How primordial is the structure of comet 67P/C-G? Combined collisional and dynamical models suggest a late formation

There is an active debate about whether the properties of comets as observed today are primordial or, alternatively, if they are a result of collisional evolution or other processes. We investigate the effects of collisions on a comet with a structure like 67P/C-G. We develop scaling laws for the critical specific impact energies required for a significant shape alteration. These are then used in simulations of the combined dynamical and collisional evolution of comets in order to study the survival probability of a primordially formed object with a shape like 67P/C-G. The effects of impacts on comet 67P/C-G are studied using a SPH shock physics code. The resulting critical specific impact energy defines a minimal projectile size which is used to compute the number of shape-changing collisions in a set of dynamical simulations. These simulations follow the dispersion of the trans-Neptunian disk during the giant planet instability, the formation of a scattered disk, and produce 87 objects that penetrate into the inner solar system with orbits consistent with the observed JFC population. The collisional evolution before the giant planet instability is not considered here. Hence, our study is conservative in its estimation of the number of collisions. We find that in any scenario considered here, comet 67P/C-G would have experienced a significant number of shape-changing collisions, if it formed primordially. This is also the case for generic bi-lobe shapes. Our study also shows that impact heating is very localized and that collisionally processed bodies can still have a high porosity. Our study indicates that the observed bi-lobe structure of comet 67P/C-G may not be primordial, but might have originated in a rather recent event, possibly within the last 1 Gy. This may be the case for any kilometer-sized two-component cometary nuclei.Comment: Astronomy & Astrophysics, accepted pending minor revision

A long-lived horseshoe companion to the Earth

We present a dynamical investigation of a newly found asteroid, 2010 SO16, and the discovery that it is a horseshoe companion of the Earth. The object's absolute magnitude (H=20.7) makes this the largest object of its type known to-date. By carrying out numerical integrations of dynamical clones, we find that (a) its status as a horseshoe is secure given the current accuracy of its ephemeris, and (b) the time spent in horseshoe libration with the Earth is several times 10^5 yr, two orders of magnitude longer than determined for other horseshoe asteroids of the Earth. Further, using a model based on Hill's approximation to the three-body problem, we show that, apart from the low eccentricity which prevents close encounters with other planets or the Earth itself, its stability can be attributed to the value of its Jacobi constant far from the regime that allows transitions into other coorbital modes or escape from the resonance altogether. We provide evidence that the eventual escape of the asteroid from horseshoe libration is caused by the action of planetary secular perturbations and the stochastic evolution of the eccentricity. The questions of its origin and the existence of as-yet-undiscovered co-orbital companions of the Earth are discussed.Comment: Accepted in MNRAS; 6 pages, 3 figures, 2 table

The tidal parameters of TRAPPIST-1b and c

The TRAPPIST-1 planetary system consists of seven planets within 0.05 au of each other, five of which are in a multiresonant chain. These resonances suggest the system formed via planet migration; subsequent tidal evolution has damped away most of the initial eccentricities. We used dynamical N-body simulations to estimate how long it takes for the multiresonant configuration that arises during planet formation to break. From there we use secular theory to pose limits on the tidal parameters of planets b and c. We calibrate our results against multilayered interior models constructed to fit the masses and radii of the planets, from which the tidal parameters are computed independently. The dynamical simulations show that the planets typically go unstable 30 Myr after their formation. Assuming synchronous rotation throughout, we compute k_2/Q ≳ 2× 10^{-4} for planet b and k_2/Q ≳ 10^{-3} for planet c. Interior models yield (0.075-0.37) × 10-4 for TRAPPIST-1b and (0.4-2) × 10-4 for TRAPPIST-1c. The agreement between the dynamical and interior models is not too strong, but is still useful to constrain the dynamical history of the system. We suggest that this two-pronged approach could be of further use in other multiresonant systems if the planet's orbital and interior parameters are sufficiently well known

Decreasing Computing Time with Symplectic Correctors in Adaptive Timestepping Routines

It has previously been shown that varying the numerical timestep during a symplectic orbital integration leads to a random walk in energy and angular momentum, destroying the phase space-conserving property of symplectic integrators. Here we show that when altering the timestep symplectic correctors can be used to reduce this error to a negligible level. Furthermore, these correctors can also be employed to avoid a large error introduction when changing the Hamiltonian's partitioning. We have constructed a numerical integrator using this technique that is nearly as accurate as widely used fixed-step routines. In addition, our algorithm is drastically faster for integrations of highly eccentricitic, large semimajor axis orbits, such as those found in the Oort Cloud.Comment: Accepted to AJ, 29 pages, 8 figure

Long-term tidal evolution of the TRAPPIST-1 system

The ultracool M-dwarf star TRAPPIST-1 is surrounded by seven planets configured in a resonant chain. Transit-timing variations have shown that the planets are caught in multiple three-body resonances and that their orbits are slightly eccentric, probably caused by resonant forcing. The current values of the eccentricities could be a remnant from their formation. Here we run numerical simulations using fictitious forces of trapping the fully-grown planets in resonances as they migrated in the gas disc, followed by numerical simulations detailing their tidal evolution. For a reduced disc scale height $h\sim 0.03$--0.05, the eccentricities of the planets upon capture in resonance are higher than their current values by factors of a few. We show that the current eccentricities and spacing of planets d to h are natural outcomes of coupled tidal evolution wherein the planets simultaneously damp their eccentricities and separate due to their resonant interaction. We further show that the planets evolve along a set of equilibrium curves in semimajor axis--eccentricity phase space that are defined by the resonances, and that conserve angular momentum. As such, the current 8:5--5:3--(3:2)$^2$--4:3--3:2 resonant configuration cannot be reproduced from a primordial (3:2)$^4$--4:3--3:2 resonant configuration from tidal dissipation in the planets alone. We use our simulations to constrain the long-term tidal parameters $k_2/Q$ for planets b to e, which are in the range $10^{-3}$ to $10^{-2}$, and show that these are mostly consistent with those obtained from interior modelling following reasonable assumptions.Comment: Accepted in Monthly Notices of the Royal Astronomical Societ

Plausible home stars of the interstellar object 'Oumuamua found in Gaia DR2

The first detected interstellar object 'Oumuamua that passed within 0.25au of the Sun on 2017 September 9 was presumably ejected from a stellar system. We use its newly determined non-Keplerian trajectory together with the reconstructed Galactic orbits of 7 million stars from Gaia DR2 to identify past close encounters. Such an "encounter" could reveal the home system from which 'Oumuamua was ejected. The closest encounter, at 0.60pc (0.53-0.67pc, 90% confidence interval), was with the M2.5 dwarf HIP 3757 at a relative velocity of 24.7km/s, 1Myr ago. A more distant encounter (1.6pc) but with a lower encounter (ejection) velocity of 10.7km/s was with the G5 dwarf HD 292249, 3.8Myr ago. Two more stars have encounter distances and velocities intermediate to these. The encounter parameters are similar across six different non-gravitational trajectories for 'Oumuamua. Ejection of 'Oumuamua by scattering from a giant planet in one of the systems is plausible, but requires a rather unlikely configuration to achieve the high velocities found. A binary star system is more likely to produce the observed velocities. None of the four home candidates have published exoplanets or are known to be binaries. Given that the 7 million stars in Gaia DR2 with 6D phase space information is just a small fraction of all stars for which we can eventually reconstruct orbits, it is a priori unlikely that our current search would find 'Oumuamua's home star system. As 'Oumuamua is expected to pass within 1pc of about 20 stars and brown dwarfs every Myr, the plausibility of a home system depends also on an appropriate (low) encounter velocity.Comment: Accepted to The Astronomical Journa

Dynamics of two planets in co-orbital motion

We study the stability regions and families of periodic orbits of two planets locked in a co-orbital configuration. We consider different ratios of planetary masses and orbital eccentricities, also we assume that both planets share the same orbital plane. Initially we perform numerical simulations over a grid of osculating initial conditions to map the regions of stable/chaotic motion and identify equilibrium solutions. These results are later analyzed in more detail using a semi-analytical model. Apart from the well known quasi-satellite (QS) orbits and the classical equilibrium Lagrangian points L4 and L5, we also find a new regime of asymmetric periodic solutions. For low eccentricities these are located at $(\sigma,\Delta\omega) = (\pm 60\deg, \mp 120\deg)$, where \sigma is the difference in mean longitudes and \Delta\omega is the difference in longitudes of pericenter. The position of these Anti-Lagrangian solutions changes with the mass ratio and the orbital eccentricities, and are found for eccentricities as high as ~ 0.7. Finally, we also applied a slow mass variation to one of the planets, and analyzed its effect on an initially asymmetric periodic orbit. We found that the resonant solution is preserved as long as the mass variation is adiabatic, with practically no change in the equilibrium values of the angles.Comment: 9 pages, 11 figure

Genome-wide association study of aphid abundance highlights a locus affecting plant growth and flowering in Arabidopsis thaliana

Plant life-history traits, such as size and flowering, contribute to shaping variation in herbivore abundance. Although plant genes involved in physical and chemical traits have been well studied, less is known about the loci linking plant life-history traits and herbivore abundance. Here, we conducted a genome-wide association study (GWAS) of aphid abundance in a field population of Arabidopsis thaliana. This GWAS of aphid abundance detected a relatively rare but significant variant on the third chromosome of A. thaliana, which was also suggestively but non-significantly associated with the presence or absence of inflorescence. Out of candidate genes near this significant variant, a mutant of a ribosomal gene (AT3G13882) exhibited slower growth and later flowering than a wild type under laboratory conditions. A no-choice assay with the turnip aphid, Lipaphis erysimi, found that aphids were unable to successfully establish on the mutant. Our GWAS of aphid abundance unexpectedly found a locus affecting plant growth and flowering