An official website of the United States government
Abstract There is a complex inclination structure present in the trans-Neptunian object (TNO) orbital distribution in the main classical-belt region (between orbital semimajor axes of 39 and 48 au). The long-term gravitational effects of the giant planets make TNO orbits precess, but nonresonant objects maintain a nearly constant “free” inclination (Ifree) with respect to a local forced precession pole. Because of the likely cosmogonic importance of the distribution of this quantity, we tabulate free inclinations for all main-belt TNOs, each individually computed using barycentric orbital elements with respect to each object’s local forcing pole. We show that the simplest method, based on the Laplace–Lagrange secular theory, is unable to give correct forcing poles for objects near theν18secular resonance, resulting in poorly conservedIfreevalues in much of the main belt. We thus instead implemented an averaged Hamiltonian to obtain the expected nodal precession for each TNO, yielding significantly more accurate free inclinations for nonresonant objects. For the vast majority (96%) of classical-belt TNOs, theseIfreevalues are conserved to < 1° over 4 Gyr numerical simulations, demonstrating the advantage of using this well-conserved quantity in studies of the TNO population and its primordial inclination profile; our computed distributions only reinforce the idea of a very coplanar surviving “cold” primordial population, overlain by a largeI-width implanted “hot” population.
more »
« less
Modeling the Free Inclinations of the Classical Kuiper Belt with the von Mises–Fisher Distribution
Abstract The orientations of orbital planes of minor planets are directional random variables. Their free inclination is the deviation of the orbit plane from the plane forced by the major planets. We construct a model of the distribution of free inclinations of classical Kuiper Belt objects (CKBOs) based on the von Mises–Fisher (vMF) distribution function, the analog of the normal distribution for directional statistics. The CKBOs are known to have a “cold” component of orbit planes concentrated near the forced plane and a more widely dispersed “hot” component. Adopting a model with a linear combination of two vMF functions, we find that the cold and hot components account for 57% and 43%, characterized by widths of 1.°7 and 12.°9, respectively. This model improves upon previous models based on smaller observational samples and empirical choices of functional forms for inclination distributions.
more »
« less
- Award ID(s):
- 1824869
- PAR ID:
- 10430001
- Publisher / Repository:
- DOI PREFIX: 10.3847
- Date Published:
- Journal Name:
- Research Notes of the AAS
- Volume:
- 7
- Issue:
- 7
- ISSN:
- 2515-5172
- Format(s):
- Medium: X Size: Article No. 143
- Size(s):
- Article No. 143
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
ABSTRACT Small Solar system bodies have widely dispersed orbital poles, posing challenges to dynamical models of Solar system origin and evolution. To characterize the orbit pole distribution of dynamical groups of small bodies it helps to have a functional form for a model of the distribution function. Previous studies have used the small-inclination approximation and adopted variations of the normal distribution to model orbital inclination dispersions. Because the orbital pole is a directional variable, its distribution can be more appropriately modelled with directional statistics. We describe the von Mises–Fisher (vMF) distribution on the surface of the unit sphere for application to small bodies’ orbital poles. We apply it to the orbit pole distribution of the observed Plutinos. We find a mean pole located at inclination i0 = 3.57° and longitude of ascending node Ω0 = 124.38° (in the J2000 reference frame), with a 99.7 per cent confidence cone of half-angle 1.68°. We also estimate a debiased mean pole located 4.6° away, at i0 = 2.26°, Ω0 = 292.69°, of similar-size confidence cone. The vMF concentration parameter of Plutino inclinations (relative to either mean pole estimate) is κ = 31.6. This resembles a Rayleigh distribution function, with width parameter σ = 10.2°. Unlike previous models, the vMF model naturally accommodates all physical inclinations (and no others), whereas Rayleigh or Gaussian models must be truncated to the physical inclination range 0–180°. Further work is needed to produce a theory for the mean pole of the Plutinos against which to compare the observational results.more » « less
-
ABSTRACT We study the evolution of eccentricity and inclination of massive planets in low-density cavities of protoplanetary discs using three-dimensional (3D) simulations. When the planet’s orbit is aligned with the equatorial plane of the disc, the eccentricity increases to high values of 0.7–0.9 due to the resonant interaction with the inner parts of the disc. For planets on inclined orbits, the eccentricity increases due to the Kozai–Lidov mechanism, where the disc acts as an external massive body, which perturbs the planet’s orbit. At small inclination angles, $${\lesssim}30^\circ$$, the resonant interaction with the inner disc strongly contributes to the eccentricity growth, while at larger angles, eccentricity growth is mainly due to the Kozai–Lidov mechanism. We conclude that planets inside low-density cavities tend to acquire high eccentricity if favourable conditions give sufficient time for growth. The final value of the planet’s eccentricity after the disc dispersal depends on the planet’s mass and the properties of the cavity and protoplanetary disc.more » « less
-
Abstract Mutually misaligned circumbinary planets may form in a warped or broken gas disk or from later planet–planet interactions. With numerical simulations and analytic estimates we explore the dynamics of two circumbinary planets with a large mutual inclination. A coplanar inner planet causes prograde apsidal precession of the binary and the stationary inclination for the outer planet is higher for larger outer planet orbital radius. In this case a coplanar outer planet always remains coplanar. On the other hand, a polar inner planet causes retrograde apsidal precession of the binary orbit and the stationary inclination is smaller for larger outer planet orbital radius. For a range of outer planet semimajor axes, an initially coplanar orbit is librating meaning that the outer planet undergoes large tilt oscillations. Circumbinary planets that are highly inclined to the binary are difficult to detect—it is unlikely for a planet to have an inclination below the transit detection limit in the presence of a polar inner planet. These results suggest that there could be a population of circumbinary planets that are undergoing large tilt oscillations.more » « less
-
Abstract V907 Scorpii is a unique triple system in which the inner binary component has been reported to have switched on and off eclipses several times in modern history. In spite of its peculiarity, observational data on this system are surprisingly scarce. Here we make use of the recent Transiting Exoplanet Survey Satellite observations, as well as our own photometric and spectroscopic data, to expand the overall data set and study the V907 Sco system in more detail. Our analysis provides both new and improved values for several of its fundamental parameters: (i) the masses of the stars in the eclipsing binary are 2.74 ± 0.02 M ⊙ and 2.56 ± 0.02 M ⊙ ; and (ii) the third component is a solar-type star with mass 1.06 − 0.10 + 0.11 M ⊙ (90% C.L.), orbiting the binary on an elongated orbit with an eccentricity of 0.47 ± 0.02 and a period of 142.01 ± 0.05 days. The intermittent intervals of time when eclipses of the inner binary are switched on and off are caused by a mutual 26 .° 2 − 2.2 + 2.6 inclination of the inner- and outer-orbit planes, and a favorable inclination of about 71° of the total angular momentum of the system. The nodal precession period is P ν = 63.5 − 2.6 + 3.3 yr. The inner binary will remain eclipsing for another ≃26 yr, offering an opportunity to significantly improve the parameters of the model. This is especially true during the next decade when the inner-orbit inclination will increase to nearly 90°. Further spectroscopic observations are also desirable, as they can help to improve constraints on the system’s orbital architecture and its physical parameters.more » « less
