Evidence for a high mutual inclination between the cold Jupiter and transiting super Earth orbiting π Men

ABSTRACT π Men hosts a transiting super Earth (P ≈ 6.27 d, m ≈ 4.82 M⊕, R ≈ 2.04 R⊕) discovered by TESS and a cold Jupiter (P ≈ 2093 d, msin I ≈ 10.02 MJup, e ≈ 0.64) discovered from radial velocity. We use Gaia DR2 and Hipparcos astrometry to derive the star’s velocity caused by the orbiting planets and constrain the cold Jupiter’s sky-projected inclination (Ib = 41°−65°). From this, we derive the mutual inclination (ΔI) between the two planets, and find that 49° < ΔI < 131° (1σ) and 28° < ΔI < 152° (2σ). We examine the dynamics of the system using N-body simulations, and find that potentially large oscillations in the super Earth’s eccentricity and inclination are suppressed by general relativistic precession. However, nodal precession of the inner orbit around the invariable plane causes the super Earth to only transit between 7 and 22 per cent of the time, and to usually be observed as misaligned with the stellar spin axis. We repeat our analysis for HAT-P-11, finding a large ΔI between its close-in Neptune and cold Jupiter and similar dynamics. π Men and HAT-P-11 are prime examples of systems where dynamically hot outer planets excite their inner planets, with the effects of increasing planet eccentricities, planet–star misalignments, and potentially reducing the transit multiplicity. Formation of such systems likely involves scattering between multiple giant planets or misaligned protoplanetary discs. Future imaging of the faint debris disc in π Men and precise constraints on its stellar spin orientation would provide strong tests for these formation scenarios.

Mean plane of the Kuiper belt beyond 50 AU in the presence of Planet 9

Context. A recent observational census of Kuiper belt objects (KBOs) has unveiled anomalous orbital structures. This has led to the hypothesis that an additional ∼5 − 10 m⊕ planet exists. This planet, known as Planet 9, occupies an eccentric and inclined orbit at hundreds of astronomical units. However, the KBOs under consideration have the largest known semimajor axes at a > 250 AU; thus they are very difficult to detect. Aims. In the context of the proposed Planet 9, we aim to measure the mean plane of the Kuiper belt at a > 50 AU. In a comparison of the expected and observed mean planes, some constraints would be put on the mass and orbit of this undiscovered planet. Methods. We adopted and developed the theoretical approach of Volk & Malhotra (2017, AJ, 154, 62) to the relative angle δ between the expected mean plane of the Kuiper belt and the invariable plane determined by the eight known planets. Numerical simulations were constructed to validate our theoretical approach. Then similar to Volk & Malhotra (2017, AJ, 154, 62), we derived the angle δ for the real observed KBOs with 100 < a < 200 AU, and the measurement uncertainties were also estimated. Finally, for comparison, maps of the theoretically expected δ were created for different combinations of possible Planet 9 parameters. Results. The expected mean plane of the Kuiper belt nearly coincides with the said invariable plane interior to a = 90 AU. But these two planes deviate noticeably from each other at a > 100 AU owing to the presence of Planet 9 because the relative angle δ could be as large as ∼10°. Using the 1σ upper limit of δ < 5° deduced from real KBO samples as a constraint, we present the most probable parameters of Planet 9: for mass m9 = 10 m⊕, orbits with inclinations i9 = 30°, 20°, and 15° should have semimajor axes a9 > 530 AU, 450 AU, and 400 AU, respectively; for m9 = 5 m⊕, the orbit is i9 = 30° and a9 > 440 AU, or i9 < 20° and a9 > 400 AU. In this work, the minimum a9 increases with the eccentricity e9 (∈[0.2, 0.6]) but not significantly.

Calibration of the angular momenta of the minor planets in the solar system

Aims. We aim to determine the relative angle between the total angular momentum of the minor planets and that of the Sun-planets system, and to improve the orientation of the invariable plane of the solar system. Methods. By utilizing physical parameters available in public domain archives, we assigned reasonable masses to 718 041 minor planets throughout the solar system, including near-Earth objects, main belt asteroids, Jupiter trojans, trans-Neptunian objects, scattered-disk objects, and centaurs. Then we combined the orbital data to calibrate the angular momenta of these small bodies, and evaluated the specific contribution of the massive dwarf planets. The effects of uncertainties on the mass determination and the observational incompleteness were also estimated. Results. We determine the total angular momentum of the known minor planets to be 1.7817 × 1046 g cm2 s−1. The relative angle α between this vector and the total angular momentum of the Sun-planets system is calculated to be about 14.74°. By excluding the dwarf planets Eris, Pluto, and Haumea, which have peculiar angular momentum directions, the angle α drops sharply to 1.76°; a similar result applies to each individual minor planet group (e.g., trans-Neptunian objects). This suggests that, without these three most massive bodies, the plane perpendicular to the total angular momentum of the minor planets would be close to the invariable plane of the solar system. On the other hand, the inclusion of Eris, Haumea, and Makemake can produce a difference of 1254 mas in the inclination of the invariable plane, which is much larger than the difference of 9 mas induced by Ceres, Vesta, and Pallas as found previously. By taking into account the angular momentum contributions from all minor planets, including the unseen ones, the orientation improvement of the invariable plane is larger than 1000 mas in inclination with a 1σ error of ∼50−140 mas.

Understanding the evolution of Atira-class asteroid 2019 AQ3, a major step towards the future discovery of the Vatira population

ABSTRACT Orbiting the Sun at an average distance of 0.59 au and with the shortest aphelion of any known minor body, at 0.77 au, the Atira-class asteroid 2019 AQ3 may be an orbital outlier or perhaps an early indication of the presence of a new population of objects: those following orbits entirely encompassed within that of Venus, the so-called Vatiras. Here, we explore the orbital evolution of 2019 AQ3 within the context of the known Atiras to show that, like many of them, it displays a present-day conspicuous coupled oscillation of the values of eccentricity and inclination, but no libration of the value of the argument of perihelion with respect to the invariable plane of the Solar system. The observed dynamics is consistent with being the result of the combined action of two dominant perturbers, the Earth–Moon system and Jupiter, and a secondary one, Venus. Such a multiperturber-induced secular dynamics translates into a chaotic evolution that can eventually lead to a resonant behaviour of the Lidov–Kozai type. Asteroid 2019 AQ3 may have experienced brief stints as a Vatira in the relatively recent past and it may become a true Vatira in the future, outlining possible dynamical pathways that may transform Atiras into Vatiras and vice versa. Our results strongly suggest that 2019 AQ3 is only the tip of the iceberg: a likely numerous population of similar bodies may remain hidden in plain sight, permanently confined inside the Sun’s glare.

Solar barycentric dynamics from a new solar-planetary ephemeris

Aims. The barycentric dynamics of the Sun has increasingly been attracting the attention of researchers from several fields, due to the idea that interactions between the Sun’s orbital motion and solar internal functioning could be possible. Existing high-precision ephemerides that have been used for that purpose do not include the effects of trans-Neptunian bodies, which cause a significant offset in the definition of the solar system’s barycentre. In addition, the majority of the dynamical parameters of the solar barycentric orbit are not routinely calculated according to these ephemerides or are not publicly available. Methods. We developed a special version of the IAA RAS lunar–solar–planetary ephemerides, EPM2017H, to cover the whole Holocene and 1 kyr into the future. We studied the basic and derived (e.g., orbital torque) barycentric dynamical quantities of the Sun for that time span. A harmonic analysis (which involves an application of VSOP2013 and TOP2013 planetary theories) was performed on these parameters to obtain a physics-based interpretation of the main periodicities present in the solar barycentric movement. Results. We present a high-precision solar barycentric orbit and derived dynamical parameters (using the solar system’s invariable plane as the reference plane), widely accessible for the whole Holocene and 1 kyr in the future. Several particularities and barycentric phenomena are presented and explained on dynamical bases. A comparison with the Jet Propulsion Laboratory DE431 ephemeris, whose main differences arise from the modelling of trans-Neptunian bodies, shows significant discrepancies in several parameters (i.e., not only limited to angular elements) related to the solar barycentric dynamics. In addition, we identify the main periodicities of the Sun’s barycentric movement and the main giant planets perturbations related to them.

CONSTRAINING THE PREFERRED-FRAME α1, α2 PARAMETERS FROM SOLAR SYSTEM PLANETARY PRECESSIONS

Analytical expressions for the orbital precessions affecting the relative motion of the components of a local binary system induced by Lorentz-violating Preferred Frame Effects (PFE) are explicitly computed in terms of the Parametrized Post-Newtonian (PPN) parameters α1, α2. Preliminary constraints on α1, α2 are inferred from the latest determinations of the observationally admitted ranges [Formula: see text] for any anomalous Solar System planetary perihelion precessions. Other bounds existing in the literature are critically reviewed, with particular emphasis on the constraint [Formula: see text] based on an interpretation of the current close alignment of the Sun's equator with the invariable plane of the Solar System in terms of the action of a α2-induced torque throughout the entire Solar System's existence. Taken individually, the supplementary precessions [Formula: see text] of Earth and Mercury, recently determined with the INPOP10a ephemerides without modeling PFE, yield α1 = (0.8±4) × 10-6 and α2 = (4±6) × 10-6, respectively. A linear combination of the supplementary perihelion precessions of all the inner planets of the Solar System, able to remove the a priori bias of unmodeled/mismodeled standard effects such as the general relativistic Lense–Thirring precessions and the classical rates due to the Sun's oblateness J2, allows to infer α1 = (-1 ± 6) × 10-6, α2 = (-0.9 ± 3.5) × 10-5. Such figures are obtained by assuming that the ranges of values for the anomalous perihelion precessions are entirely due to the unmodeled effects of α1 and α2. Our bounds should be improved in the near-mid future with the MESSENGER and, especially, BepiColombo spacecrafts. Nonetheless, it is worthwhile noticing that our constraints are close to those predicted for BepiColombo in two independent studies. In further dedicated planetary analyses, PFE may be explicitly modeled to estimate α1, α2 simultaneously with the other PPN parameters as well.

IAU North Poles and Rotation Parameters for Natural Satellites

In 1970 the IAU defined any object'snorthpole to be that axis of rotation which lies north of the solar system's invariable plane. A competing definition in widespread use at some institutions followed the “right hand rule” whereby the “north” axis of rotation was generally said to be that that of the rotational angular momentum.A Working Group has periodically updated the recommended values of planet and satellite poles and rotation rates in accordance with the IAU definition of north and the IAU definition of prime meridian.In this paper we review the IAU definitions ofnorthand of the location ofprime meridianand we present the algorithm which has been employed in determining the rotational parameters of the natural satellites.

Precession Theory Using the Invariable Plane of the Solar System

Standard precession theory builds up the precession matrix P, which rotates coordinates from the mean equator and equinox of epoch to the mean equator and equinox of date, by a sequence of three elementary rotations by the accumulated Euler angles ϚA, θA and zA: P = R3(−zA)R2(θA)R3(−ϚA). This scheme works well provided both the epoch and the date are within a few centuries of J2000. For long-term applications, the alternative formulation using the accumulated luni-solar and planetary precession, P = R3(ᵡA)R1(−ѡA)R3(−ψA)R1(ɛ), is more stable.Yet another formulation for P is possible, using the invariable plane of the Solar System as an intermediate plane: P = R3(−L) R1(−I) R3(−Δ) R1(I0) R3(L0). The angles I0 and L0 are the inclination and ascending node of the invariable plane at epoch; I and L are the same quantities at the date. Only the angle Δ is a function of both times. This scheme works for both short-term and long-term applications.For the short term, polynomial coefficients for I, L, and Δ are derived from the currently-accepted coefficients of the angles ϚA, θA and zA. For the long term, these angles are expressed as sums of Chebyshev polynomials obtained from analysis of a million-year numerical integration.If the intersection of the mean equator and the invariable plane were adopted as the origin of right ascensions, the theory would be simplified further: since L0 and L would no longer be required, P would again consist of the minimum three rotations.