smaller than the radii of the particle's initial orbits.For consistency with the paper, we describe next the corrected image for a mass ratio of m 12 = 20.0 (see Fig. 1b). For the particles which remain bound to the host, the difference is not large. The particles that are captured by the perturber have, in general, final semi-major axes which are much larger (factor > ∼ 2) than the radii of their initial orbits around the host.For the mass ratio of m 12 = 1.0 the difference in the images is larger. Most particles that remain bound to the host or are captured by the perturber, have final semi-major axes which are smaller than the radii of their initial orbits. In contrast, almost all particles with VPPs in the second quadrant (see Fig. 1c) have finally semi-major axes that are more than twice as large as the radii of their initial orbits. This region is a continuation of the region where the particles are centrifugally removed. Here, the energy gain is just not enough to become unbound.Due to the changed figures, one sentence in the Summary also has to be adjusted. For the low-mass case (m 12 = 0.1) the summary of the effect on the particles that remain bound reads now: The closer to the perturber orbit, the higher the final eccentricities and the larger the semi-major axes of the particles that remain bound to the host.All other results a...

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From star-disc encounters to numerical solutions for a subset of the restricted three-body problem

Cited by 14 publications

References 30 publications

Creating retrogradely orbiting planets by prograde stellar fly-bys

Creating retrogradely orbiting planets by prograde stellar fly-bys

Did a stellar fly-by shape the planetary system around Pr 0211 in the cluster M44?

From star-disc encounters to numerical solutions for a subset of the restricted three-body problem (Corrigendum)

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